pax_global_header 0000666 0000000 0000000 00000000064 14535740236 0014523 g ustar 00root root 0000000 0000000 52 comment=cc6851d952fea4dd415fcb7443932f65d1bb5a52
gofa-1.19.1/ 0000775 0000000 0000000 00000000000 14535740236 0012530 5 ustar 00root root 0000000 0000000 gofa-1.19.1/LICENSE 0000664 0000000 0000000 00000002053 14535740236 0013535 0 ustar 00root root 0000000 0000000 MIT License
Copyright (c) 2022 HE Boliang
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
gofa-1.19.1/README-zh_CN.md 0000664 0000000 0000000 00000004015 14535740236 0015006 0 ustar 00root root 0000000 0000000 
[英文](README.md)
# GoFA (基础天文标准库，Golang standards Of Fundamental Astronomy)
GoFA 是一个纯Go实现的基础天文计算库，基于国际天文联合会官方的`基础天文标准库`【`Standards Of Fundamental Astronomy (SOFA)`, [http://iausofa.org](http://iausofa.org)】实现。
GoFA 开发文档： 。
GoFA 当前版本为`v1.19`，与SOFA `v19`([2023-10-11](http://iausofa.org/2023_1011_C/))
保持同步。
官方文档中的示例程序在目录[examples](examples)下。
所有的函数已经通过测试，[测试](test)程序参考自`t_sofa_c.c`。
## 安装
```shell
go get -u github.com/hebl/gofa
```
或者
```shell
go install github.com/hebl/gofa@latest
```
## 函数
### 向量/矩阵函数库 [vml.go](vml.go)
- 初始化 (4)
- 拷贝/扩展等 (5)
- 构建旋转函数 (3)
- 向量操作 (17)
- 矩阵操作 (2)
- 矩阵-向量乘法 (4)
- 旋转向量 (2)
### 角度计算 [angle.go](angle.go)
- 球面/笛卡儿坐标转换 (6)
- 球面角距离 (4)
- 角度运算 (8)
### 天体测量 (38) [astrometry.go](astrometry.go)
### 日历 (7) [jd.go](jd.go)
### 时间尺度 (20) [ts.go](ts.go)
### 坐标系 [coord.go](coord.go)
- 黄道坐标系 (6)
- 银道坐标系 (2)
- 地平/赤道坐标系 (3)
- 地心坐标与大地坐标转换 (5)
### 地球转动与恒星时 (15) [erast.go](erast.go)
### 星历 (3) [ephem.go](ephem.go)
### 基础参数 (14) [fundargs.go](fundargs.go)
### 球心投影 (6) [projection.go](projection.go)
### 岁差/章动/极移 (64) [pn.go](pn.go)
### 星表转换 (9) [catalog.go](catalog.go)
## 版本
### v1.19
Version 1.19 包含有192个天文函数（包括时间、地球转动、恒星时、星历、岁差、岁差/章动、天体测量和坐标转换等），55个向量/矩阵函数。
## 许可证
- [SOFA License](sofa_copyr.txt)
- [MIT License](LICENSE)
2023-10-23
gofa-1.19.1/README.md 0000664 0000000 0000000 00000004331 14535740236 0014010 0 ustar 00root root 0000000 0000000
[中文](README-zh_CN.md)
# GoFA (Golang standards Of Fundamental Astronomy)
GoFA is a pure Golang implementation derived from the International Astronomical
Union's (*IAU*) "`Standards Of Fundamental Astronomy (SOFA)` [http://iausofa.org](http://iausofa.org)" library
official C release. .
Reference documents are in:
GoFA Current version is 1.19. It is based on SOFA version `19` ([2023-10-11](http://iausofa.org/2023_1011_C/)).
Examples in manuals are in the subdirectory: [examples](examples)
All function are tested. The [test](test) functions are derived from `t_sofa_c.c` .
## Installation
```shell
go get -u github.com/hebl/gofa
```
or
```shell
go install github.com/hebl/gofa@latest
```
## Functions
### Vector/Matrix Library [vml.go](vml.go)
- Initialization (4)
- Copy/Extend/Extract (5)
- Build rotations (3)
- Operations on vectors (17)
- Operations on matrices (2)
- Matrix-vector products (4)
- Rotation vectors (2)
### Angle [angle.go](angle.go)
- Spherical/Cartesian conversions (6)
- Separation and position-angle (4)
- Operations on angles (8)
### Astrometry (38) [astrometry.go](astrometry.go)
### Calendars (7) [jd.go](jd.go)
### Time Scales (20) [ts.go](ts.go)
### Coordinates [coord.go](coord.go)
- Ecliptic Coordinates (6)
- Galactic Coordinates (2)
- Horizon/Equatorial Coordinates (3)
- Geocentric/Geodetic Transformations (5)
### Earth Rotation and Sidereal Time (15) [erast.go](erast.go)
### Ephemerides (3) [ephem.go](ephem.go)
### Fundamental Arguments (14) [fundargs.go](fundargs.go)
### Gnomonic Projections (6) [projection.go](projection.go)
### Precession/Nutation/Polar Motion (64) [pn.go](pn.go)
### Star Catalog Conversions (9) [catalog.go](catalog.go)
## Versions
### v1.19
Version 1.19 offers 192 routines for astronomy library (including time scales, earth rotation, sidereal time, precession, nutation, polar motion, ephemerides, astrometry and transforms between various reference systems.), 55 routines for vector/matrix library.
## License
- [SOFA License](sofa_copyr.txt)
- [MIT License](LICENSE)
2023-10-23
gofa-1.19.1/angle.go 0000664 0000000 0000000 00000034610 14535740236 0014151 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Angle
// Operations on Angles
/*
Anp Normalize angle into the range 0 <= a < 2pi.
Given:
a float64 angle (radians)
Returned (function value):
float64 angle in range 0-2pi
*/
func Anp(a float64) float64 {
var w float64
w = fmod(a, D2PI)
if w < 0 {
w += D2PI
}
return w
}
/*
Anpm Normalize angle into the range -pi <= a < +pi.
Given:
a float64 angle (radians)
Returned (function value):
float64 angle in range +/-pi
*/
func Anpm(a float64) float64 {
var w float64
w = fmod(a, D2PI)
if fabs(w) >= DPI {
w -= dsign(D2PI, a)
}
return w
}
/*
A2af Decompose radians into degrees, arcminutes, arcseconds, fraction.
Given:
ndp int resolution (Note 1)
angle float64 angle in radians
Returned:
sign byte '+' or '-'
idmsf [4]int degrees, arcminutes, arcseconds, fraction
Notes:
1) The argument ndp is interpreted as follows:
ndp resolution
: ...0000 00 00
-7 1000 00 00
-6 100 00 00
-5 10 00 00
-4 1 00 00
-3 0 10 00
-2 0 01 00
-1 0 00 10
0 0 00 01
1 0 00 00.1
2 0 00 00.01
3 0 00 00.001
: 0 00 00.000...
2) The largest positive useful value for ndp is determined by the
size of angle, the format of float64s on the target platform, and
the risk of overflowing idmsf[3]. On a typical platform, for
angle up to 2pi, the available floating-point precision might
correspond to ndp=12. However, the practical limit is typically
ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
only 16 bits.
3) The absolute value of angle may exceed 2pi. In cases where it
does not, it is up to the caller to test for and handle the
case where angle is very nearly 2pi and rounds up to 360 degrees,
by testing for idmsf[0]=360 and setting idmsf[0-3] to zero.
Called:
D2tf decompose days to hms
*/
func A2af(ndp int, angle float64, sign *byte, idmsf *[4]int) {
/* Hours to degrees * radians to turns */
F := 15.0 / D2PI
/* Scale then use days to h,m,s function. */
D2tf(ndp, angle*F, sign, idmsf)
}
/*
A2tf Decompose radians into hours, minutes, seconds, fraction.
Given:
ndp int resolution (Note 1)
angle float64 angle in radians
Returned:
sign byte '+' or '-'
ihmsf [4]int hours, minutes, seconds, fraction
Notes:
1) The argument ndp is interpreted as follows:
ndp resolution
: ...0000 00 00
-7 1000 00 00
-6 100 00 00
-5 10 00 00
-4 1 00 00
-3 0 10 00
-2 0 01 00
-1 0 00 10
0 0 00 01
1 0 00 00.1
2 0 00 00.01
3 0 00 00.001
: 0 00 00.000...
2) The largest positive useful value for ndp is determined by the
size of angle, the format of float64s on the target platform, and
the risk of overflowing ihmsf[3]. On a typical platform, for
angle up to 2pi, the available floating-point precision might
correspond to ndp=12. However, the practical limit is typically
ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
only 16 bits.
3) The absolute value of angle may exceed 2pi. In cases where it
does not, it is up to the caller to test for and handle the
case where angle is very nearly 2pi and rounds up to 24 hours,
by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero.
Called:
D2tf decompose days to hms
*/
func A2tf(ndp int, angle float64, sign *byte, ihmsf *[4]int) {
D2tf(ndp, angle/D2PI, sign, ihmsf)
}
/*
D2tf Decompose days to hours, minutes, seconds, fraction.
Given:
ndp int resolution (Note 1)
days float64 interval in days
Returned:
sign byte '+' or '-'
ihmsf [4]int hours, minutes, seconds, fraction
Notes:
1) The argument ndp is interpreted as follows:
ndp resolution
: ...0000 00 00
-7 1000 00 00
-6 100 00 00
-5 10 00 00
-4 1 00 00
-3 0 10 00
-2 0 01 00
-1 0 00 10
0 0 00 01
1 0 00 00.1
2 0 00 00.01
3 0 00 00.001
: 0 00 00.000...
2) The largest positive useful value for ndp is determined by the
size of days, the format of float64 on the target platform, and
the risk of overflowing ihmsf[3]. On a typical platform, for
days up to 1.0, the available floating-point precision might
correspond to ndp=12. However, the practical limit is typically
ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
only 16 bits.
3) The absolute value of days may exceed 1.0. In cases where it
does not, it is up to the caller to test for and handle the
case where days is very nearly 1.0 and rounds up to 24 hours,
by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero.
*/
func D2tf(ndp int, days float64, sign *byte, ihmsf *[4]int) {
var nrs, n int
var rs, rm, rh, a, w, ah, am, as, af float64
/* Handle sign. */
if days >= 0.0 {
*sign = '+'
} else {
*sign = '-'
}
/* Interval in seconds. */
a = DAYSEC * fabs(days)
/* Pre-round if resolution coarser than 1s (then pretend ndp=1). */
if ndp < 0 {
nrs = 1
for n = 1; n <= -ndp; n++ {
if n == 2 || n == 4 {
nrs *= 6
} else {
nrs *= 4
}
}
rs = float64(nrs)
w = a / rs
a = rs * dnint(w)
}
/* Express the unit of each field in resolution units. */
nrs = 1
for n = 1; n <= ndp; n++ {
nrs *= 10
}
rs = float64(nrs)
rm = rs * 60.0
rh = rm * 60.0
/* Round the interval and express in resolution units. */
a = dnint(rs * a)
/* Break into fields. */
ah = a / rh
ah = dint(ah)
a -= ah * rh
am = a / rm
am = dint(am)
a -= am * rm
as = a / rs
as = dint(as)
af = a - as*rs
/* Return results. */
ihmsf[0] = int(ah)
ihmsf[1] = int(am)
ihmsf[2] = int(as)
ihmsf[3] = int(af)
}
/*
Af2a Convert degrees, arcminutes, arcseconds to radians.
Given:
s byte sign: '-' = negative, otherwise positive
ideg int degrees
iamin int arcminutes
asec float64 arcseconds
Returned:
rad float64 angle in radians
Returned (function value):
int status: 0 = OK
1 = ideg outside range 0-359
2 = iamin outside range 0-59
3 = asec outside range 0-59.999...
Notes:
1) The result is computed even if any of the range checks fail.
2) Negative ideg, iamin and/or asec produce a warning status, but
the absolute value is used in the conversion.
3) If there are multiple errors, the status value reflects only the
first, the smallest taking precedence.
*/
func Af2a(s byte, ideg, iamin int, asec float64, rad *float64) int {
/* Compute the interval. */
if s == '-' {
*rad = -1.0
} else {
*rad = 1.0
}
*rad *= (60.0*(60.0*(fabs(float64(ideg)))+(fabs(float64(iamin)))) + fabs(asec)) * DAS2R
/* Validate arguments and return status. */
if ideg < 0 || ideg > 359 {
return 1
}
if iamin < 0 || iamin > 59 {
return 2
}
if asec < 0.0 || asec >= 60.0 {
return 3
}
return 0
}
/*
Tf2a Convert hours, minutes, seconds to radians.
Given:
s byte sign: '-' = negative, otherwise positive
ihour int hours
imin int minutes
sec float64 seconds
Returned:
rad float64 angle in radians
Returned (function value):
int status: 0 = OK
1 = ihour outside range 0-23
2 = imin outside range 0-59
3 = sec outside range 0-59.999...
Notes:
1) The result is computed even if any of the range checks fail.
2) Negative ihour, imin and/or sec produce a warning status, but
the absolute value is used in the conversion.
3) If there are multiple errors, the status value reflects only the
first, the smallest taking precedence.
*/
func Tf2a(s byte, ihour, imin int, sec float64, rad *float64) int {
/* Compute the interval. */
if s == '-' {
*rad = -1.0
} else {
*rad = 1.0
}
*rad *= (60.0*(60.0*(fabs(float64(ihour)))+(fabs(float64(imin)))) + fabs(sec)) * DS2R
/* Validate arguments and return status. */
if ihour < 0 || ihour > 23 {
return 1
}
if imin < 0 || imin > 59 {
return 2
}
if sec < 0.0 || sec >= 60.0 {
return 3
}
return 0
}
/*
Tf2d Convert hours, minutes, seconds to days.
Given:
s byte sign: '-' = negative, otherwise positive
ihour int hours
imin int minutes
sec float64 seconds
Returned:
days float64 interval in days
Returned (function value):
int status: 0 = OK
1 = ihour outside range 0-23
2 = imin outside range 0-59
3 = sec outside range 0-59.999...
Notes:
1) The result is computed even if any of the range checks fail.
2) Negative ihour, imin and/or sec produce a warning status, but
the absolute value is used in the conversion.
3) If there are multiple errors, the status value reflects only the
first, the smallest taking precedence.
*/
func Tf2d(s byte, ihour, imin int, sec float64, days *float64) int {
/* Compute the interval. */
// *days = ( s == '-' ? -1.0 : 1.0 ) *
if s == '-' {
*days = -1.0
} else {
*days = 1.0
}
*days *= (60.0*(60.0*(fabs(float64(ihour)))+(fabs(float64(imin)))) + fabs(sec)) / DAYSEC
/* Validate arguments and return status. */
if ihour < 0 || ihour > 23 {
return 1
}
if imin < 0 || imin > 59 {
return 2
}
if sec < 0.0 || sec >= 60.0 {
return 3
}
return 0
}
// Separation and position-angle
/*
Sepp Angular separation between two p-vectors.
Given:
a [3]float64 first p-vector (not necessarily unit length)
b [3]float64 second p-vector (not necessarily unit length)
Returned (function value):
float64 angular separation (radians, always positive)
Notes:
1) If either vector is null, a zero result is returned.
2) The angular separation is most simply formulated in terms of
scalar product. However, this gives poor accuracy for angles
near zero and pi. The present algorithm uses both cross product
and dot product, to deliver full accuracy whatever the size of
the angle.
Called:
Pxp vector product of two p-vectors
Pm modulus of p-vector
Pdp scalar product of two p-vectors
*/
func Sepp(a, b [3]float64) float64 {
var axb [3]float64
var ss, cs, s float64
/* Sine of angle between the vectors, multiplied by the two moduli. */
Pxp(a, b, &axb)
ss = Pm(axb)
/* Cosine of the angle, multiplied by the two moduli. */
cs = Pdp(a, b)
/* The angle. */
if (ss != 0.0) || (cs != 0.0) {
s = atan2(ss, cs)
} else {
s = 0.0
}
return s
}
/*
Seps Angular separation between two sets of spherical coordinates.
Given:
al float64 first longitude (radians)
ap float64 first latitude (radians)
bl float64 second longitude (radians)
bp float64 second latitude (radians)
Returned (function value):
float64 angular separation (radians)
Called:
S2c spherical coordinates to unit vector
Sepp angular separation between two p-vectors
*/
func Seps(al, ap, bl, bp float64) float64 {
var ac, bc [3]float64
var s float64
/* Spherical to Cartesian. */
S2c(al, ap, &ac)
S2c(bl, bp, &bc)
/* Angle between the vectors. */
s = Sepp(ac, bc)
return s
}
/*
Pap Position-angle from two p-vectors.
Given:
a [3]float64 direction of reference point
b [3]float64 direction of point whose PA is required
Returned (function value):
float64 position angle of b with respect to a (radians)
Notes:
1) The result is the position angle, in radians, of direction b with
respect to direction a. It is in the range -pi to +pi. The
sense is such that if b is a small distance "north" of a the
position angle is approximately zero, and if b is a small
distance "east" of a the position angle is approximately +pi/2.
2) The vectors a and b need not be of unit length.
3) Zero is returned if the two directions are the same or if either
vector is null.
4) If vector a is at a pole, the result is ill-defined.
Called:
Pn decompose p-vector into modulus and direction
Pm modulus of p-vector
Pxp vector product of two p-vectors
Pmp p-vector minus p-vector
Pdp scalar product of two p-vectors
*/
func Pap(a, b [3]float64) float64 {
var am, bm, st, ct, xa, ya, za, pa float64
var au, eta, xi, a2b [3]float64
/* Modulus and direction of the a vector. */
Pn(a, &am, &au)
/* Modulus of the b vector. */
bm = Pm(b)
/* Deal with the case of a null vector. */
if (am == 0.0) || (bm == 0.0) {
st = 0.0
ct = 1.0
} else {
/* The "north" axis tangential from a (arbitrary length). */
xa = a[0]
ya = a[1]
za = a[2]
eta[0] = -xa * za
eta[1] = -ya * za
eta[2] = xa*xa + ya*ya
/* The "east" axis tangential from a (same length). */
Pxp(eta, au, &xi)
/* The vector from a to b. */
Pmp(b, a, &a2b)
/* Resolve into components along the north and east axes. */
st = Pdp(a2b, xi)
ct = Pdp(a2b, eta)
/* Deal with degenerate cases. */
if (st == 0.0) && (ct == 0.0) {
ct = 1.0
}
}
/* Position angle. */
pa = atan2(st, ct)
return pa
}
/*
Pas Position-angle from spherical coordinates.
Given:
al float64 longitude of point A (e.g. RA) in radians
ap float64 latitude of point A (e.g. Dec) in radians
bl float64 longitude of point B
bp float64 latitude of point B
Returned (function value):
float64 position angle of B with respect to A
Notes:
1) The result is the bearing (position angle), in radians, of point
B with respect to point A. It is in the range -pi to +pi. The
sense is such that if B is a small distance "east" of point A,
the bearing is approximately +pi/2.
2) Zero is returned if the two points are coincident.
*/
func Pas(al, ap, bl, bp float64) float64 {
var dl, x, y, pa float64
dl = bl - al
y = sin(dl) * cos(bp)
x = sin(bp)*cos(ap) - cos(bp)*sin(ap)*cos(dl)
// pa = ((x != 0.0) || (y != 0.0)) ? atan2(y, x) : 0.0;
if (x != 0.0) || (y != 0.0) {
pa = atan2(y, x)
} else {
pa = 0.0
}
return pa
}
gofa-1.19.1/astrometry.go 0000664 0000000 0000000 00000533223 14535740236 0015300 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// SOFA Astrometry Tools
/*
Ab Apply stellar aberration
Apply aberration to transform natural direction into proper
direction.
Given:
pnat [3]float64 natural direction to the source (unit vector)
v [3]float64 observer barycentric velocity in units of c
s float64 distance between the Sun and the observer (au)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
Returned:
ppr [3]float64 proper direction to source (unit vector)
Notes:
1. The algorithm is based on Expr. (7.40) in the Explanatory
Supplement (Urban & Seidelmann 2013), but with the following
changes:
o Rigorous rather than approximate normalization is applied.
o The gravitational potential term from Expr. (7) in
Klioner (2003) is added, taking into account only the Sun's
contribution. This has a maximum effect of about
0.4 microarcsecond.
2. In almost all cases, the maximum accuracy will be limited by the
supplied velocity. For example, if the SOFA Epv00 function is
used, errors of up to 5 microarcseconds could occur.
References:
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013).
Klioner, Sergei A., "A practical relativistic model for micro-
arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
Called:
Pdp scalar product of two p-vectors
*/
func Ab(pnat, v [3]float64, s, bm1 float64, ppr *[3]float64) {
var i int
var pdv, w1, w2, r2, w, r float64
var p [3]float64
pdv = Pdp(pnat, v)
w1 = 1.0 + pdv/(1.0+bm1)
w2 = SRS / s
r2 = 0.0
for i = 0; i < 3; i++ {
w = pnat[i]*bm1 + w1*v[i] + w2*(v[i]-pdv*pnat[i])
p[i] = w
r2 = r2 + w*w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
ppr[i] = p[i] / r
}
}
/*
Apcg Prepare for ICRS <-> GCRS, geocentric, special
For a geocentric observer, prepare star-independent astrometry
parameters for transformations between ICRS and GCRS coordinates.
The Earth ephemeris is supplied by the caller.
The parameters produced by this function are required in the
parallax, light deflection and aberration parts of the astrometric
transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
ebpv [2][3]float64 Earth barycentric pos/vel (au, au/day)
ehp [3]float64 Earth heliocentric position (au)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
4. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Apcs astrometry parameters, ICRS-GCRS, space observer
*/
func Apcg(date1, date2 float64, ebpv [2][3]float64, ehp [3]float64, astrom *ASTROM) {
/* Geocentric observer */
pv := [2][3]float64{
{0.0, 0.0, 0.0},
{0.0, 0.0, 0.0},
}
/* Compute the star-independent astrometry parameters. */
Apcs(date1, date2, pv, ebpv, ehp, astrom)
}
/*
Apcg13 Prepare for ICRS <-> GCRS, geocentric
For a geocentric observer, prepare star-independent astrometry
parameters for transformations between ICRS and GCRS coordinates.
The caller supplies the date, and SOFA models are used to predict
the Earth ephemeris.
The parameters produced by this function are required in the
parallax, light deflection and aberration parts of the astrometric
transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. In cases where the caller wishes to supply his own Earth
ephemeris, the function Apcg can be used instead of the present
function.
4. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
5. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Epv00 Earth position and velocity
Apcg astrometry parameters, ICRS-GCRS, geocenter
*/
func Apcg13(date1, date2 float64, astrom *ASTROM) {
var ehpv, ebpv [2][3]float64
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
Epv00(date1, date2, &ehpv, &ebpv)
/* Compute the star-independent astrometry parameters. */
Apcg(date1, date2, ebpv, ehpv[0], astrom)
}
/*
Apci Prepare for ICRS <-> CIRS, terrestrial, special
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between ICRS and geocentric CIRS
coordinates. The Earth ephemeris and CIP/CIO are supplied by the
caller.
The parameters produced by this function are required in the
parallax, light deflection, aberration, and bias-precession-nutation
parts of the astrometric transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
ebpv [2][3]float64 Earth barycentric position/velocity (au, au/day)
ehp [3]float64 Earth heliocentric position (au)
x,y float64 CIP X,Y (components of unit vector)
s float64 the CIO locator s (radians)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. In cases where the caller does not wish to provide the Earth
ephemeris and CIP/CIO, the function Apci13 can be used instead
of the present function. This computes the required quantities
using other SOFA functions.
4. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
5. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Apcg astrometry parameters, ICRS-GCRS, geocenter
C2ixys celestial-to-intermediate matrix, given X,Y and s
*/
func Apci(date1, date2 float64, ebpv [2][3]float64, ehp [3]float64, x, y, s float64, astrom *ASTROM) {
/* Star-independent astrometry parameters for geocenter. */
Apcg(date1, date2, ebpv, ehp, astrom)
/* CIO based BPN matrix. */
C2ixys(x, y, s, &astrom.Bpn)
}
/*
Apci13 Prepare for ICRS <-> CIRS, terrestrial
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between ICRS and geocentric CIRS
coordinates. The caller supplies the date, and SOFA models are used
to predict the Earth ephemeris and CIP/CIO.
The parameters produced by this function are required in the
parallax, light deflection, aberration, and bias-precession-nutation
parts of the astrometric transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
eo float64 equation of the origins (ERA-GST)
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. In cases where the caller wishes to supply his own Earth
ephemeris and CIP/CIO, the function Apci can be used instead
of the present function.
4. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
5. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Epv00 Earth position and velocity
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
Apci astrometry parameters, ICRS-CIRS
Eors equation of the origins, given NPB matrix and s
*/
func Apci13(date1, date2 float64, astrom *ASTROM, eo *float64) {
var ehpv, ebpv [2][3]float64
var r [3][3]float64
var x, y, s float64
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
Epv00(date1, date2, &ehpv, &ebpv)
/* Form the equinox based BPN matrix, IAU 2006/2000A. */
Pnm06a(date1, date2, &r)
/* Extract CIP X,Y. */
Bpn2xy(r, &x, &y)
/* Obtain CIO locator s. */
s = S06(date1, date2, x, y)
/* Compute the star-independent astrometry parameters. */
Apci(date1, date2, ebpv, ehpv[0], x, y, s, astrom)
/* Equation of the origins. */
*eo = Eors(r, s)
}
/*
Apco Prepare for ICRS <-> observed, terrestrial, special
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between ICRS and observed
coordinates. The caller supplies the Earth ephemeris, the Earth
rotation information and the refraction constants as well as the
site coordinates.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
ebpv [2][3]float64 Earth barycentric PV (au, au/day, Note 2)
ehp [3]float64 Earth heliocentric P (au, Note 2)
x,y float64 CIP X,Y (components of unit vector)
s float64 the CIO locator s (radians)
theta float64 Earth rotation angle (radians)
elong float64 longitude (radians, east +ve, Note 3)
phi float64 latitude (geodetic, radians, Note 3)
hm float64 height above ellipsoid (m, geodetic, Note 3)
xp,yp float64 polar motion coordinates (radians, Note 4)
sp float64 the TIO locator s' (radians, Note 4)
refa float64 refraction constant A (radians, Note 5)
refb float64 refraction constant B (radians, Note 5)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 adjusted longitude (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. The vectors eb, eh, and all the astrom vectors, are with respect
to BCRS axes.
3. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN
CONVENTION: the longitude required by the present function is
right-handed, i.e. east-positive, in accordance with geographical
convention.
The adjusted longitude stored in the astrom array takes into
account the TIO locator and polar motion.
4. xp and yp are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions), measured along the
meridians 0 and 90 deg west respectively. sp is the TIO locator
s', in radians, which positions the Terrestrial Intermediate
Origin on the equator. For many applications, xp, yp and
(especially) sp can be set to zero.
Internally, the polar motion is stored in a form rotated onto the
local meridian.
5. The refraction constants refa and refb are for use in a
dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
(i.e. refracted) zenith distance and dZ is the amount of
refraction.
6. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
7. In cases where the caller does not wish to provide the Earth
Ephemeris, the Earth rotation information and refraction
constants, the function Apco13 can be used instead of the
present function. This starts from UTC and weather readings etc.
and computes suitable values using other SOFA functions.
8. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
9. The context structure astrom produced by this function is used by
Atioq, Atoiq, Atciq* and Aticq*.
Called:
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Ry rotate around Y-axis
Rx rotate around X-axis
Anpm normalize angle into range +/- pi
C2ixys celestial-to-intermediate matrix, given X,Y and s
Pvtob position/velocity of terrestrial station
Trxpv product of transpose of r-matrix and pv-vector
Apcs astrometry parameters, ICRS-GCRS, space observer
Cr copy r-matrix
*/
func Apco(date1, date2 float64, ebpv [2][3]float64, ehp [3]float64, x, y, s float64, theta,
elong, phi float64, hm, xp, yp, sp float64, refa, refb float64, astrom *ASTROM) {
var r [3][3]float64
var a, b, eral, c float64
var pvc, pv [2][3]float64
/* Form the rotation matrix, CIRS to apparent [HA,Dec]. */
Ir(&r)
Rz(theta+sp, &r)
Ry(-xp, &r)
Rx(-yp, &r)
Rz(elong, &r)
/* Solve for local Earth rotation angle. */
a = r[0][0]
b = r[0][1]
// eral = ( a != 0.0 || b != 0.0 ) ? atan2(b, a) : 0.0;
if a != 0.0 || b != 0.0 {
eral = atan2(b, a)
} else {
eral = 0.0
}
astrom.Eral = eral
/* Solve for polar motion [X,Y] with respect to local meridian. */
a = r[0][0]
c = r[0][2]
astrom.Xpl = atan2(c, sqrt(a*a+b*b))
a = r[1][2]
b = r[2][2]
// astrom.Ypl = ( a != 0.0 || b != 0.0 ) ? -atan2(a, b) : 0.0;
if a != 0.0 || b != 0.0 {
astrom.Ypl = -atan2(a, b)
} else {
astrom.Ypl = 0.0
}
/* Adjusted longitude. */
astrom.Along = Anpm(eral - theta)
/* Functions of latitude. */
astrom.Sphi = sin(phi)
astrom.Cphi = cos(phi)
/* Refraction constants. */
astrom.Refa = refa
astrom.Refb = refb
/* Disable the (redundant) diurnal aberration step. */
astrom.Diurab = 0.0
/* CIO based BPN matrix. */
C2ixys(x, y, s, &r)
/* Observer's geocentric position and velocity (m, m/s, CIRS). */
Pvtob(elong, phi, hm, xp, yp, sp, theta, &pvc)
/* Rotate into GCRS. */
Trxpv(r, pvc, &pv)
/* ICRS <-> GCRS parameters. */
Apcs(date1, date2, pv, ebpv, ehp, astrom)
/* Store the CIO based BPN matrix. */
Cr(r, &astrom.Bpn)
}
/*
Apco13 Prepare for ICRS <-> observed, terrestrial
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between ICRS and observed
coordinates. The caller supplies UTC, site coordinates, ambient air
conditions and observing wavelength, and SOFA models are used to
obtain the Earth ephemeris, CIP/CIO and refraction constants.
The parameters produced by this function are required in the
parallax, light deflection, aberration, and bias-precession-nutation
parts of the ICRS/CIRS transformations.
Given:
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 1,2)
dut1 float64 UT1-UTC (seconds, Note 3)
elong float64 longitude (radians, east +ve, Note 4)
phi float64 latitude (geodetic, radians, Note 4)
hm float64 height above ellipsoid (m, geodetic, Notes 4,6)
xp,yp float64 polar motion coordinates (radians, Note 5)
phpa float64 pressure at the observer (hPa = mB, Note 6)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 7)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 adjusted longitude (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
eo float64 equation of the origins (ERA-GST)
Returned (function value):
int status: +1 = dubious year (Note 2)
0 = OK
-1 = unacceptable date
Notes:
1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
2. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the
future to be trusted. See Dat for further details.
3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
4. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
5. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many
applications, xp and yp can be set to zero.
Internally, the polar motion is stored in a form rotated onto
the local meridian.
6. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB), is
available, an adequate estimate of hm can be obtained from the
expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to
the pressure and that an accurate phpa value is important for
precise work.
7. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
8. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
9. In cases where the caller wishes to supply his own Earth
ephemeris, Earth rotation information and refraction constants,
the function Apco can be used instead of the present function.
10)This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
11)The context structure astrom produced by this function is used
by Atioq, Atoiq, Atciq* and Aticq*.
Called:
Utctai UTC to TAI
Taitt TAI to TT
Utcut1 UTC to UT1
Epv00 Earth position and velocity
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
Era00 Earth rotation angle, IAU 2000
Sp00 the TIO locator s', IERS 2000
Refco refraction constants for given ambient conditions
Apco astrometry parameters, ICRS-observed
Eors equation of the origins, given NPB matrix and s
*/
func Apco13(utc1, utc2, dut1 float64, elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64, astrom *ASTROM, eo *float64) int {
var j int
var tai1, tai2, tt1, tt2, ut11, ut12 float64
var ehpv, ebpv [2][3]float64
var r [3][3]float64
var x, y, s, theta, sp, refa, refb float64
/* UTC to other time scales. */
j = Utctai(utc1, utc2, &tai1, &tai2)
if j < 0 {
return -1
}
Taitt(tai1, tai2, &tt1, &tt2)
j = Utcut1(utc1, utc2, dut1, &ut11, &ut12)
if j < 0 {
return -1
}
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
Epv00(tt1, tt2, &ehpv, &ebpv)
/* Form the equinox based BPN matrix, IAU 2006/2000A. */
Pnm06a(tt1, tt2, &r)
/* Extract CIP X,Y. */
Bpn2xy(r, &x, &y)
/* Obtain CIO locator s. */
s = S06(tt1, tt2, x, y)
/* Earth rotation angle. */
theta = Era00(ut11, ut12)
/* TIO locator s'. */
sp = Sp00(tt1, tt2)
/* Refraction constants A and B. */
Refco(phpa, tc, rh, wl, &refa, &refb)
/* Compute the star-independent astrometry parameters. */
Apco(tt1, tt2, ebpv, ehpv[0], x, y, s, theta,
elong, phi, hm, xp, yp, sp, refa, refb, astrom)
/* Equation of the origins. */
*eo = Eors(r, s)
/* Return any warning status. */
return j
}
/*
Apcs Prepare for ICRS <-> CIRS, space, special
For an observer whose geocentric position and velocity are known,
prepare star-independent astrometry parameters for transformations
between ICRS and GCRS. The Earth ephemeris is supplied by the
caller.
The parameters produced by this function are required in the space
motion, parallax, light deflection and aberration parts of the
astrometric transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
pv [2][3]float64 observer's geocentric pos/vel (m, m/s)
ebpv [2][3]float64 Earth barycentric PV (au, au/day)
ehp [3]float64 Earth heliocentric P (au)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. Providing separate arguments for (i) the observer's geocentric
position and velocity and (ii) the Earth ephemeris is done for
convenience in the geocentric, terrestrial and Earth orbit cases.
For deep space applications it maybe more convenient to specify
zero geocentric position and velocity and to supply the
observer's position and velocity information directly instead of
with respect to the Earth. However, note the different units:
m and m/s for the geocentric vectors, au and au/day for the
heliocentric and barycentric vectors.
4. In cases where the caller does not wish to provide the Earth
ephemeris, the function Apcs13 can be used instead of the
present function. This computes the Earth ephemeris using the
SOFA function Epv00.
5. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
6. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Cp copy p-vector
Pm modulus of p-vector
Pn decompose p-vector into modulus and direction
Ir initialize r-matrix to identity
*/
func Apcs(date1, date2 float64, pv, ebpv [2][3]float64, ehp [3]float64, astrom *ASTROM) {
/* au/d to m/s */
const AUDMS = DAU / DAYSEC
/* Light time for 1 au (day) */
const CR = AULT / DAYSEC
var i int
var dp, dv float64
var pb, vb, ph [3]float64
var v2, w float64
/* Time since reference epoch, years (for proper motion calculation). */
astrom.Pmt = ((date1 - DJ00) + date2) / DJY
/* Adjust Earth ephemeris to observer. */
for i = 0; i < 3; i++ {
dp = pv[0][i] / DAU
dv = pv[1][i] / AUDMS
pb[i] = ebpv[0][i] + dp
vb[i] = ebpv[1][i] + dv
ph[i] = ehp[i] + dp
}
/* Barycentric position of observer (au). */
Cp(pb, &astrom.Eb)
/* Heliocentric direction and distance (unit vector and au). */
Pn(ph, &astrom.Em, &astrom.Eh)
/* Barycentric vel. in units of c, and reciprocal of Lorenz factor. */
v2 = 0.0
for i = 0; i < 3; i++ {
w = vb[i] * CR
astrom.V[i] = w
v2 += w * w
}
astrom.Bm1 = sqrt(1.0 - v2)
/* Reset the NPB matrix. */
Ir(&astrom.Bpn)
}
/*
Apcs13 Prepare for ICRS <-> CIRS, space
For an observer whose geocentric position and velocity are known,
prepare star-independent astrometry parameters for transformations
between ICRS and GCRS. The Earth ephemeris is from SOFA models.
The parameters produced by this function are required in the space
motion, parallax, light deflection and aberration parts of the
astrometric transformation chain.
Given:
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
pv [2][3]float64 observer's geocentric pos/vel (Note 3)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 unchanged
refa float64 unchanged
refb float64 unchanged
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. All the vectors are with respect to BCRS axes.
3. The observer's position and velocity pv are geocentric but with
respect to BCRS axes, and in units of m and m/s. No assumptions
are made about proximity to the Earth, and the function can be
used for deep space applications as well as Earth orbit and
terrestrial.
4. In cases where the caller wishes to supply his own Earth
ephemeris, the function Apcs can be used instead of the present
function.
5. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
6. The context structure astrom produced by this function is used by
Atciq* and Aticq*.
Called:
Epv00 Earth position and velocity
Apcs astrometry parameters, ICRS-GCRS, space observer
*/
func Apcs13(date1, date2 float64, pv [2][3]float64, astrom *ASTROM) {
var ehpv, ebpv [2][3]float64
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
Epv00(date1, date2, &ehpv, &ebpv)
/* Compute the star-independent astrometry parameters. */
Apcs(date1, date2, pv, ebpv, ehpv[0], astrom)
}
/*
Aper Insert ERA into context
In the star-independent astrometry parameters, update only the
Earth rotation angle, supplied by the caller explicitly.
Given:
theta float64 Earth rotation angle (radians, Note 2)
astrom ASTROM star-independent astrometry parameters:
pmt float64 not used
eb [3]float64 not used
eh [3]float64 not used
em float64 not used
v [3]float64 not used
bm1 float64 not used
bpn [3][3]float64 not used
along float64 longitude + s' (radians)
xpl float64 not used
ypl float64 not used
sphi float64 not used
cphi float64 not used
diurab float64 not used
eral float64 not used
refa float64 not used
refb float64 not used
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 unchanged
eb [3]float64 unchanged
eh [3]float64 unchanged
em float64 unchanged
v [3]float64 unchanged
bm1 float64 unchanged
bpn [3][3]float64 unchanged
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 "local" Earth rotation angle (radians)
refa float64 unchanged
refb float64 unchanged
Notes:
1. This function exists to enable sidereal-tracking applications to
avoid wasteful recomputation of the bulk of the astrometry
parameters: only the Earth rotation is updated.
2. For targets expressed as equinox based positions, such as
classical geocentric apparent (RA,Dec), the supplied theta can be
Greenwich apparent sidereal time rather than Earth rotation
angle.
3. The function Aper13 can be used instead of the present
function, and starts from UT1 rather than ERA itself.
4. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
*/
func Aper(theta float64, astrom *ASTROM) {
astrom.Eral = theta + astrom.Along
}
/*
Aper13 Update context for Earth rotation
In the star-independent astrometry parameters, update only the
Earth rotation angle. The caller provides UT1, (n.b. not UTC).
Given:
ut11 float64 UT1 as a 2-part...
ut12 float64 ...Julian Date (Note 1)
astrom ASTROM star-independent astrometry parameters:
pmt float64 not used
eb [3]float64 not used
eh [3]float64 not used
em float64 not used
v [3]float64 not used
bm1 float64 not used
bpn [3][3]float64 not used
along float64 longitude + s' (radians)
xpl float64 not used
ypl float64 not used
sphi float64 not used
cphi float64 not used
diurab float64 not used
eral float64 not used
refa float64 not used
refb float64 not used
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 unchanged
eb [3]float64 unchanged
eh [3]float64 unchanged
em float64 unchanged
v [3]float64 unchanged
bm1 float64 unchanged
bpn [3][3]float64 unchanged
along float64 unchanged
xpl float64 unchanged
ypl float64 unchanged
sphi float64 unchanged
cphi float64 unchanged
diurab float64 unchanged
eral float64 "local" Earth rotation angle (radians)
refa float64 unchanged
refb float64 unchanged
Notes:
1. The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date,
apportioned in any convenient way between the arguments ut11 and
ut12. For example, JD(UT1)=2450123.7 could be expressed in any
of these ways, among others:
ut11 ut12
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. The date & time method is
best matched to the algorithm used: maximum precision is
delivered when the ut11 argument is for 0hrs UT1 on the day in
question and the ut12 argument lies in the range 0 to 1, or vice
versa.
2. If the caller wishes to provide the Earth rotation angle itself,
the function Aper can be used instead. One use of this
technique is to substitute Greenwich apparent sidereal time and
thereby to support equinox based transformations directly.
3. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
Called:
Aper astrometry parameters: update ERA
Era00 Earth rotation angle, IAU 2000
*/
func Aper13(ut11, ut12 float64, astrom *ASTROM) {
Aper(Era00(ut11, ut12), astrom)
}
/*
Apio Prepare for CIRS <-> observed, terrestrial, special
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between CIRS and observed
coordinates. The caller supplies the Earth orientation information
and the refraction constants as well as the site coordinates.
Given:
sp float64 the TIO locator s' (radians, Note 1)
theta float64 Earth rotation angle (radians)
elong float64 longitude (radians, east +ve, Note 2)
phi float64 geodetic latitude (radians, Note 2)
hm float64 height above ellipsoid (m, geodetic Note 2)
xp,yp float64 polar motion coordinates (radians, Note 3)
refa float64 refraction constant A (radians, Note 4)
refb float64 refraction constant B (radians, Note 4)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 unchanged
eb [3]float64 unchanged
eh [3]float64 unchanged
em float64 unchanged
v [3]float64 unchanged
bm1 float64 unchanged
bpn [3][3]float64 unchanged
along float64 adjusted longitude (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Notes:
1. sp, the TIO locator s', is a tiny quantity needed only by the
most precise applications. It can either be set to zero or
predicted using the SOFA function Sp00.
2. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
3. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many applications,
xp and yp can be set to zero.
Internally, the polar motion is stored in a form rotated onto the
local meridian.
4. The refraction constants refa and refb are for use in a
dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
(i.e. refracted) zenith distance and dZ is the amount of
refraction.
5. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
6. In cases where the caller does not wish to provide the Earth
rotation information and refraction constants, the function
Apio13 can be used instead of the present function. This
starts from UTC and weather readings etc. and computes suitable
values using other SOFA functions.
7. This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
8. The context structure astrom produced by this function is used by
Atioq and Atoiq.
Called:
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Ry rotate around Y-axis
Rx rotate around X-axis
Anpm normalize angle into range +/- pi
Pvtob position/velocity of terrestrial station
*/
func Apio(sp, theta float64, elong, phi, hm, xp, yp float64, refa, refb float64, astrom *ASTROM) {
var r [3][3]float64
var a, b, eral, c float64
var pv [2][3]float64
/* Form the rotation matrix, CIRS to apparent [HA,Dec]. */
Ir(&r)
Rz(theta+sp, &r)
Ry(-xp, &r)
Rx(-yp, &r)
Rz(elong, &r)
/* Solve for local Earth rotation angle. */
a = r[0][0]
b = r[0][1]
// eral = ( a != 0.0 || b != 0.0 ) ? atan2(b, a) : 0.0;
if a != 0.0 || b != 0.0 {
eral = atan2(b, a)
} else {
eral = 0.0
}
astrom.Eral = eral
/* Solve for polar motion [X,Y] with respect to local meridian. */
a = r[0][0]
c = r[0][2]
astrom.Xpl = atan2(c, sqrt(a*a+b*b))
a = r[1][2]
b = r[2][2]
// astrom.Ypl = ( a != 0.0 || b != 0.0 ) ? -atan2(a, b) : 0.0;
if a != 0.0 || b != 0.0 {
astrom.Ypl = -atan2(a, b)
} else {
astrom.Ypl = 0.0
}
/* Adjusted longitude. */
astrom.Along = Anpm(eral - theta)
/* Functions of latitude. */
astrom.Sphi = sin(phi)
astrom.Cphi = cos(phi)
/* Observer's geocentric position and velocity (m, m/s, CIRS). */
Pvtob(elong, phi, hm, xp, yp, sp, theta, &pv)
/* Magnitude of diurnal aberration vector. */
astrom.Diurab = sqrt(pv[1][0]*pv[1][0]+pv[1][1]*pv[1][1]) / CMPS
/* Refraction constants. */
astrom.Refa = refa
astrom.Refb = refb
}
/*
Apio13 Prepare for CIRS <-> observed, terrestrial
For a terrestrial observer, prepare star-independent astrometry
parameters for transformations between CIRS and observed
coordinates. The caller supplies UTC, site coordinates, ambient air
conditions and observing wavelength.
Given:
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 1,2)
dut1 float64 UT1-UTC (seconds)
elong float64 longitude (radians, east +ve, Note 3)
phi float64 geodetic latitude (radians, Note 3)
hm float64 height above ellipsoid (m, geodetic Notes 4,6)
xp,yp float64 polar motion coordinates (radians, Note 5)
phpa float64 pressure at the observer (hPa = mB, Note 6)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 7)
Returned:
astrom ASTROM star-independent astrometry parameters:
pmt float64 unchanged
eb [3]float64 unchanged
eh [3]float64 unchanged
em float64 unchanged
v [3]float64 unchanged
bm1 float64 unchanged
bpn [3][3]float64 unchanged
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned (function value):
int status: +1 = dubious year (Note 2)
0 = OK
-1 = unacceptable date
Notes:
1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
2. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
4. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
5. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many applications,
xp and yp can be set to zero.
Internally, the polar motion is stored in a form rotated onto
the local meridian.
6. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB), is
available, an adequate estimate of hm can be obtained from the
expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to the
pressure and that an accurate phpa value is important for
precise work.
7. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
8. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
9. In cases where the caller wishes to supply his own Earth
rotation information and refraction constants, the function
Apc can be used instead of the present function.
10)This is one of several functions that inserts into the astrom
structure star-independent parameters needed for the chain of
astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and
portions of the transformation chain:
functions observer transformation
Apcg Apcg13 geocentric ICRS <-> GCRS
Apci Apci13 terrestrial ICRS <-> CIRS
Apco Apco13 terrestrial ICRS <-> observed
Apcs Apcs13 space ICRS <-> GCRS
Aper Aper13 terrestrial update Earth rotation
Apio Apio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary SOFA models to
compute the various ephemerides. The others accept ephemerides
supplied by the caller.
The transformation from ICRS to GCRS covers space motion,
parallax, light deflection, and aberration. From GCRS to CIRS
comprises frame bias and precession-nutation. From CIRS to
observed takes account of Earth rotation, polar motion, diurnal
aberration and parallax (unless subsumed into the ICRS <-> GCRS
transformation), and atmospheric refraction.
11)The context structure astrom produced by this function is used
by Atioq and Atoiq.
Called:
Utctai UTC to TAI
Taitt TAI to TT
Utcut1 UTC to UT1
Sp00 the TIO locator s', IERS 2000
Era00 Earth rotation angle, IAU 2000
Refco refraction constants for given ambient conditions
Apio astrometry parameters, CIRS-observed
*/
func Apio13(utc1, utc2, dut1 float64, elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64, astrom *ASTROM) int {
var j int
var tai1, tai2, tt1, tt2, ut11, ut12, sp, theta, refa, refb float64
/* UTC to other time scales. */
j = Utctai(utc1, utc2, &tai1, &tai2)
if j < 0 {
return -1
}
Taitt(tai1, tai2, &tt1, &tt2)
j = Utcut1(utc1, utc2, dut1, &ut11, &ut12)
if j < 0 {
return -1
}
/* TIO locator s'. */
sp = Sp00(tt1, tt2)
/* Earth rotation angle. */
theta = Era00(ut11, ut12)
/* Refraction constants A and B. */
Refco(phpa, tc, rh, wl, &refa, &refb)
/* CIRS <-> observed astrometry parameters. */
Apio(sp, theta, elong, phi, hm, xp, yp, refa, refb, astrom)
/* Return any warning status. */
return j
}
/*
Atcc13 J2000.0 catalog ICRS -> astrometric ICRS
Transform a star's ICRS catalog entry (epoch J2000.0) into ICRS
astrometric place.
Given:
rc float64 ICRS right ascension at J2000.0 (radians, Note 1)
dc float64 ICRS declination at J2000.0 (radians, Note 1)
pr float64 RA proper motion (radians/year, Note 2)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 3)
Returned:
ra,da float64 ICRS astrometric RA,Dec (radians)
Notes:
1. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require a
preliminary call to Pmsafe before use.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
3. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
Called:
Apci13 astrometry parameters, ICRS-CIRS, 2013
Atccq quick catalog ICRS to astrometric
*/
func Atcc13(rc, dc float64, pr, pd, px, rv float64, date1, date2 float64, ra, da *float64) {
/* Star-independent astrometry parameters */
var astrom ASTROM
var w float64
/* The transformation parameters. */
Apci13(date1, date2, &astrom, &w)
/* Catalog ICRS (epoch J2000.0) to astrometric. */
Atccq(rc, dc, pr, pd, px, rv, &astrom, ra, da)
}
/*
Atccq Astrometric ICRS -> J2000.0 catalog ICRS
Quick transformation of a star's ICRS catalog entry (epoch J2000.0)
into ICRS astrometric place, given precomputed star-independent
astrometry parameters.
Use of this function is appropriate when efficiency is important and
where many star positions are to be transformed for one date. The
star-independent parameters can be obtained by calling one of the
functions Apci[13], Apcg[13], Apco[13] or Apcs[13].
If the parallax and proper motions are zero the transformation has
no effect.
Given:
rc,dc float64 ICRS RA,Dec at J2000.0 (radians)
pr float64 RA proper motion (radians/year, Note 3)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
ra,da float64 ICRS astrometric RA,Dec (radians)
Notes:
1. All the vectors are with respect to BCRS axes.
2. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require a
preliminary call to Pmsafe before use.
3. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
Called:
Pmpx proper motion and parallax
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
*/
func Atccq(rc, dc float64, pr, pd, px, rv float64, astrom *ASTROM, ra, da *float64) {
var p [3]float64
var w float64
/* Proper motion and parallax, giving BCRS coordinate direction. */
Pmpx(rc, dc, pr, pd, px, rv, astrom.Pmt, astrom.Eb, &p)
/* ICRS astrometric RA,Dec. */
C2s(p, &w, da)
*ra = Anp(w)
}
/*
Atci13 Catalog -> CIRS
Transform ICRS star data, epoch J2000.0, to CIRS.
Given:
rc float64 ICRS right ascension at J2000.0 (radians, Note 1)
dc float64 ICRS declination at J2000.0 (radians, Note 1)
pr float64 RA proper motion (radians/year, Note 2)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 3)
Returned:
ri,di float64 CIRS geocentric RA,Dec (radians)
eo float64 equation of the origins (ERA-GST, Note 5)
Notes:
1. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require a
preliminary call to Pmsafe before use.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
3. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
4. The available accuracy is better than 1 milliarcsecond, limited
mainly by the precession-nutation model that is used, namely
2000A/2006. Very close to solar system bodies, additional
errors of up to several milliarcseconds can occur because of
unmodeled light deflection; however, the Sun's contribution is
taken into account, to first order. The accuracy limitations of
the SOFA function Epv00 (used to compute Earth position and
velocity) can contribute aberration errors of up to
5 microarcseconds. Light deflection at the Sun's limb is
uncertain at the 0.4 mas level.
5. Should the transformation to (equinox based) apparent place be
required rather than (CIO based) intermediate place, subtract the
equation of the origins from the returned right ascension:
RA = RI - EO. (The Anp function can then be applied, as
required, to keep the result in the conventional 0-2pi range.)
Called:
Apci13 astrometry parameters, ICRS-CIRS, 2013
Atciq quick ICRS to CIRS
*/
func Atci13(rc, dc float64, pr, pd, px, rv float64, date1, date2 float64, ri, di, eo *float64) {
/* Star-independent astrometry parameters */
var astrom ASTROM
/* The transformation parameters. */
Apci13(date1, date2, &astrom, eo)
/* ICRS (epoch J2000.0) to CIRS. */
Atciq(rc, dc, pr, pd, px, rv, &astrom, ri, di)
}
/*
Atciq Quick ICRS -> CIRS
Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
star-independent astrometry parameters.
Use of this function is appropriate when efficiency is important and
where many star positions are to be transformed for one date. The
star-independent parameters can be obtained by calling one of the
functions Apci[13], Apcg[13], Apco[13] or Apcs[13].
If the parallax and proper motions are zero the Atciqz function
can be used instead.
Given:
rc,dc float64 ICRS RA,Dec at J2000.0 (radians)
pr float64 RA proper motion (radians/year, Note 3)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
ri,di float64 CIRS RA,Dec (radians)
Notes:
1. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require a
preliminary call to Pmsafe before use.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
Called:
Pmpx proper motion and parallax
Ldsun light deflection by the Sun
Ab stellar aberration
Rxp product of r-matrix and pv-vector
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
*/
func Atciq(rc, dc float64, pr, pd, px, rv float64, astrom *ASTROM, ri, di *float64) {
var pco, pnat, ppr, pi [3]float64
var w float64
/* Proper motion and parallax, giving BCRS coordinate direction. */
Pmpx(rc, dc, pr, pd, px, rv, astrom.Pmt, astrom.Eb, &pco)
/* Light deflection by the Sun, giving BCRS natural direction. */
Ldsun(pco, astrom.Eh, astrom.Em, &pnat)
/* Aberration, giving GCRS proper direction. */
Ab(pnat, astrom.V, astrom.Em, astrom.Bm1, &ppr)
/* Bias-precession-nutation, giving CIRS proper direction. */
Rxp(astrom.Bpn, ppr, &pi)
/* CIRS RA,Dec. */
C2s(pi, &w, di)
*ri = Anp(w)
}
/*
Atciqn Quick ICRS -> CIRS, multiple deflections
Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
star-independent astrometry parameters plus a list of light-
deflecting bodies.
Use of this function is appropriate when efficiency is important and
where many star positions are to be transformed for one date. The
star-independent parameters can be obtained by calling one of the
functions Apci[13], Apcg[13], Apco[13] or Apcs[13].
If the only light-deflecting body to be taken into account is the
Sun, the Atciq function can be used instead. If in addition the
parallax and proper motions are zero, the Atciqz function can be
used.
Given:
rc,dc float64 ICRS RA,Dec at J2000.0 (radians)
pr float64 RA proper motion (radians/year, Note 3)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
n int number of bodies (Note 3)
b LDBODY[n] data for each of the n bodies (Notes 3,4):
bm float64 mass of the body (solar masses, Note 5)
dl float64 deflection limiter (Note 6)
pv [2][3]float64 barycentric PV of the body (au, au/day)
Returned:
ri,di float64 CIRS RA,Dec (radians)
Notes:
1. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require a
preliminary call to Pmsafe before use.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
3. The struct b contains n entries, one for each body to be
considered. If n = 0, no gravitational light deflection will be
applied, not even for the Sun.
4. The struct b should include an entry for the Sun as well as for
any planet or other body to be taken into account. The entries
should be in the order in which the light passes the body.
5. In the entry in the b struct for body i, the mass parameter
b[i].bm can, as required, be adjusted in order to allow for such
effects as quadrupole field.
6. The deflection limiter parameter b[i].dl is phi^2/2, where phi is
the angular separation (in radians) between star and body at
which limiting is applied. As phi shrinks below the chosen
threshold, the deflection is artificially reduced, reaching zero
for phi = 0. Example values suitable for a terrestrial
observer, together with masses, are as follows:
body i b[i].bm b[i].dl
Sun 1.0 6e-6
Jupiter 0.00095435 3e-9
Saturn 0.00028574 3e-10
7. For efficiency, validation of the contents of the b array is
omitted. The supplied masses must be greater than zero, the
position and velocity vectors must be right, and the deflection
limiter greater than zero.
Called:
Pmpx proper motion and parallax
Ldn light deflection by n bodies
Ab stellar aberration
Rxp product of r-matrix and pv-vector
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
*/
func Atciqn(rc, dc float64, pr, pd, px, rv float64, astrom *ASTROM, n int, b []LDBODY, ri, di *float64) {
var pco, pnat, ppr, pi [3]float64
var w float64
/* Proper motion and parallax, giving BCRS coordinate direction. */
Pmpx(rc, dc, pr, pd, px, rv, astrom.Pmt, astrom.Eb, &pco)
/* Light deflection, giving BCRS natural direction. */
Ldn(n, b, astrom.Eb, pco, &pnat)
/* Aberration, giving GCRS proper direction. */
Ab(pnat, astrom.V, astrom.Em, astrom.Bm1, &ppr)
/* Bias-precession-nutation, giving CIRS proper direction. */
Rxp(astrom.Bpn, ppr, &pi)
/* CIRS RA,Dec. */
C2s(pi, &w, di)
*ri = Anp(w)
}
/*
Atciqz Quick astrometric ICRS -> CIRS
Quick ICRS to CIRS transformation, given precomputed star-
independent astrometry parameters, and assuming zero parallax and
proper motion.
Use of this function is appropriate when efficiency is important and
where many star positions are to be transformed for one date. The
star-independent parameters can be obtained by calling one of the
functions Apci[13], Apcg[13], Apco[13] or Apcs[13].
The corresponding function for the case of non-zero parallax and
proper motion is Atciq.
Given:
rc,dc float64 ICRS astrometric RA,Dec (radians)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
ri,di float64 CIRS RA,Dec (radians)
Note:
All the vectors are with respect to BCRS axes.
References:
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013).
Klioner, Sergei A., "A practical relativistic model for micro-
arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
Called:
S2c spherical coordinates to unit vector
Ldsun light deflection due to Sun
Ab stellar aberration
Rxp product of r-matrix and p-vector
C2s p-vector to spherical
Anp normalize angle into range +/- pi
*/
func Atciqz(rc, dc float64, astrom *ASTROM, ri, di *float64) {
var pco, pnat, ppr, pi [3]float64
var w float64
/* BCRS coordinate direction (unit vector). */
S2c(rc, dc, &pco)
/* Light deflection by the Sun, giving BCRS natural direction. */
Ldsun(pco, astrom.Eh, astrom.Em, &pnat)
/* Aberration, giving GCRS proper direction. */
Ab(pnat, astrom.V, astrom.Em, astrom.Bm1, &ppr)
/* Bias-precession-nutation, giving CIRS proper direction. */
Rxp(astrom.Bpn, ppr, &pi)
/* CIRS RA,Dec. */
C2s(pi, &w, di)
*ri = Anp(w)
}
/*
Atco13 ICRS -> observed
ICRS RA,Dec to observed place. The caller supplies UTC, site
coordinates, ambient air conditions and observing wavelength.
SOFA models are used for the Earth ephemeris, bias-precession-
nutation, Earth orientation and refraction.
Given:
rc,dc float64 ICRS right ascension at J2000.0 (radians, Note 1)
pr float64 RA proper motion (radians/year, Note 2)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 3-4)
dut1 float64 UT1-UTC (seconds, Note 5)
elong float64 longitude (radians, east +ve, Note 6)
phi float64 latitude (geodetic, radians, Note 6)
hm float64 height above ellipsoid (m, geodetic, Notes 6,8)
xp,yp float64 polar motion coordinates (radians, Note 7)
phpa float64 pressure at the observer (hPa = mB, Note 8)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 9)
Returned:
aob float64 observed azimuth (radians: N=0,E=90)
zob float64 observed zenith distance (radians)
hob float64 observed hour angle (radians)
dob float64 observed declination (radians)
rob float64 observed right ascension (CIO-based, radians)
eo float64 equation of the origins (ERA-GST)
Returned (function value):
int status: +1 = dubious year (Note 4)
0 = OK
-1 = unacceptable date
Notes:
1. Star data for an epoch other than J2000.0 (for example from the
Hipparcos catalog, which has an epoch of J1991.25) will require
a preliminary call to Pmsafe before use.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
4. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the
future to be trusted. See Dat for further details.
5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
6. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
7. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many
applications, xp and yp can be set to zero.
8. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB),
is available, an adequate estimate of hm can be obtained from
the expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to
the pressure and that an accurate phpa value is important for
precise work.
9. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
10)The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted observed
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better
than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
Without refraction, the complementary functions Atco13 and
Atoc13 are self-consistent to better than 1 microarcsecond
all over the celestial sphere. With refraction included,
consistency falls off at high zenith distances, but is still
better than 0.05 arcsec at 85 degrees.
11)"Observed" Az,ZD means the position that would be seen by a
perfect geodetically aligned theodolite. (Zenith distance is
used rather than altitude in order to reflect the fact that no
allowance is made for depression of the horizon.) This is
related to the observed HA,Dec via the standard rotation, using
the geodetic latitude (corrected for polar motion), while the
observed HA and RA are related simply through the Earth rotation
angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
means the position that would be seen by a perfect equatorial
with its polar axis aligned to the Earth's axis of rotation.
12)It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
Called:
Apco13 astrometry parameters, ICRS-observed, 2013
Atciq quick ICRS to CIRS
Atioq quick CIRS to observed
*/
func Atco13(rc, dc float64, pr, pd, px, rv float64, utc1, utc2, dut1 float64,
elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64,
aob, zob, hob *float64, dob, rob, eo *float64) int {
var j int
var astrom ASTROM
var ri, di float64
/* Star-independent astrometry parameters. */
j = Apco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
phpa, tc, rh, wl, &astrom, eo)
/* Abort if bad UTC. */
if j < 0 {
return j
}
/* Transform ICRS to CIRS. */
Atciq(rc, dc, pr, pd, px, rv, &astrom, &ri, &di)
/* Transform CIRS to observed. */
Atioq(ri, di, &astrom, aob, zob, hob, dob, rob)
/* Return OK/warning status. */
return j
}
/*
Atic13 CIRS -> ICRS
Transform star RA,Dec from geocentric CIRS to ICRS astrometric.
Given:
ri,di float64 CIRS geocentric RA,Dec (radians)
date1 float64 TDB as a 2-part...
date2 float64 ...Julian Date (Note 1)
Returned:
rc,dc float64 ICRS astrometric RA,Dec (radians)
eo float64 equation of the origins (ERA-GST, Note 4)
Notes:
1. The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. For most
applications of this function the choice will not be at all
critical.
TT can be used instead of TDB without any significant impact on
accuracy.
2. Iterative techniques are used for the aberration and light
deflection corrections so that the functions Atic13 (or
Aticq) and Atci13 (or Atciq) are accurate inverses;
even at the edge of the Sun's disk the discrepancy is only about
1 nanoarcsecond.
3. The available accuracy is better than 1 milliarcsecond, limited
mainly by the precession-nutation model that is used, namely
2000A/2006. Very close to solar system bodies, additional
errors of up to several milliarcseconds can occur because of
unmodeled light deflection; however, the Sun's contribution is
taken into account, to first order. The accuracy limitations of
the SOFA function Epv00 (used to compute Earth position and
velocity) can contribute aberration errors of up to
5 microarcseconds. Light deflection at the Sun's limb is
uncertain at the 0.4 mas level.
4. Should the transformation to (equinox based) J2000.0 mean place
be required rather than (CIO based) ICRS coordinates, subtract the
equation of the origins from the returned right ascension:
RA = RI - EO. (The Anp function can then be applied, as
required, to keep the result in the conventional 0-2pi range.)
Called:
Apci13 astrometry parameters, ICRS-CIRS, 2013
Aticq quick CIRS to ICRS astrometric
*/
func Atic13(ri, di float64, date1, date2 float64, rc, dc, eo *float64) {
/* Star-independent astrometry parameters */
var astrom ASTROM
/* Star-independent astrometry parameters. */
Apci13(date1, date2, &astrom, eo)
/* CIRS to ICRS astrometric. */
Aticq(ri, di, &astrom, rc, dc)
}
/*
Aticq Quick CIRS -> ICRS
Quick CIRS RA,Dec to ICRS astrometric place, given the star-
independent astrometry parameters.
Use of this function is appropriate when efficiency is important and
where many star positions are all to be transformed for one date.
The star-independent astrometry parameters can be obtained by
calling one of the functions Apci[13], Apcg[13], Apco[13]
or Apcs[13].
Given:
ri,di float64 CIRS RA,Dec (radians)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
rc,dc float64 ICRS astrometric RA,Dec (radians)
Notes:
1. Only the Sun is taken into account in the light deflection
correction.
2. Iterative techniques are used for the aberration and light
deflection corrections so that the functions Atic13 (or
Aticq) and Atci13 (or Atciq) are accurate inverses;
even at the edge of the Sun's disk the discrepancy is only about
1 nanoarcsecond.
Called:
S2c spherical coordinates to unit vector
Trxp product of transpose of r-matrix and p-vector
Zp zero p-vector
Ab stellar aberration
Ldsun light deflection by the Sun
C2s p-vector to spherical
Anp normalize angle into range +/- pi
*/
func Aticq(ri, di float64, astrom *ASTROM, rc, dc *float64) {
var j, i int
var pi, ppr, pnat, pco, d, before, after [3]float64
var w, r2, r float64
/* CIRS RA,Dec to Cartesian. */
S2c(ri, di, &pi)
/* Bias-precession-nutation, giving GCRS proper direction. */
Trxp(astrom.Bpn, pi, &ppr)
/* Aberration, giving GCRS natural direction. */
Zp(&d)
for j = 0; j < 2; j++ {
r2 = 0.0
for i = 0; i < 3; i++ {
w = ppr[i] - d[i]
before[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
before[i] /= r
}
Ab(before, astrom.V, astrom.Em, astrom.Bm1, &after)
r2 = 0.0
for i = 0; i < 3; i++ {
d[i] = after[i] - before[i]
w = ppr[i] - d[i]
pnat[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
pnat[i] /= r
}
}
/* Light deflection by the Sun, giving BCRS coordinate direction. */
Zp(&d)
for j = 0; j < 5; j++ {
r2 = 0.0
for i = 0; i < 3; i++ {
w = pnat[i] - d[i]
before[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
before[i] /= r
}
Ldsun(before, astrom.Eh, astrom.Em, &after)
r2 = 0.0
for i = 0; i < 3; i++ {
d[i] = after[i] - before[i]
w = pnat[i] - d[i]
pco[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
pco[i] /= r
}
}
/* ICRS astrometric RA,Dec. */
C2s(pco, &w, dc)
*rc = Anp(w)
}
/*
Aticqn Quick CIRS -> ICRS, multiple deflections
Quick CIRS to ICRS astrometric place transformation, given the star-
independent astrometry parameters plus a list of light-deflecting
bodies.
Use of this function is appropriate when efficiency is important and
where many star positions are all to be transformed for one date.
The star-independent astrometry parameters can be obtained by
calling one of the functions Apci[13], Apcg[13], Apco[13]
or Apcs[13].
If the only light-deflecting body to be taken into account is the
Sun, the Aticq function can be used instead.
Given:
ri,di double CIRS RA,Dec (radians)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
n int number of bodies (Note 3)
b LDBODY[n] data for each of the n bodies (Notes 3,4):
bm float64 mass of the body (solar masses, Note 5)
dl float64 deflection limiter (Note 6)
pv [2][3]float64 barycentric PV of the body (au, au/day)
Returned:
rc,dc float64 ICRS astrometric RA,Dec (radians)
Notes:
1. Iterative techniques are used for the aberration and light
deflection corrections so that the functions Aticqn and
Atciqn are accurate inverses; even at the edge of the Sun's
disk the discrepancy is only about 1 nanoarcsecond.
2. If the only light-deflecting body to be taken into account is the
Sun, the Aticq function can be used instead.
3. The struct b contains n entries, one for each body to be
considered. If n = 0, no gravitational light deflection will be
applied, not even for the Sun.
4. The struct b should include an entry for the Sun as well as for
any planet or other body to be taken into account. The entries
should be in the order in which the light passes the body.
5. In the entry in the b struct for body i, the mass parameter
b[i].bm can, as required, be adjusted in order to allow for such
effects as quadrupole field.
6. The deflection limiter parameter b[i].dl is phi^2/2, where phi is
the angular separation (in radians) between star and body at
which limiting is applied. As phi shrinks below the chosen
threshold, the deflection is artificially reduced, reaching zero
for phi = 0. Example values suitable for a terrestrial
observer, together with masses, are as follows:
body i b[i].bm b[i].dl
Sun 1.0 6e-6
Jupiter 0.00095435 3e-9
Saturn 0.00028574 3e-10
7. For efficiency, validation of the contents of the b array is
omitted. The supplied masses must be greater than zero, the
position and velocity vectors must be right, and the deflection
limiter greater than zero.
Called:
S2c spherical coordinates to unit vector
Trxp product of transpose of r-matrix and p-vector
Zp zero p-vector
Ab stellar aberration
Ldn light deflection by n bodies
C2s p-vector to spherical
Anp normalize angle into range +/- pi
*/
func Aticqn(ri, di float64, astrom *ASTROM, n int, b []LDBODY, rc, dc *float64) {
var j, i int
var pi, ppr, pnat, pco, d, before, after [3]float64
var w, r2, r float64
/* CIRS RA,Dec to Cartesian. */
S2c(ri, di, &pi)
/* Bias-precession-nutation, giving GCRS proper direction. */
Trxp(astrom.Bpn, pi, &ppr)
/* Aberration, giving GCRS natural direction. */
Zp(&d)
for j = 0; j < 2; j++ {
r2 = 0.0
for i = 0; i < 3; i++ {
w = ppr[i] - d[i]
before[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
before[i] /= r
}
Ab(before, astrom.V, astrom.Em, astrom.Bm1, &after)
r2 = 0.0
for i = 0; i < 3; i++ {
d[i] = after[i] - before[i]
w = ppr[i] - d[i]
pnat[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
pnat[i] /= r
}
}
/* Light deflection, giving BCRS coordinate direction. */
Zp(&d)
for j = 0; j < 5; j++ {
r2 = 0.0
for i = 0; i < 3; i++ {
w = pnat[i] - d[i]
before[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
before[i] /= r
}
Ldn(n, b, astrom.Eb, before, &after)
r2 = 0.0
for i = 0; i < 3; i++ {
d[i] = after[i] - before[i]
w = pnat[i] - d[i]
pco[i] = w
r2 += w * w
}
r = sqrt(r2)
for i = 0; i < 3; i++ {
pco[i] /= r
}
}
/* ICRS astrometric RA,Dec. */
C2s(pco, &w, dc)
*rc = Anp(w)
}
/*
Atio13 CIRS -> observed
CIRS RA,Dec to observed place. The caller supplies UTC, site
coordinates, ambient air conditions and observing wavelength.
Given:
ri float64 CIRS right ascension (CIO-based, radians)
di float64 CIRS declination (radians)
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 1,2)
dut1 float64 UT1-UTC (seconds, Note 3)
elong float64 longitude (radians, east +ve, Note 4)
phi float64 geodetic latitude (radians, Note 4)
hm float64 height above ellipsoid (m, geodetic Notes 4,6)
xp,yp float64 polar motion coordinates (radians, Note 5)
phpa float64 pressure at the observer (hPa = mB, Note 6)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 7)
Returned:
aob float64 observed azimuth (radians: N=0,E=90)
zob float64 observed zenith distance (radians)
hob float64 observed hour angle (radians)
dob float64 observed declination (radians)
rob float64 observed right ascension (CIO-based, radians)
Returned (function value):
int status: +1 = dubious year (Note 2)
0 = OK
-1 = unacceptable date
Notes:
1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
2. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the
future to be trusted. See Dat for further details.
3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
4. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
5. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many
applications, xp and yp can be set to zero.
6. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB), is
available, an adequate estimate of hm can be obtained from the
expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to
the pressure and that an accurate phpa value is important for
precise work.
7. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
8. "Observed" Az,ZD means the position that would be seen by a
perfect geodetically aligned theodolite. (Zenith distance is
used rather than altitude in order to reflect the fact that no
allowance is made for depression of the horizon.) This is
related to the observed HA,Dec via the standard rotation, using
the geodetic latitude (corrected for polar motion), while the
observed HA and RA are related simply through the Earth rotation
angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
means the position that would be seen by a perfect equatorial
with its polar axis aligned to the Earth's axis of rotation.
9. The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted astrometric
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better
than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
10)The complementary functions Atio13 and Atoi13 are self-
consistent to better than 1 microarcsecond all over the
celestial sphere.
11)It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
Called:
Apio13 astrometry parameters, CIRS-observed, 2013
Atioq quick CIRS to observed
*/
func Atio13(ri, di float64, utc1, utc2, dut1 float64, elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64,
aob, zob, hob *float64, dob, rob *float64) int {
var j int
var astrom ASTROM
/* Star-independent astrometry parameters for CIRS->observed. */
j = Apio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
phpa, tc, rh, wl, &astrom)
/* Abort if bad UTC. */
if j < 0 {
return j
}
/* Transform CIRS to observed. */
Atioq(ri, di, &astrom, aob, zob, hob, dob, rob)
/* Return OK/warning status. */
return j
}
/*
Atioq Quick CIRS -> observed
Quick CIRS to observed place transformation.
Use of this function is appropriate when efficiency is important and
where many star positions are all to be transformed for one date.
The star-independent astrometry parameters can be obtained by
calling Apio[13] or Apco[13].
Given:
ri float64 CIRS right ascension
di float64 CIRS declination
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
aob float64 observed azimuth (radians: N=0,E=90)
zob float64 observed zenith distance (radians)
hob float64 observed hour angle (radians)
dob float64 observed declination (radians)
rob float64 observed right ascension (CIO-based, radians)
Notes:
1. This function returns zenith distance rather than altitude in
order to reflect the fact that no allowance is made for
depression of the horizon.
2. The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted observed
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better
than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
Without refraction, the complementary functions Atioq and
Atoiq are self-consistent to better than 1 microarcsecond all
over the celestial sphere. With refraction included, consistency
falls off at high zenith distances, but is still better than
0.05 arcsec at 85 degrees.
3. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
4. The CIRS RA,Dec is obtained from a star catalog mean place by
allowing for space motion, parallax, the Sun's gravitational lens
effect, annual aberration and precession-nutation. For star
positions in the ICRS, these effects can be applied by means of
the Atci13 (etc.) functions. Starting from classical "mean
place" systems, additional transformations will be needed first.
5. "Observed" Az,El means the position that would be seen by a
perfect geodetically aligned theodolite. This is obtained from
the CIRS RA,Dec by allowing for Earth orientation and diurnal
aberration, rotating from equator to horizon coordinates, and
then adjusting for refraction. The HA,Dec is obtained by
rotating back into equatorial coordinates, and is the position
that would be seen by a perfect equatorial with its polar axis
aligned to the Earth's axis of rotation. Finally, the RA is
obtained by subtracting the HA from the local ERA.
6. The star-independent CIRS-to-observed-place parameters in ASTROM
may be computed with Apio[13] or Apco[13]. If nothing has
changed significantly except the time, Aper[13] may be used to
perform the requisite adjustment to the astrom structure.
Called:
S2c spherical coordinates to unit vector
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
*/
func Atioq(ri, di float64, astrom *ASTROM, aob, zob *float64, hob, dob, rob *float64) {
/* Minimum cos(alt) and sin(alt) for refraction purposes */
const CELMIN = 1e-6
const SELMIN = 0.05
var v [3]float64
var x, y, z, sx, cx, sy, cy, xhd, yhd, zhd, f,
xhdt, yhdt, zhdt, xaet, yaet, zaet, azobs, r, tz, w, del,
cosdel, xaeo, yaeo, zaeo, zdobs, hmobs, dcobs, raobs float64
/* CIRS RA,Dec to Cartesian -HA,Dec. */
S2c(ri-astrom.Eral, di, &v)
x = v[0]
y = v[1]
z = v[2]
/* Polar motion. */
sx = sin(astrom.Xpl)
cx = cos(astrom.Xpl)
sy = sin(astrom.Ypl)
cy = cos(astrom.Ypl)
xhd = cx*x + sx*z
yhd = sx*sy*x + cy*y - cx*sy*z
zhd = -sx*cy*x + sy*y + cx*cy*z
/* Diurnal aberration. */
f = (1.0 - astrom.Diurab*yhd)
xhdt = f * xhd
yhdt = f * (yhd + astrom.Diurab)
zhdt = f * zhd
/* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */
xaet = astrom.Sphi*xhdt - astrom.Cphi*zhdt
yaet = yhdt
zaet = astrom.Cphi*xhdt + astrom.Sphi*zhdt
/* Azimuth (N=0,E=90). */
// azobs = ( xaet != 0.0 || yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0;
if xaet != 0.0 || yaet != 0.0 {
azobs = atan2(yaet, -xaet)
} else {
azobs = 0.0
}
/* ---------- */
/* Refraction */
/* ---------- */
/* Cosine and sine of altitude, with precautions. */
r = sqrt(xaet*xaet + yaet*yaet)
// r = r > CELMIN ? r : CELMIN;
if r <= CELMIN {
r = CELMIN
}
// z = zaet > SELMIN ? zaet : SELMIN;
if zaet > SELMIN {
z = zaet
} else {
z = SELMIN
}
/* A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. */
tz = r / z
w = astrom.Refb * tz * tz
del = (astrom.Refa + w) * tz /
(1.0 + (astrom.Refa+3.0*w)/(z*z))
/* Apply the change, giving observed vector. */
cosdel = 1.0 - del*del/2.0
f = cosdel - del*z/r
xaeo = xaet * f
yaeo = yaet * f
zaeo = cosdel*zaet + del*r
/* Observed ZD. */
zdobs = atan2(sqrt(xaeo*xaeo+yaeo*yaeo), zaeo)
/* Az/El vector to HA,Dec vector (both right-handed). */
v[0] = astrom.Sphi*xaeo + astrom.Cphi*zaeo
v[1] = yaeo
v[2] = -astrom.Cphi*xaeo + astrom.Sphi*zaeo
/* To spherical -HA,Dec. */
C2s(v, &hmobs, &dcobs)
/* Right ascension (with respect to CIO). */
raobs = astrom.Eral + hmobs
/* Return the results. */
*aob = Anp(azobs)
*zob = zdobs
*hob = -hmobs
*dob = dcobs
*rob = Anp(raobs)
}
/*
Atoc13 Observed -> astrometric ICRS
Observed place at a groundbased site to to ICRS astrometric RA,Dec.
The caller supplies UTC, site coordinates, ambient air conditions
and observing wavelength.
Given:
typ string type of coordinates - "R", "H" or "A" (Notes 1,2)
ob1 float64 observed Az, HA or RA (radians; Az is N=0,E=90)
ob2 float64 observed ZD or Dec (radians)
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 3,4)
dut1 float64 UT1-UTC (seconds, Note 5)
elong float64 longitude (radians, east +ve, Note 6)
phi float64 geodetic latitude (radians, Note 6)
hm float64 height above ellipsoid (m, geodetic Notes 6,8)
xp,yp float64 polar motion coordinates (radians, Note 7)
phpa float64 pressure at the observer (hPa = mB, Note 8)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 9)
Returned:
rc,dc float64 ICRS astrometric RA,Dec (radians)
Returned (function value):
int status: +1 = dubious year (Note 4)
0 = OK
-1 = unacceptable date
Notes:
1. "Observed" Az,ZD means the position that would be seen by a
perfect geodetically aligned theodolite. (Zenith distance is
used rather than altitude in order to reflect the fact that no
allowance is made for depression of the horizon.) This is
related to the observed HA,Dec via the standard rotation, using
the geodetic latitude (corrected for polar motion), while the
observed HA and RA are related simply through the Earth rotation
angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
means the position that would be seen by a perfect equatorial
with its polar axis aligned to the Earth's axis of rotation.
2. Only the first character of the type argument is significant.
"R" or "r" indicates that ob1 and ob2 are the observed right
ascension and declination; "H" or "h" indicates that they are
hour angle (west +ve) and declination; anything else ("A" or
"a" is recommended) indicates that ob1 and ob2 are azimuth
(north zero, east 90 deg) and zenith distance.
3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
4. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the
future to be trusted. See Dat for further details.
5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
6. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
7. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many
applications, xp and yp can be set to zero.
8. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB), is
available, an adequate estimate of hm can be obtained from the
expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to
the pressure and that an accurate phpa value is important for
precise work.
9. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
10)The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted astrometric
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better
than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
Without refraction, the complementary functions Atco13 and
Atoc13 are self-consistent to better than 1 microarcsecond
all over the celestial sphere. With refraction included,
consistency falls off at high zenith distances, but is still
better than 0.05 arcsec at 85 degrees.
11)It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
Called:
Apco13 astrometry parameters, ICRS-observed
Atoiq quick observed to CIRS
Aticq quick CIRS to ICRS
*/
func Atoc13(typ string, ob1, ob2 float64, utc1, utc2, dut1 float64,
elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64,
rc, dc *float64) int {
var j int
var astrom ASTROM
var eo, ri, di float64
/* Star-independent astrometry parameters. */
j = Apco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
phpa, tc, rh, wl, &astrom, &eo)
/* Abort if bad UTC. */
if j < 0 {
return j
}
/* Transform observed to CIRS. */
Atoiq(typ, ob1, ob2, &astrom, &ri, &di)
/* Transform CIRS to ICRS. */
Aticq(ri, di, &astrom, rc, dc)
/* Return OK/warning status. */
return j
}
/*
Atoi13 Observed -> CIRS
Observed place to CIRS. The caller supplies UTC, site coordinates,
ambient air conditions and observing wavelength.
Given:
typ string type of coordinates - "R", "H" or "A" (Notes 1,2)
ob1 float64 observed Az, HA or RA (radians; Az is N=0,E=90)
ob2 float64 observed ZD or Dec (radians)
utc1 float64 UTC as a 2-part...
utc2 float64 ...quasi Julian Date (Notes 3,4)
dut1 float64 UT1-UTC (seconds, Note 5)
elong float64 longitude (radians, east +ve, Note 6)
phi float64 geodetic latitude (radians, Note 6)
hm float64 height above the ellipsoid (meters, Notes 6,8)
xp,yp float64 polar motion coordinates (radians, Note 7)
phpa float64 pressure at the observer (hPa = mB, Note 8)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers, Note 9)
Returned:
ri float64 CIRS right ascension (CIO-based, radians)
di float64 CIRS declination (radians)
Returned (function value):
int status: +1 = dubious year (Note 2)
0 = OK
-1 = unacceptable date
Notes:
1. "Observed" Az,ZD means the position that would be seen by a
perfect geodetically aligned theodolite. (Zenith distance is
used rather than altitude in order to reflect the fact that no
allowance is made for depression of the horizon.) This is
related to the observed HA,Dec via the standard rotation, using
the geodetic latitude (corrected for polar motion), while the
observed HA and RA are related simply through the Earth rotation
angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
means the position that would be seen by a perfect equatorial
with its polar axis aligned to the Earth's axis of rotation.
2. Only the first character of the type argument is significant.
"R" or "r" indicates that ob1 and ob2 are the observed right
ascension and declination; "H" or "h" indicates that they are
hour angle (west +ve) and declination; anything else ("A" or
"a" is recommended) indicates that ob1 and ob2 are azimuth
(north zero, east 90 deg) and zenith distance.
3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
However, JD cannot unambiguously represent UTC during a leap
second unless special measures are taken. The convention in the
present function is that the JD day represents UTC days whether
the length is 86399, 86400 or 86401 SI seconds.
Applications should use the function Dtf2d to convert from
calendar date and time of day into 2-part quasi Julian Date, as
it implements the leap-second-ambiguity convention just
described.
4. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the
future to be trusted. See Dat for further details.
5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly
one second at the end of each positive UTC leap second,
introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
practice is under review, and in the future UT1-UTC may grow
essentially without limit.
6. The geographical coordinates are with respect to the WGS84
reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
longitude required by the present function is east-positive
(i.e. right-handed), in accordance with geographical convention.
7. The polar motion xp,yp can be obtained from IERS bulletins. The
values are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions 2003), measured along the
meridians 0 and 90 deg west respectively. For many
applications, xp and yp can be set to zero.
8. If hm, the height above the ellipsoid of the observing station
in meters, is not known but phpa, the pressure in hPa (=mB), is
available, an adequate estimate of hm can be obtained from the
expression
hm = -29.3 * tsl * log ( phpa / 1013.25 );
where tsl is the approximate sea-level air temperature in K
(See Astrophysical Quantities, C.W.Allen, 3rd edition, section
52). Similarly, if the pressure phpa is not known, it can be
estimated from the height of the observing station, hm, as
follows:
phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
Note, however, that the refraction is nearly proportional to
the pressure and that an accurate phpa value is important for
precise work.
9. The argument wl specifies the observing wavelength in
micrometers. The transition from optical to radio is assumed to
occur at 100 micrometers (about 3000 GHz).
10)The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted astrometric
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better
than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
Without refraction, the complementary functions Atio13 and
Atoi13 are self-consistent to better than 1 microarcsecond
all over the celestial sphere. With refraction included,
consistency falls off at high zenith distances, but is still
better than 0.05 arcsec at 85 degrees.
12)It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
Called:
Apio13 astrometry parameters, CIRS-observed, 2013
Atoiq quick observed to CIRS
*/
func Atoi13(typ string, ob1, ob2 float64, utc1, utc2, dut1 float64,
elong, phi, hm, xp, yp float64, phpa, tc, rh, wl float64,
ri, di *float64) int {
var j int
var astrom ASTROM
/* Star-independent astrometry parameters for CIRS->observed. */
j = Apio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
phpa, tc, rh, wl, &astrom)
/* Abort if bad UTC. */
if j < 0 {
return j
}
/* Transform observed to CIRS. */
Atoiq(typ, ob1, ob2, &astrom, ri, di)
/* Return OK/warning status. */
return j
}
/*
Atoiq Quick observed -> CIRS
Quick observed place to CIRS, given the star-independent astrometry
parameters.
Use of this function is appropriate when efficiency is important and
where many star positions are all to be transformed for one date.
The star-independent astrometry parameters can be obtained by
calling Apio[13] or Apco[13].
Given:
typ string type of coordinates: "R", "H" or "A" (Note 1)
ob1 float64 observed Az, HA or RA (radians; Az is N=0,E=90)
ob2 float64 observed ZD or Dec (radians)
astrom ASTROM star-independent astrometry parameters:
pmt float64 PM time interval (SSB, Julian years)
eb [3]float64 SSB to observer (vector, au)
eh [3]float64 Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
v [3]float64 barycentric observer velocity (vector, c)
bm1 float64 sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn [3][3]float64 bias-precession-nutation matrix
along float64 longitude + s' (radians)
xpl float64 polar motion xp wrt local meridian (radians)
ypl float64 polar motion yp wrt local meridian (radians)
sphi float64 sine of geodetic latitude
cphi float64 cosine of geodetic latitude
diurab float64 magnitude of diurnal aberration vector
eral float64 "local" Earth rotation angle (radians)
refa float64 refraction constant A (radians)
refb float64 refraction constant B (radians)
Returned:
ri float64 CIRS right ascension (CIO-based, radians)
di float64 CIRS declination (radians)
Notes:
1. "Observed" Az,ZD means the position that would be seen by a
perfect geodetically aligned theodolite. This is related to
the observed HA,Dec via the standard rotation, using the geodetic
latitude (corrected for polar motion), while the observed HA and
RA are related simply through the Earth rotation angle and the
site longitude. "Observed" RA,Dec or HA,Dec thus means the
position that would be seen by a perfect equatorial with its
polar axis aligned to the Earth's axis of rotation. By removing
from the observed place the effects of atmospheric refraction and
diurnal aberration, the CIRS RA,Dec is obtained.
2. Only the first character of the type argument is significant.
"R" or "r" indicates that ob1 and ob2 are the observed right
ascension and declination; "H" or "h" indicates that they are
hour angle (west +ve) and declination; anything else ("A" or
"a" is recommended) indicates that ob1 and ob2 are azimuth (north
zero, east 90 deg) and zenith distance. (Zenith distance is used
rather than altitude in order to reflect the fact that no
allowance is made for depression of the horizon.)
3. The accuracy of the result is limited by the corrections for
refraction, which use a simple A*tan(z) + B*tan^3(z) model.
Providing the meteorological parameters are known accurately and
there are no gross local effects, the predicted intermediate
coordinates should be within 0.05 arcsec (optical) or 1 arcsec
(radio) for a zenith distance of less than 70 degrees, better
than 30 arcsec (optical or radio) at 85 degrees and better than
20 arcmin (optical) or 25 arcmin (radio) at the horizon.
Without refraction, the complementary functions Atioq and
Atoiq are self-consistent to better than 1 microarcsecond all
over the celestial sphere. With refraction included, consistency
falls off at high zenith distances, but is still better than
0.05 arcsec at 85 degrees.
4. It is advisable to take great care with units, as even unlikely
values of the input parameters are accepted and processed in
accordance with the models used.
Called:
S2c spherical coordinates to unit vector
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
*/
func Atoiq(typ string, ob1, ob2 float64, astrom *ASTROM, ri, di *float64) {
/* Minimum sin(alt) for refraction purposes */
const SELMIN = 0.05
var c byte
var c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo,
xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref,
zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda,
f, xhd, yhd, zhd, sx, cx, sy, cy, hma float64
var v [3]float64
/* Coordinate type. */
c = typ[0]
/* Coordinates. */
c1 = ob1
c2 = ob2
/* Sin, cos of latitude. */
sphi = astrom.Sphi
cphi = astrom.Cphi
/* Standardize coordinate type. */
if c == 'r' || c == 'R' {
c = 'R'
} else if c == 'h' || c == 'H' {
c = 'H'
} else {
c = 'A'
}
/* If Az,ZD, convert to Cartesian (S=0,E=90). */
if c == 'A' {
ce = sin(c2)
xaeo = -cos(c1) * ce
yaeo = sin(c1) * ce
zaeo = cos(c2)
} else {
/* If RA,Dec, convert to HA,Dec. */
if c == 'R' {
c1 = astrom.Eral - c1
}
/* To Cartesian -HA,Dec. */
S2c(-c1, c2, &v)
xmhdo = v[0]
ymhdo = v[1]
zmhdo = v[2]
/* To Cartesian Az,El (S=0,E=90). */
xaeo = sphi*xmhdo - cphi*zmhdo
yaeo = ymhdo
zaeo = cphi*xmhdo + sphi*zmhdo
}
/* Azimuth (S=0,E=90). */
// az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0;
if xaeo != 0.0 || yaeo != 0.0 {
az = atan2(yaeo, xaeo)
} else {
az = 0.0
}
/* Sine of observed ZD, and observed ZD. */
sz = sqrt(xaeo*xaeo + yaeo*yaeo)
zdo = atan2(sz, zaeo)
/*
Refraction
----------
*/
/* Fast algorithm using two constant model. */
refa = astrom.Refa
refb = astrom.Refb
// tz = sz / ( zaeo > SELMIN ? zaeo : SELMIN );
if zaeo > SELMIN {
tz = sz / zaeo
} else {
tz = sz / SELMIN
}
dref = (refa + refb*tz*tz) * tz
zdt = zdo + dref
/* To Cartesian Az,ZD. */
ce = sin(zdt)
xaet = cos(az) * ce
yaet = sin(az) * ce
zaet = cos(zdt)
/* Cartesian Az,ZD to Cartesian -HA,Dec. */
xmhda = sphi*xaet + cphi*zaet
ymhda = yaet
zmhda = -cphi*xaet + sphi*zaet
/* Diurnal aberration. */
f = (1.0 + astrom.Diurab*ymhda)
xhd = f * xmhda
yhd = f * (ymhda - astrom.Diurab)
zhd = f * zmhda
/* Polar motion. */
sx = sin(astrom.Xpl)
cx = cos(astrom.Xpl)
sy = sin(astrom.Ypl)
cy = cos(astrom.Ypl)
v[0] = cx*xhd + sx*sy*yhd - sx*cy*zhd
v[1] = cy*yhd + sy*zhd
v[2] = sx*xhd - cx*sy*yhd + cx*cy*zhd
/* To spherical -HA,Dec. */
C2s(v, &hma, di)
/* Right ascension. */
*ri = Anp(astrom.Eral + hma)
}
/*
Ld Light deflection by a single solar-system body
Apply light deflection by a solar-system body, as part of
transforming coordinate direction into natural direction.
Given:
bm float64 mass of the gravitating body (solar masses)
p [3]float64 direction from observer to source (unit vector)
q [3]float64 direction from body to source (unit vector)
e [3]float64 direction from body to observer (unit vector)
em float64 distance from body to observer (au)
dlim float64 deflection limiter (Note 4)
Returned:
p1 [3]float64 observer to deflected source (unit vector)
Notes:
1. The algorithm is based on Expr. (70) in Klioner (2003) and
Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
2013), with some rearrangement to minimize the effects of machine
precision.
2. The mass parameter bm can, as required, be adjusted in order to
allow for such effects as quadrupole field.
3. The barycentric position of the deflecting body should ideally
correspond to the time of closest approach of the light ray to
the body.
4. The deflection limiter parameter dlim is phi^2/2, where phi is
the angular separation (in radians) between source and body at
which limiting is applied. As phi shrinks below the chosen
threshold, the deflection is artificially reduced, reaching zero
for phi = 0.
5. The returned vector p1 is not normalized, but the consequential
departure from unit magnitude is always negligible.
6. The arguments p and p1 can be the same array.
7. To accumulate total light deflection taking into account the
contributions from several bodies, call the present function for
each body in succession, in decreasing order of distance from the
observer.
8. For efficiency, validation is omitted. The supplied vectors must
be of unit magnitude, and the deflection limiter non-zero and
positive.
References:
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013).
Klioner, Sergei A., "A practical relativistic model for micro-
arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
Called:
Pdp scalar product of two p-vectors
Pxp vector product of two p-vectors
*/
func Ld(bm float64, p, q, e [3]float64, em, dlim float64, p1 *[3]float64) {
var i int
var qpe, eq, peq [3]float64
var qdqpe, w float64
/* q . (q + e). */
for i = 0; i < 3; i++ {
qpe[i] = q[i] + e[i]
}
qdqpe = Pdp(q, qpe)
/* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
w = bm * SRS / em / gmax(qdqpe, dlim)
/* p x (e x q). */
Pxp(e, q, &eq)
Pxp(p, eq, &peq)
/* Apply the deflection. */
for i = 0; i < 3; i++ {
p1[i] = p[i] + w*peq[i]
}
}
/*
Ldn Light deflection by multiple solar-system bodies
For a star, apply light deflection by multiple solar-system bodies,
as part of transforming coordinate direction into natural direction.
Given:
n int number of bodies (note 1)
b LDBODY[n] data for each of the n bodies (Notes 1,2):
bm float64 mass of the body (solar masses, Note 3)
dl float64 deflection limiter (Note 4)
pv [2][3]float64 barycentric PV of the body (au, au/day)
ob [3]float64 barycentric position of the observer (au)
sc [3]float64 observer to star coord direction (unit vector)
Returned:
sn [3]float64 observer to deflected star (unit vector)
Notes:
1. The array b contains n entries, one for each body to be
considered. If n = 0, no gravitational light deflection will be
applied, not even for the Sun.
2. The array b should include an entry for the Sun as well as for
any planet or other body to be taken into account. The entries
should be in the order in which the light passes the body.
3. In the entry in the b array for body i, the mass parameter
b[i].bm can, as required, be adjusted in order to allow for such
effects as quadrupole field.
4. The deflection limiter parameter b[i].dl is phi^2/2, where phi is
the angular separation (in radians) between star and body at
which limiting is applied. As phi shrinks below the chosen
threshold, the deflection is artificially reduced, reaching zero
for phi = 0. Example values suitable for a terrestrial
observer, together with masses, are as follows:
body i b[i].bm b[i].dl
Sun 1.0 6e-6
Jupiter 0.00095435 3e-9
Saturn 0.00028574 3e-10
5. For cases where the starlight passes the body before reaching the
observer, the body is placed back along its barycentric track by
the light time from that point to the observer. For cases where
the body is "behind" the observer no such shift is applied. If
a different treatment is preferred, the user has the option of
instead using the Ld function. Similarly, Ld can be used
for cases where the source is nearby, not a star.
6. The returned vector sn is not normalized, but the consequential
departure from unit magnitude is always negligible.
7. The arguments sc and sn can be the same array.
8. For efficiency, validation is omitted. The supplied masses must
be greater than zero, the position and velocity vectors must be
right, and the deflection limiter greater than zero.
Reference:
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013), Section 7.2.4.
Called:
Cp copy p-vector
Pdp scalar product of two p-vectors
Pmp p-vector minus p-vector
Ppsp p-vector plus scaled p-vector
Pn decompose p-vector into modulus and direction
Ld light deflection by a solar-system body
*/
func Ldn(n int, b []LDBODY, ob, sc [3]float64, sn *[3]float64) {
/* Light time for 1 au (days) */
const CR = AULT / DAYSEC
var i int
var v, ev, e [3]float64
var dt, em float64
/* Star direction prior to deflection. */
Cp(sc, sn)
/* Body by body. */
for i = 0; i < n; i++ {
/* Body to observer vector at epoch of observation (au). */
Pmp(ob, b[i].Pv[0], &v)
/* Minus the time since the light passed the body (days). */
dt = Pdp(*sn, v) * CR
/* Neutralize if the star is "behind" the observer. */
dt = gmin(dt, 0.0)
/* Backtrack the body to the time the light was passing the body. */
Ppsp(v, -dt, b[i].Pv[1], &ev)
/* Body to observer vector as magnitude and direction. */
Pn(ev, &em, &e)
/* Apply light deflection for this body. */
Ld(b[i].Bm, *sn, *sn, e, em, b[i].Dl, sn)
/* Next body. */
}
}
/*
Ldsun Light deflection by the Sun
Deflection of starlight by the Sun.
Given:
p [3]float64 direction from observer to star (unit vector)
e [3]float64 direction from Sun to observer (unit vector)
em float64 distance from Sun to observer (au)
Returned:
p1 [3]float64 observer to deflected star (unit vector)
Notes:
1. The source is presumed to be sufficiently distant that its
directions seen from the Sun and the observer are essentially
the same.
2. The deflection is restrained when the angle between the star and
the center of the Sun is less than a threshold value, falling to
zero deflection for zero separation. The chosen threshold value
is within the solar limb for all solar-system applications, and
is about 5 arcminutes for the case of a terrestrial observer.
3. The arguments p and p1 can be the same array.
Called:
Ld light deflection by a solar-system body
*/
func Ldsun(p, e [3]float64, em float64, p1 *[3]float64) {
var em2, dlim float64
/* Deflection limiter (smaller for distant observers). */
em2 = em * em
if em2 < 1.0 {
em2 = 1.0
}
// dlim = 1e-6 / (em2 > 1.0 ? em2 : 1.0);
if em2 > 1.0 {
dlim = 1e-6 / em2
} else {
dlim = 1e-6
}
/* Apply the deflection. */
Ld(1.0, p, p, e, em, dlim, p1)
}
/*
Pmpx Apply proper motion and parallax
Given:
rc,dc float64 ICRS RA,Dec at catalog epoch (radians)
pr float64 RA proper motion (radians/year, Note 1)
pd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, +ve if receding)
pmt float64 proper motion time interval (SSB, Julian years)
pob [3]float64 SSB to observer vector (au)
Returned:
pco [3]float64 coordinate direction (BCRS unit vector)
Notes:
1. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
2. The proper motion time interval is for when the starlight
reaches the solar system barycenter.
3. To avoid the need for iteration, the Roemer effect (i.e. the
small annual modulation of the proper motion coming from the
changing light time) is applied approximately, using the
direction of the star at the catalog epoch.
References:
1984 Astronomical Almanac, pp B39-B41.
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013), Section 7.2.
Called:
Pdp scalar product of two p-vectors
Pn decompose p-vector into modulus and direction
*/
func Pmpx(rc, dc float64, pr, pd, px, rv, pmt float64, pob [3]float64, pco *[3]float64) {
/* Km/s to au/year */
const VF = DAYSEC * DJM / DAU
/* Light time for 1 au, Julian years */
const AULTY = AULT / DAYSEC / DJY
var i int
var sr, cr, sd, cd, x, y, z, dt, pxr, w, pdz float64
var p, pm [3]float64
/* Spherical coordinates to unit vector (and useful functions). */
sr = sin(rc)
cr = cos(rc)
sd = sin(dc)
cd = cos(dc)
x = cr * cd
p[0] = x
y = sr * cd
p[1] = y
z = sd
p[2] = z
/* Proper motion time interval (y) including Roemer effect. */
dt = pmt + Pdp(p, pob)*AULTY
/* Space motion (radians per year). */
pxr = px * DAS2R
w = VF * rv * pxr
pdz = pd * z
pm[0] = -pr*y - pdz*cr + w*x
pm[1] = pr*x - pdz*sr + w*y
pm[2] = pd*cd + w*z
/* Coordinate direction of star (unit vector, BCRS). */
for i = 0; i < 3; i++ {
p[i] += dt*pm[i] - pxr*pob[i]
}
Pn(p, &w, pco)
}
/*
Pmsafe Apply proper motion, with zero-parallax precautions
Star proper motion: update star catalog data for space motion, with
special handling to handle the zero parallax case.
Given:
ra1 float64 right ascension (radians), before
dec1 float64 declination (radians), before
pmr1 float64 RA proper motion (radians/year), before
pmd1 float64 Dec proper motion (radians/year), before
px1 float64 parallax (arcseconds), before
rv1 float64 radial velocity (km/s, +ve = receding), before
ep1a float64 "before" epoch, part A (Note 1)
ep1b float64 "before" epoch, part B (Note 1)
ep2a float64 "after" epoch, part A (Note 1)
ep2b float64 "after" epoch, part B (Note 1)
Returned:
ra2 float64 right ascension (radians), after
dec2 float64 declination (radians), after
pmr2 float64 RA proper motion (radians/year), after
pmd2 float64 Dec proper motion (radians/year), after
px2 float64 parallax (arcseconds), after
rv2 float64 radial velocity (km/s, +ve = receding), after
Returned (function value):
int status:
-1 = system error (should not occur)
0 = no warnings or errors
1 = distance overridden (Note 6)
2 = excessive velocity (Note 7)
4 = solution didn't converge (Note 8)
else = binary logical OR of the above warnings
Notes:
1. The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are
Julian Dates, apportioned in any convenient way between the two
parts (A and B). For example, JD(TDB)=2450123.7 could be
expressed in any of these ways, among others:
epNa epNb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience.
2. In accordance with normal star-catalog conventions, the object's
right ascension and declination are freed from the effects of
secular aberration. The frame, which is aligned to the catalog
equator and equinox, is Lorentzian and centered on the SSB.
The proper motions are the rate of change of the right ascension
and declination at the catalog epoch and are in radians per TDB
Julian year.
The parallax and radial velocity are in the same frame.
3. Care is needed with units. The star coordinates are in radians
and the proper motions in radians per Julian year, but the
parallax is in arcseconds.
4. The RA proper motion is in terms of coordinate angle, not true
angle. If the catalog uses arcseconds for both RA and Dec proper
motions, the RA proper motion will need to be divided by cos(Dec)
before use.
5. Straight-line motion at constant speed, in the inertial frame, is
assumed.
6. An extremely small (or zero or negative) parallax is overridden
to ensure that the object is at a finite but very large distance,
but not so large that the proper motion is equivalent to a large
but safe speed (about 0.1c using the chosen constant). A warning
status of 1 is added to the status if this action has been taken.
7. If the space velocity is a significant fraction of c (see the
constant VMAX in the function Starpv), it is arbitrarily set
to zero. When this action occurs, 2 is added to the status.
8. The relativistic adjustment carried out in the Starpv function
involves an iterative calculation. If the process fails to
converge within a set number of iterations, 4 is added to the
status.
Called:
Seps angle between two points
Starpm update star catalog data for space motion
*/
func Pmsafe(ra1, dec1, pmr1, pmd1, px1, rv1 float64,
ep1a, ep1b, ep2a, ep2b float64,
ra2, dec2, pmr2, pmd2, px2, rv2 *float64) int {
/* Minimum allowed parallax (arcsec) */
const PXMIN = 5e-7
/* Factor giving maximum allowed transverse speed of about 1% c */
const F = 326.0
var jpx, j int
var pm, px1a float64
/* Proper motion in one year (radians). */
pm = Seps(ra1, dec1, ra1+pmr1, dec1+pmd1)
/* Override the parallax to reduce the chances of a warning status. */
jpx = 0
px1a = px1
pm *= F
if px1a < pm {
jpx = 1
px1a = pm
}
if px1a < PXMIN {
jpx = 1
px1a = PXMIN
}
/* Carry out the transformation using the modified parallax. */
j = Starpm(ra1, dec1, pmr1, pmd1, px1a, rv1,
ep1a, ep1b, ep2a, ep2b,
ra2, dec2, pmr2, pmd2, px2, rv2)
/* Revise and return the status. */
if (j % 2) != 1 {
j += jpx
}
return j
}
/*
Pvstar Star position+velocity vector to catalog coordinates
Convert star position+velocity vector to catalog coordinates.
Given (Note 1):
pv [2][3]float64 pv-vector (au, au/day)
Returned (Note 2):
ra float64 right ascension (radians)
dec float64 declination (radians)
pmr float64 RA proper motion (radians/year)
pmd float64 Dec proper motion (radians/year)
px float64 parallax (arcsec)
rv float64 radial velocity (km/s, positive = receding)
Returned (function value):
int status:
0 = OK
-1 = superluminal speed (Note 5)
-2 = null position vector
Notes:
1. The specified pv-vector is the coordinate direction (and its rate
of change) for the date at which the light leaving the star
reached the solar-system barycenter.
2. The star data returned by this function are "observables" for an
imaginary observer at the solar-system barycenter. Proper motion
and radial velocity are, strictly, in terms of barycentric
coordinate time, TCB. For most practical applications, it is
permissible to neglect the distinction between TCB and ordinary
"proper" time on Earth (TT/TAI). The result will, as a rule, be
limited by the intrinsic accuracy of the proper-motion and
radial-velocity data; moreover, the supplied pv-vector is likely
to be merely an intermediate result (for example generated by the
function Starpv), so that a change of time unit will cancel
out overall.
In accordance with normal star-catalog conventions, the object's
right ascension and declination are freed from the effects of
secular aberration. The frame, which is aligned to the catalog
equator and equinox, is Lorentzian and centered on the SSB.
Summarizing, the specified pv-vector is for most stars almost
identical to the result of applying the standard geometrical
"space motion" transformation to the catalog data. The
differences, which are the subject of the Stumpff paper cited
below, are:
(i) In stars with significant radial velocity and proper motion,
the constantly changing light-time distorts the apparent proper
motion. Note that this is a classical, not a relativistic,
effect.
(ii) The transformation complies with special relativity.
3. Care is needed with units. The star coordinates are in radians
and the proper motions in radians per Julian year, but the
parallax is in arcseconds; the radial velocity is in km/s, but
the pv-vector result is in au and au/day.
4. The proper motions are the rate of change of the right ascension
and declination at the catalog epoch and are in radians per Julian
year. The RA proper motion is in terms of coordinate angle, not
true angle, and will thus be numerically larger at high
declinations.
5. Straight-line motion at constant speed in the inertial frame is
assumed. If the speed is greater than or equal to the speed of
light, the function aborts with an error status.
6. The inverse transformation is performed by the function Starpv.
Called:
Pn decompose p-vector into modulus and direction
Pdp scalar product of two p-vectors
Sxp multiply p-vector by scalar
Pmp p-vector minus p-vector
Pm modulus of p-vector
Ppp p-vector plus p-vector
Pv2s pv-vector to spherical
Anp normalize angle into range 0 to 2pi
Reference:
Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
*/
func Pvstar(pv [2][3]float64, ra, dec, pmr, pmd, px, rv *float64) int {
var r, vr, vt, bett, betr, d, w, del, a, rad, decd, rd float64
var pu, ur, ut, usr, ust [3]float64
/* Isolate the radial component of the velocity (au/day, inertial). */
Pn(pv[0], &r, &pu)
vr = Pdp(pu, pv[1])
Sxp(vr, pu, &ur)
/* Isolate the transverse component of the velocity (au/day, inertial). */
Pmp(pv[1], ur, &ut)
vt = Pm(ut)
/* Special-relativity dimensionless parameters. */
bett = vt / DC
betr = vr / DC
/* The observed-to-inertial correction terms. */
d = 1.0 + betr
w = betr*betr + bett*bett
if d == 0.0 || w > 1.0 {
return -1
}
del = -w / (sqrt(1.0-w) + 1.0)
/* Scale inertial tangential velocity vector into observed (au/d). */
Sxp(1.0/d, ut, &ust)
/* Compute observed radial velocity vector (au/d). */
Sxp(DC*(betr-del)/d, pu, &usr)
/* Combine the two to obtain the observed velocity vector (au/day). */
Ppp(usr, ust, &pv[1])
/* Cartesian to spherical. */
Pv2s(pv, &a, dec, &r, &rad, &decd, &rd)
if r == 0.0 {
return -2
}
/* Return RA in range 0 to 2pi. */
*ra = Anp(a)
/* Return proper motions in radians per year. */
*pmr = rad * DJY
*pmd = decd * DJY
/* Return parallax in arcsec. */
*px = DR2AS / r
/* Return radial velocity in km/s. */
*rv = 1e-3 * rd * DAU / DAYSEC
/* Success. */
return 0
}
/*
Pvtob Observatory position and velocity
Position and velocity of a terrestrial observing station.
Given:
elong float64 longitude (radians, east +ve, Note 1)
phi float64 latitude (geodetic, radians, Note 1)
hm float64 height above ref. ellipsoid (geodetic, m)
xp,yp float64 coordinates of the pole (radians, Note 2)
sp float64 the TIO locator s' (radians, Note 2)
theta float64 Earth rotation angle (radians, Note 3)
Returned:
pv [2][3]float64 position/velocity vector (m, m/s, CIRS)
Notes:
1. The terrestrial coordinates are with respect to the WGS84
reference ellipsoid.
2. xp and yp are the coordinates (in radians) of the Celestial
Intermediate Pole with respect to the International Terrestrial
Reference System (see IERS Conventions), measured along the
meridians 0 and 90 deg west respectively. sp is the TIO locator
s', in radians, which positions the Terrestrial Intermediate
Origin on the equator. For many applications, xp, yp and
(especially) sp can be set to zero.
3. If theta is Greenwich apparent sidereal time instead of Earth
rotation angle, the result is with respect to the true equator
and equinox of date, i.e. with the x-axis at the equinox rather
than the celestial intermediate origin.
4. The velocity units are meters per UT1 second, not per SI second.
This is unlikely to have any practical consequences in the modern
era.
5. No validation is performed on the arguments. Error cases that
could lead to arithmetic exceptions are trapped by the Gd2gc
function, and the result set to zeros.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013), Section 7.4.3.3.
Called:
Gd2gc geodetic to geocentric transformation
Pom00 polar motion matrix
Trxp product of transpose of r-matrix and p-vector
*/
func Pvtob(elong, phi, hm float64, xp, yp, sp, theta float64, pv *[2][3]float64) {
/* Earth rotation rate in radians per UT1 second */
const OM = 1.00273781191135448 * D2PI / DAYSEC
var xyz, xyzm [3]float64
var rpm [3][3]float64
var x, y, z, s, c float64
/* Geodetic to geocentric transformation (WGS84). */
Gd2gc(1, elong, phi, hm, &xyzm)
/* Polar motion and TIO position. */
Pom00(xp, yp, sp, &rpm)
Trxp(rpm, xyzm, &xyz)
x = xyz[0]
y = xyz[1]
z = xyz[2]
/* Functions of ERA. */
s = sin(theta)
c = cos(theta)
/* Position. */
pv[0][0] = c*x - s*y
pv[0][1] = s*x + c*y
pv[0][2] = z
/* Velocity. */
pv[1][0] = OM * (-s*x - c*y)
pv[1][1] = OM * (c*x - s*y)
pv[1][2] = 0.0
}
/*
Refco Refraction constants
Determine the constants A and B in the atmospheric refraction model
dZ = A tan Z + B tan^3 Z.
Z is the "observed" zenith distance (i.e. affected by refraction)
and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
zenith distance.
Given:
phpa float64 pressure at the observer (hPa = millibar)
tc float64 ambient temperature at the observer (deg C)
rh float64 relative humidity at the observer (range 0-1)
wl float64 wavelength (micrometers)
Returned:
refa float64 tan Z coefficient (radians)
refb float64 tan^3 Z coefficient (radians)
Notes:
1. The model balances speed and accuracy to give good results in
applications where performance at low altitudes is not paramount.
Performance is maintained across a range of conditions, and
applies to both optical/IR and radio.
2. The model omits the effects of (i) height above sea level (apart
from the reduced pressure itself), (ii) latitude (i.e. the
flattening of the Earth), (iii) variations in tropospheric lapse
rate and (iv) dispersive effects in the radio.
The model was tested using the following range of conditions:
lapse rates 0.0055, 0.0065, 0.0075 deg/meter
latitudes 0, 25, 50, 75 degrees
heights 0, 2500, 5000 meters ASL
pressures mean for height -10% to +5% in steps of 5%
temperatures -10 deg to +20 deg with respect to 280 deg at SL
relative humidity 0, 0.5, 1
wavelengths 0.4, 0.6, ... 2 micron, + radio
zenith distances 15, 45, 75 degrees
The accuracy with respect to raytracing through a model
atmosphere was as follows:
worst RMS
optical/IR 62 mas 8 mas
radio 319 mas 49 mas
For this particular set of conditions:
lapse rate 0.0065 K/meter
latitude 50 degrees
sea level
pressure 1005 mb
temperature 280.15 K
humidity 80%
wavelength 5740 Angstroms
the results were as follows:
ZD raytrace Refco Saastamoinen
10 10.27 10.27 10.27
20 21.19 21.20 21.19
30 33.61 33.61 33.60
40 48.82 48.83 48.81
45 58.16 58.18 58.16
50 69.28 69.30 69.27
55 82.97 82.99 82.95
60 100.51 100.54 100.50
65 124.23 124.26 124.20
70 158.63 158.68 158.61
72 177.32 177.37 177.31
74 200.35 200.38 200.32
76 229.45 229.43 229.42
78 267.44 267.29 267.41
80 319.13 318.55 319.10
deg arcsec arcsec arcsec
The values for Saastamoinen's formula (which includes terms
up to tan^5) are taken from Hohenkerk and Sinclair (1985).
3. A wl value in the range 0-100 selects the optical/IR case and is
wavelength in micrometers. Any value outside this range selects
the radio case.
4. Outlandish input parameters are silently limited to
mathematically safe values. Zero pressure is permissible, and
causes zeroes to be returned.
5. The algorithm draws on several sources, as follows:
a) The formula for the saturation vapour pressure of water as
a function of temperature and temperature is taken from
Equations (A4.5-A4.7) of Gill (1982).
b) The formula for the water vapour pressure, given the
saturation pressure and the relative humidity, is from
Crane (1976), Equation (2.5.5).
c) The refractivity of air is a function of temperature,
total pressure, water-vapour pressure and, in the case
of optical/IR, wavelength. The formulae for the two cases are
developed from Hohenkerk & Sinclair (1985) and Rueger (2002).
The IAG (1999) optical refractivity for dry air is used.
d) The formula for beta, the ratio of the scale height of the
atmosphere to the geocentric distance of the observer, is
an adaption of Equation (9) from Stone (1996). The
adaptations, arrived at empirically, consist of (i) a small
adjustment to the coefficient and (ii) a humidity term for the
radio case only.
e) The formulae for the refraction constants as a function of
n-1 and beta are from Green (1987), Equation (4.31).
References:
Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
Academic Press, 1976.
Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,
1982.
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987.
Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,
1985.
IAG Resolutions adopted at the XXIIth General Assembly in
Birmingham, 1999, Resolution 3.
Rueger, J.M., "Refractive Index Formulae for Electronic Distance
Measurement with Radio and Millimetre Waves", in Unisurv Report
S-68, School of Surveying and Spatial Information Systems,
University of New South Wales, Sydney, Australia, 2002.
Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.
*/
func Refco(phpa, tc, rh, wl float64, refa, refb *float64) {
var optic bool
var p, t, r, w, ps, pw, tk, wlsq, gamma, beta float64
/* Decide whether optical/IR or radio case: switch at 100 microns. */
optic = (wl <= 100.0)
/* Restrict parameters to safe values. */
t = gmax(tc, -150.0)
t = gmin(t, 200.0)
p = gmax(phpa, 0.0)
p = gmin(p, 10000.0)
r = gmax(rh, 0.0)
r = gmin(r, 1.0)
w = gmax(wl, 0.1)
w = gmin(w, 1e6)
/* Water vapour pressure at the observer. */
if p > 0.0 {
ps = pow(10.0, (0.7859+0.03477*t)/
(1.0+0.00412*t)) *
(1.0 + p*(4.5e-6+6e-10*t*t))
pw = r * ps / (1.0 - (1.0-r)*ps/p)
} else {
pw = 0.0
}
/* Refractive index minus 1 at the observer. */
tk = t + 273.15
if optic {
wlsq = w * w
gamma = ((77.53484e-6+
(4.39108e-7+3.666e-9/wlsq)/wlsq)*p -
11.2684e-6*pw) / tk
} else {
gamma = (77.6890e-6*p - (6.3938e-6-0.375463/tk)*pw) / tk
}
/* Formula for beta from Stone, with empirical adjustments. */
beta = 4.4474e-6 * tk
if !optic {
beta -= 0.0074 * pw * beta
}
/* Refraction constants from Green. */
*refa = gamma * (1.0 - beta)
*refb = -gamma * (beta - gamma/2.0)
}
/*
Starpm Proper motion between two epochs
Star proper motion: update star catalog data for space motion.
Given:
ra1 float64 right ascension (radians), before
dec1 float64 declination (radians), before
pmr1 float64 RA proper motion (radians/year), before
pmd1 float64 Dec proper motion (radians/year), before
px1 float64 parallax (arcseconds), before
rv1 float64 radial velocity (km/s, +ve = receding), before
ep1a float64 "before" epoch, part A (Note 1)
ep1b float64 "before" epoch, part B (Note 1)
ep2a float64 "after" epoch, part A (Note 1)
ep2b float64 "after" epoch, part B (Note 1)
Returned:
ra2 float64 right ascension (radians), after
dec2 float64 declination (radians), after
pmr2 float64 RA proper motion (radians/year), after
pmd2 float64 Dec proper motion (radians/year), after
px2 float64 parallax (arcseconds), after
rv2 float64 radial velocity (km/s, +ve = receding), after
Returned (function value):
int status:
-1 = system error (should not occur)
0 = no warnings or errors
1 = distance overridden (Note 6)
2 = excessive velocity (Note 7)
4 = solution didn't converge (Note 8)
else = binary logical OR of the above warnings
Notes:
1. The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are
Julian Dates, apportioned in any convenient way between the two
parts (A and B). For example, JD(TDB)=2450123.7 could be
expressed in any of these ways, among others:
epna epnb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2. In accordance with normal star-catalog conventions, the object's
right ascension and declination are freed from the effects of
secular aberration. The frame, which is aligned to the catalog
equator and equinox, is Lorentzian and centered on the SSB.
The proper motions are the rate of change of the right ascension
and declination at the catalog epoch and are in radians per TDB
Julian year.
The parallax and radial velocity are in the same frame.
3. Care is needed with units. The star coordinates are in radians
and the proper motions in radians per Julian year, but the
parallax is in arcseconds.
4. The RA proper motion is in terms of coordinate angle, not true
angle. If the catalog uses arcseconds for both RA and Dec proper
motions, the RA proper motion will need to be divided by cos(Dec)
before use.
5. Straight-line motion at constant speed, in the inertial frame,
is assumed.
6. An extremely small (or zero or negative) parallax is interpreted
to mean that the object is on the "celestial sphere", the radius
of which is an arbitrary (large) value (see the Starpv
function for the value used). When the distance is overridden in
this way, the status, initially zero, has 1 added to it.
7. If the space velocity is a significant fraction of c (see the
constant VMAX in the function Starpv), it is arbitrarily set
to zero. When this action occurs, 2 is added to the status.
8. The relativistic adjustment carried out in the Starpv function
involves an iterative calculation. If the process fails to
converge within a set number of iterations, 4 is added to the
status.
Called:
Starpv star catalog data to space motion pv-vector
Pvu update a pv-vector
Pdp scalar product of two p-vectors
Pvstar space motion pv-vector to star catalog data
*/
func Starpm(ra1, dec1, pmr1, pmd1, px1, rv1 float64, ep1a, ep1b, ep2a, ep2b float64,
ra2, dec2, pmr2, pmd2, px2, rv2 *float64) int {
var pv1, pv, pv2 [2][3]float64
var tl1, dt, r2, rdv, v2, c2mv2, tl2 float64
var j1, j2 int
/* RA,Dec etc. at the "before" epoch to space motion pv-vector. */
j1 = Starpv(ra1, dec1, pmr1, pmd1, px1, rv1, &pv1)
/* Light time when observed (days). */
tl1 = Pm(pv1[0]) / DC
/* Time interval, "before" to "after" (days). */
dt = (ep2a - ep1a) + (ep2b - ep1b)
/* Move star along track from the "before" observed position to the */
/* "after" geometric position. */
Pvu(dt+tl1, pv1, &pv)
/* From this geometric position, deduce the observed light time (days) */
/* at the "after" epoch (with theoretically unneccessary error check). */
r2 = Pdp(pv[0], pv[0])
rdv = Pdp(pv[0], pv[1])
v2 = Pdp(pv[1], pv[1])
c2mv2 = DC*DC - v2
if c2mv2 <= 0 {
return -1
}
tl2 = (-rdv + sqrt(rdv*rdv+c2mv2*r2)) / c2mv2
/* Move the position along track from the observed place at the */
/* "before" epoch to the observed place at the "after" epoch. */
Pvu(dt+(tl1-tl2), pv1, &pv2)
/* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */
j2 = Pvstar(pv2, ra2, dec2, pmr2, pmd2, px2, rv2)
/* Final status. */
if j2 == 0 {
return j1
}
return -1
}
/*
Starpv Star catalog coordinates to position+velocity vector
Convert star catalog coordinates to position+velocity vector.
Given (Note 1):
ra float64 right ascension (radians)
dec float64 declination (radians)
pmr float64 RA proper motion (radians/year)
pmd float64 Dec proper motion (radians/year)
px float64 parallax (arcseconds)
rv float64 radial velocity (km/s, positive = receding)
Returned (Note 2):
pv [2][3]float64 pv-vector (au, au/day)
Returned (function value):
int status:
0 = no warnings
1 = distance overridden (Note 6)
2 = excessive speed (Note 7)
4 = solution didn't converge (Note 8)
else = binary logical OR of the above
Notes:
1. The star data accepted by this function are "observables" for an
imaginary observer at the solar-system barycenter. Proper motion
and radial velocity are, strictly, in terms of barycentric
coordinate time, TCB. For most practical applications, it is
permissible to neglect the distinction between TCB and ordinary
"proper" time on Earth (TT/TAI). The result will, as a rule, be
limited by the intrinsic accuracy of the proper-motion and
radial-velocity data; moreover, the pv-vector is likely to be
merely an intermediate result, so that a change of time unit
would cancel out overall.
In accordance with normal star-catalog conventions, the object's
right ascension and declination are freed from the effects of
secular aberration. The frame, which is aligned to the catalog
equator and equinox, is Lorentzian and centered on the SSB.
2. The resulting position and velocity pv-vector is with respect to
the same frame and, like the catalog coordinates, is freed from
the effects of secular aberration. Should the "coordinate
direction", where the object was located at the catalog epoch, be
required, it may be obtained by calculating the magnitude of the
position vector pv[0][0-2] dividing by the speed of light in
au/day to give the light-time, and then multiplying the space
velocity pv[1][0-2] by this light-time and adding the result to
pv[0][0-2].
Summarizing, the pv-vector returned is for most stars almost
identical to the result of applying the standard geometrical
"space motion" transformation. The differences, which are the
subject of the Stumpff paper referenced below, are:
(i) In stars with significant radial velocity and proper motion,
the constantly changing light-time distorts the apparent proper
motion. Note that this is a classical, not a relativistic,
effect.
(ii) The transformation complies with special relativity.
3. Care is needed with units. The star coordinates are in radians
and the proper motions in radians per Julian year, but the
parallax is in arcseconds; the radial velocity is in km/s, but
the pv-vector result is in au and au/day.
4. The RA proper motion is in terms of coordinate angle, not true
angle. If the catalog uses arcseconds for both RA and Dec proper
motions, the RA proper motion will need to be divided by cos(Dec)
before use.
5. Straight-line motion at constant speed, in the inertial frame,
is assumed.
6. An extremely small (or zero or negative) parallax is interpreted
to mean that the object is on the "celestial sphere", the radius
of which is an arbitrary (large) value (see the constant PXMIN).
When the distance is overridden in this way, the status,
initially zero, has 1 added to it.
7. If the space velocity is a significant fraction of c (see the
constant VMAX), it is arbitrarily set to zero. When this action
occurs, 2 is added to the status.
8. The relativistic adjustment involves an iterative calculation.
If the process fails to converge within a set number (IMAX) of
iterations, 4 is added to the status.
9. The inverse transformation is performed by the function
Pvstar.
Called:
S2pv spherical coordinates to pv-vector
Pm modulus of p-vector
Zp zero p-vector
Pn decompose p-vector into modulus and direction
Pdp scalar product of two p-vectors
Sxp multiply p-vector by scalar
Pmp p-vector minus p-vector
Ppp p-vector plus p-vector
*/
func Starpv(ra, dec, pmr, pmd, px, rv float64, pv *[2][3]float64) int {
/* Smallest allowed parallax */
const PXMIN = 1e-7
/* Largest allowed speed (fraction of c) */
const VMAX = 0.5
/* Maximum number of iterations for relativistic solution */
const IMAX = 100
var i, iwarn int
var w, r, rd, rad, decd, v,
vsr, vst, betst, betsr, bett, betr,
dd, ddel,
d, del,
odd, oddel,
od, odel float64
d, del = 0.0, 0.0 /* to prevent */
odd, oddel = 0.0, 0.0 /* compiler */
od, odel = 0.0, 0.0 /* warnings */
var pu, usr, ust, ur, ut [3]float64
/* Distance (au). */
if px >= PXMIN {
w = px
iwarn = 0
} else {
w = PXMIN
iwarn = 1
}
r = DR2AS / w
/* Radial speed (au/day). */
rd = DAYSEC * rv * 1e3 / DAU
/* Proper motion (radian/day). */
rad = pmr / DJY
decd = pmd / DJY
/* To pv-vector (au,au/day). */
S2pv(ra, dec, r, rad, decd, rd, pv)
/* If excessive velocity, arbitrarily set it to zero. */
v = Pm(pv[1])
if (v / DC) > VMAX {
Zp(&pv[1])
iwarn += 2
}
/* Isolate the radial component of the velocity (au/day). */
Pn(pv[0], &w, &pu)
vsr = Pdp(pu, pv[1])
Sxp(vsr, pu, &usr)
/* Isolate the transverse component of the velocity (au/day). */
Pmp(pv[1], usr, &ust)
vst = Pm(ust)
/* Special-relativity dimensionless parameters. */
betsr = vsr / DC
betst = vst / DC
/* Determine the observed-to-inertial relativistic correction terms. */
bett = betst
betr = betsr
for i = 0; i < IMAX; i++ {
d = 1.0 + betr
w = betr*betr + bett*bett
del = -w / (sqrt(1.0-w) + 1.0)
betr = d*betsr + del
bett = d * betst
if i > 0 {
dd = fabs(d - od)
ddel = fabs(del - odel)
if (i > 1) && (dd >= odd) && (ddel >= oddel) {
break
}
odd = dd
oddel = ddel
}
od = d
odel = del
}
if i >= IMAX {
iwarn += 4
}
// Scale observed tangential velocity vector into inertial (au/d). */
Sxp(d, ust, &ut)
/* Compute inertial radial velocity vector (au/d). */
Sxp(DC*(d*betsr+del), pu, &ur)
/* Combine the two to obtain the inertial space velocity vector. */
Ppp(ur, ut, &pv[1])
/* Return the status. */
return iwarn
}
gofa-1.19.1/catalog.go 0000664 0000000 0000000 00000101551 14535740236 0014474 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
/*
Fk425 Convert B1950.0 FK4 star catalog data to J2000.0 FK5
This function converts a star's catalog data from the old FK4
(Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system.
Given: (all B1950.0, FK4)
r1950,d1950 float64 B1950.0 RA,Dec (rad)
dr1950,dd1950 float64 B1950.0 proper motions (rad/trop.yr)
p1950 float64 parallax (arcsec)
v1950 float64 radial velocity (km/s, +ve = moving away)
Returned: (all J2000.0, FK5)
r2000,d2000 float64 J2000.0 RA,Dec (rad)
dr2000,dd2000 float64 J2000.0 proper motions (rad/Jul.yr)
p2000 float64 parallax (arcsec)
v2000 float64 radial velocity (km/s, +ve = moving away)
Notes:
1. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt,
and are per year rather than per century.
2. The conversion is somewhat complicated, for several reasons:
. Change of standard epoch from B1950.0 to J2000.0.
. An intermediate transition date of 1984 January 1.0 TT.
. A change of precession model.
. Change of time unit for proper motion (tropical to Julian).
. FK4 positions include the E-terms of aberration, to simplify
the hand computation of annual aberration. FK5 positions
assume a rigorous aberration computation based on the Earth's
barycentric velocity.
. The E-terms also affect proper motions, and in particular cause
objects at large distances to exhibit fictitious proper
motions.
The algorithm is based on Smith et al. (1989) and Yallop et al.
(1989), which presented a matrix method due to Standish (1982) as
developed by Aoki et al. (1983), using Kinoshita's development of
Andoyer's post-Newcomb precession. The numerical constants from
Seidelmann (1992) are used canonically.
3. Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for.
Conversions for different epochs and equinoxes would require
additional treatment for precession, proper motion and E-terms.
4. In the FK4 catalog the proper motions of stars within 10 degrees
of the poles do not embody differential E-terms effects and
should, strictly speaking, be handled in a different manner from
stars outside these regions. However, given the general lack of
homogeneity of the star data available for routine astrometry,
the difficulties of handling positions that may have been
determined from astrometric fields spanning the polar and non-
polar regions, the likelihood that the differential E-terms
effect was not taken into account when allowing for proper motion
in past astrometry, and the undesirability of a discontinuity in
the algorithm, the decision has been made in this SOFA algorithm
to include the effects of differential E-terms on the proper
motions for all stars, whether polar or not. At epoch J2000.0,
and measuring "on the sky" rather than in terms of RA change, the
errors resulting from this simplification are less than
1 milliarcsecond in position and 1 milliarcsecond per century in
proper motion.
Called:
Anp normalize angle into range 0 to 2pi
Pv2s pv-vector to spherical coordinates
Pdp scalar product of two p-vectors
Pvmpv pv-vector minus pv_vector
Pvppv pv-vector plus pv_vector
S2pv spherical coordinates to pv-vector
Sxp multiply p-vector by scalar
References:
Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
FK4-based positions of stars to epoch J2000.0 positions in
accordance with the new IAU resolutions". Astron.Astrophys.
128, 263-267.
Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
Astronomical Almanac", ISBN 0-935702-68-7.
Smith, C.A. et al., 1989, "The transformation of astrometric
catalog systems to the equinox J2000.0". Astron.J. 97, 265.
Standish, E.M., 1982, "Conversion of positions and proper motions
from B1950.0 to the IAU system at J2000.0". Astron.Astrophys.,
115, 1, 20-22.
Yallop, B.D. et al., 1989, "Transformation of mean star places
from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
Astron.J. 97, 274.
*/
func Fk425(r1950, d1950 float64, dr1950, dd1950 float64, p1950, v1950 float64,
r2000, d2000 *float64, dr2000, dd2000 *float64, p2000, v2000 *float64) {
/* Radians per year to arcsec per century */
const PMF = 100.0 * DR2AS
/* Small number to avoid arithmetic problems */
const TINY = 1e-30
/* Miscellaneous */
var r, d, ur, ud, px, rv, pxvf, w, rd float64
var i, j, k, l int
/* Pv-vectors */
var r0, pv1, pv2 [2][3]float64
/*
CANONICAL CONSTANTS (Seidelmann 1992)
*/
/* Km per sec to AU per tropical century */
/* = 86400 * 36524.2198782 / 149597870.7 */
const VF = 21.095
/* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) */
a := [2][3]float64{
{-1.62557e-6, -0.31919e-6, -0.13843e-6},
{+1.245e-3, -1.580e-3, -0.659e-3},
}
/* 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M) */
em := [2][3][2][3]float64{
{{{+0.9999256782, -0.0111820611, -0.0048579477},
{+0.00000242395018, -0.00000002710663, -0.00000001177656}},
{{+0.0111820610, +0.9999374784, -0.0000271765},
{+0.00000002710663, +0.00000242397878, -0.00000000006587}},
{{+0.0048579479, -0.0000271474, +0.9999881997},
{+0.00000001177656, -0.00000000006582, +0.00000242410173}}},
{{{-0.000551, -0.238565, +0.435739},
{+0.99994704, -0.01118251, -0.00485767}},
{{+0.238514, -0.002667, -0.008541},
{+0.01118251, +0.99995883, -0.00002718}},
{{-0.435623, +0.012254, +0.002117},
{+0.00485767, -0.00002714, +1.00000956}}},
}
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* The FK4 data (units radians and arcsec per tropical century). */
r = r1950
d = d1950
ur = dr1950 * PMF
ud = dd1950 * PMF
px = p1950
rv = v1950
/* Express as a pv-vector. */
pxvf = px * VF
w = rv * pxvf
S2pv(r, d, 1.0, ur, ud, w, &r0)
/* Allow for E-terms (cf. Seidelmann 3.591-2). */
Pvmpv(r0, a, &pv1)
Sxp(Pdp(r0[0], a[0]), r0[0], &pv2[0])
Sxp(Pdp(r0[0], a[1]), r0[0], &pv2[1])
Pvppv(pv1, pv2, &pv1)
/* Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3). */
for i = 0; i < 2; i++ {
for j = 0; j < 3; j++ {
w = 0.0
for k = 0; k < 2; k++ {
for l = 0; l < 3; l++ {
w += em[i][j][k][l] * pv1[k][l]
}
}
pv2[i][j] = w
}
}
/* Revert to catalog form. */
Pv2s(pv2, &r, &d, &w, &ur, &ud, &rd)
if px > TINY {
rv = rd / pxvf
px = px / w
}
/* Return the results. */
*r2000 = Anp(r)
*d2000 = d
*dr2000 = ur / PMF
*dd2000 = ud / PMF
*v2000 = rv
*p2000 = px
}
/*
Fk45z Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero proper motion in the FK5 system
This function converts a star's catalog data from the old FK4
(Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system,
in such a way that the FK5 proper motion is zero. Because such a
star has, in general, a non-zero proper motion in the FK4 system,
the function requires the epoch at which the position in the FK4
system was determined.
Given:
r1950,d1950 float64 B1950.0 FK4 RA,Dec at epoch (rad)
bepoch float64 Besselian epoch (e.g. 1979.3)
Returned:
r2000,d2000 float64 J2000.0 FK5 RA,Dec (rad)
Notes:
1. The epoch bepoch is strictly speaking Besselian, but if a
Julian epoch is supplied the result will be affected only to a
negligible extent.
2. The method is from Appendix 2 of Aoki et al. (1983), but using
the constants of Seidelmann (1992). See the function Fk425
for a general introduction to the FK4 to FK5 conversion.
3. Conversion from equinox B1950.0 FK4 to equinox J2000.0 FK5 only
is provided for. Conversions for different starting and/or
ending epochs would require additional treatment for precession,
proper motion and E-terms.
4. In the FK4 catalog the proper motions of stars within 10 degrees
of the poles do not embody differential E-terms effects and
should, strictly speaking, be handled in a different manner from
stars outside these regions. However, given the general lack of
homogeneity of the star data available for routine astrometry,
the difficulties of handling positions that may have been
determined from astrometric fields spanning the polar and non-
polar regions, the likelihood that the differential E-terms
effect was not taken into account when allowing for proper motion
in past astrometry, and the undesirability of a discontinuity in
the algorithm, the decision has been made in this SOFA algorithm
to include the effects of differential E-terms on the proper
motions for all stars, whether polar or not. At epoch J2000.0,
and measuring "on the sky" rather than in terms of RA change, the
errors resulting from this simplification are less than
1 milliarcsecond in position and 1 milliarcsecond per century in
proper motion.
References:
Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
FK4-based positions of stars to epoch J2000.0 positions in
accordance with the new IAU resolutions". Astron.Astrophys.
128, 263-267.
Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
Astronomical Almanac", ISBN 0-935702-68-7.
Called:
Anp normalize angle into range 0 to 2pi
C2s p-vector to spherical
Epb2jd Besselian epoch to Julian date
Epj Julian date to Julian epoch
Pdp scalar product of two p-vectors
Pmp p-vector minus p-vector
Ppsp p-vector plus scaled p-vector
Pvu update a pv-vector
S2c spherical to p-vector
*/
func Fk45z(r1950, d1950, bepoch float64, r2000, d2000 *float64) {
/* Radians per year to arcsec per century */
const PMF = 100.0 * DR2AS
/* Position and position+velocity vectors */
var r0, p [3]float64
var pv [2][3]float64
/* Miscellaneous */
var w, djm0, djm float64
var i, j, k int
/*
CANONICAL CONSTANTS (Seidelmann 1992)
*/
/* Vectors A and Adot (Seidelmann 3.591-2) */
a := [3]float64{-1.62557e-6, -0.31919e-6, -0.13843e-6}
ad := [3]float64{+1.245e-3, -1.580e-3, -0.659e-3}
/* 3x2 matrix of p-vectors (cf. Seidelmann 3.591-4, matrix M) */
em := [2][3][3]float64{
{{+0.9999256782, -0.0111820611, -0.0048579477},
{+0.0111820610, +0.9999374784, -0.0000271765},
{+0.0048579479, -0.0000271474, +0.9999881997}},
{{-0.000551, -0.238565, +0.435739},
{+0.238514, -0.002667, -0.008541},
{-0.435623, +0.012254, +0.002117}},
}
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Spherical coordinates to p-vector. */
S2c(r1950, d1950, &r0)
/* Adjust p-vector A to give zero proper motion in FK5. */
w = (bepoch - 1950) / PMF
Ppsp(a, w, ad, &p)
/* Remove E-terms. */
Ppsp(p, -Pdp(r0, p), r0, &p)
Pmp(r0, p, &p)
/* Convert to Fricke system pv-vector (cf. Seidelmann 3.591-3). */
for i = 0; i < 2; i++ {
for j = 0; j < 3; j++ {
w = 0.0
for k = 0; k < 3; k++ {
w += em[i][j][k] * p[k]
}
pv[i][j] = w
}
}
/* Allow for fictitious proper motion. */
Epb2jd(bepoch, &djm0, &djm)
w = (Epj(djm0, djm) - 2000.0) / PMF
Pvu(w, pv, &pv)
/* Revert to spherical coordinates. */
C2s(pv[0], &w, d2000)
*r2000 = Anp(w)
}
/*
Fk524 Convert J2000.0 FK5 star catalog data to B1950.0 FK4
Given: (all J2000.0, FK5)
r2000,d2000 float64 J2000.0 RA,Dec (rad)
dr2000,dd2000 float64 J2000.0 proper motions (rad/Jul.yr)
p2000 float64 parallax (arcsec)
v2000 float64 radial velocity (km/s, +ve = moving away)
Returned: (all B1950.0, FK4)
r1950,d1950 float64 B1950.0 RA,Dec (rad)
dr1950,dd1950 float64 B1950.0 proper motions (rad/trop.yr)
p1950 float64 parallax (arcsec)
v1950 float64 radial velocity (km/s, +ve = moving away)
Notes:
1. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt,
and are per year rather than per century.
2. The conversion is somewhat complicated, for several reasons:
. Change of standard epoch from J2000.0 to B1950.0.
. An intermediate transition date of 1984 January 1.0 TT.
. A change of precession model.
. Change of time unit for proper motion (Julian to tropical).
. FK4 positions include the E-terms of aberration, to simplify
the hand computation of annual aberration. FK5 positions
assume a rigorous aberration computation based on the Earth's
barycentric velocity.
. The E-terms also affect proper motions, and in particular cause
objects at large distances to exhibit fictitious proper
motions.
3. The algorithm is based on Smith et al. (1989) and Yallop et al.
(1989), which presented a matrix method due to Standish (1982) as
developed by Aoki et al. (1983), using Kinoshita's development of
Andoyer's post-Newcomb precession. The numerical constants from
Seidelmann (1992) are used canonically.
4. In the FK4 catalog the proper motions of stars within 10 degrees
of the poles do not embody differential E-terms effects and
should, strictly speaking, be handled in a different manner from
stars outside these regions. However, given the general lack of
homogeneity of the star data available for routine astrometry,
the difficulties of handling positions that may have been
determined from astrometric fields spanning the polar and non-
polar regions, the likelihood that the differential E-terms
effect was not taken into account when allowing for proper motion
in past astrometry, and the undesirability of a discontinuity in
the algorithm, the decision has been made in this SOFA algorithm
to include the effects of differential E-terms on the proper
motions for all stars, whether polar or not. At epoch J2000.0,
and measuring "on the sky" rather than in terms of RA change, the
errors resulting from this simplification are less than
1 milliarcsecond in position and 1 milliarcsecond per century in
proper motion.
Called:
Anp normalize angle into range 0 to 2pi
Pdp scalar product of two p-vectors
Pm modulus of p-vector
Pmp p-vector minus p-vector
Ppp p-vector pluus p-vector
Pv2s pv-vector to spherical coordinates
S2pv spherical coordinates to pv-vector
Sxp multiply p-vector by scalar
References:
Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
FK4-based positions of stars to epoch J2000.0 positions in
accordance with the new IAU resolutions". Astron.Astrophys.
128, 263-267.
Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
Astronomical Almanac", ISBN 0-935702-68-7.
Smith, C.A. et al., 1989, "The transformation of astrometric
catalog systems to the equinox J2000.0". Astron.J. 97, 265.
Standish, E.M., 1982, "Conversion of positions and proper motions
from B1950.0 to the IAU system at J2000.0". Astron.Astrophys.,
115, 1, 20-22.
Yallop, B.D. et al., 1989, "Transformation of mean star places
from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
Astron.J. 97, 274.
*/
func Fk524(r2000, d2000 float64, dr2000, dd2000 float64, p2000, v2000 float64,
r1950, d1950 *float64, dr1950, dd1950 *float64, p1950, v1950 *float64) {
/* Radians per year to arcsec per century */
const PMF = 100.0 * DR2AS
/* Small number to avoid arithmetic problems */
const TINY = 1e-30
/* Miscellaneous */
var r, d, ur, ud, px, rv, pxvf, w, rd float64
var i, j, k, l int
/* Vectors, p and pv */
var r0, r1, pv [2][3]float64
var p1, p2 [3]float64
/*
CANONICAL CONSTANTS (Seidelmann 1992)
*/
/* Km per sec to AU per tropical century */
/* = 86400 * 36524.2198782 / 149597870.7 */
const VF = 21.095
/* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) */
a := [2][3]float64{
{-1.62557e-6, -0.31919e-6, -0.13843e-6},
{+1.245e-3, -1.580e-3, -0.659e-3},
}
/* 3x2 matrix of pv-vectors (cf. Seidelmann 3.592-1, matrix M^-1) */
em := [2][3][2][3]float64{
{{
{+0.9999256795, +0.0111814828, +0.0048590039},
{-0.00000242389840, -0.00000002710544, -0.00000001177742},
}, {
{-0.0111814828, +0.9999374849, -0.0000271771},
{+0.00000002710544, -0.00000242392702, +0.00000000006585},
}, {
{-0.0048590040, -0.0000271557, +0.9999881946},
{+0.00000001177742, +0.00000000006585, -0.00000242404995},
},
},
{{
{-0.000551, +0.238509, -0.435614},
{+0.99990432, +0.01118145, +0.00485852},
}, {
{-0.238560, -0.002667, +0.012254},
{-0.01118145, +0.99991613, -0.00002717},
}, {
{+0.435730, -0.008541, +0.002117},
{-0.00485852, -0.00002716, +0.99996684},
}},
}
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* The FK5 data (units radians and arcsec per Julian century). */
r = r2000
d = d2000
ur = dr2000 * PMF
ud = dd2000 * PMF
px = p2000
rv = v2000
/* Express as a pv-vector. */
pxvf = px * VF
w = rv * pxvf
S2pv(r, d, 1.0, ur, ud, w, &r0)
/* Convert pv-vector to Bessel-Newcomb system (cf. Seidelmann 3.592-1). */
for i = 0; i < 2; i++ {
for j = 0; j < 3; j++ {
w = 0.0
for k = 0; k < 2; k++ {
for l = 0; l < 3; l++ {
w += em[i][j][k][l] * r0[k][l]
}
}
r1[i][j] = w
}
}
/* Apply E-terms (equivalent to Seidelmann 3.592-3, one iteration). */
/* Direction. */
w = Pm(r1[0])
Sxp(Pdp(r1[0], a[0]), r1[0], &p1)
Sxp(w, a[0], &p2)
Pmp(p2, p1, &p1)
Ppp(r1[0], p1, &p1)
/* Recompute length. */
w = Pm(p1)
/* Direction. */
Sxp(Pdp(r1[0], a[0]), r1[0], &p1)
Sxp(w, a[0], &p2)
Pmp(p2, p1, &p1)
Ppp(r1[0], p1, &pv[0])
/* Derivative. */
Sxp(Pdp(r1[0], a[1]), pv[0], &p1)
Sxp(w, a[1], &p2)
Pmp(p2, p1, &p1)
Ppp(r1[1], p1, &pv[1])
/* Revert to catalog form. */
Pv2s(pv, &r, &d, &w, &ur, &ud, &rd)
if px > TINY {
rv = rd / pxvf
px = px / w
}
/* Return the results. */
*r1950 = Anp(r)
*d1950 = d
*dr1950 = ur / PMF
*dd1950 = ud / PMF
*p1950 = px
*v1950 = rv
}
/*
Fk52h Transform FK5 (J2000.0) star data into the Hipparcos frame
Given (all FK5, equinox J2000.0, epoch J2000.0):
r5 float64 RA (radians)
d5 float64 Dec (radians)
dr5 float64 proper motion in RA (dRA/dt, rad/Jyear)
dd5 float64 proper motion in Dec (dDec/dt, rad/Jyear)
px5 float64 parallax (arcsec)
rv5 float64 radial velocity (km/s, positive = receding)
Returned (all Hipparcos, epoch J2000.0):
rh float64 RA (radians)
dh float64 Dec (radians)
drh float64 proper motion in RA (dRA/dt, rad/Jyear)
ddh float64 proper motion in Dec (dDec/dt, rad/Jyear)
pxh float64 parallax (arcsec)
rvh float64 radial velocity (km/s, positive = receding)
Notes:
1. This function transforms FK5 star positions and proper motions
into the system of the Hipparcos catalog.
2. The proper motions in RA are dRA/dt rather than
cos(Dec)*dRA/dt, and are per year rather than per century.
3. The FK5 to Hipparcos transformation is modeled as a pure
rotation and spin; zonal errors in the FK5 catalog are not
taken into account.
4. See also H2fk5, Fk5hz, Hfk5z.
Called:
Starpv star catalog data to space motion pv-vector
Fk5hip FK5 to Hipparcos rotation and spin
Rxp product of r-matrix and p-vector
Pxp vector product of two p-vectors
Ppp p-vector plus p-vector
Pvstar space motion pv-vector to star catalog data
Reference:
F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).
*/
func Fk52h(r5, d5 float64, dr5, dd5, px5, rv5 float64,
rh, dh *float64, drh, ddh, pxh, rvh *float64) {
var i int
var pv5, pvh [2][3]float64
var r5h [3][3]float64
var s5h, wxp, vv [3]float64
/* FK5 barycentric position/velocity pv-vector (normalized). */
Starpv(r5, d5, dr5, dd5, px5, rv5, &pv5)
/* FK5 to Hipparcos orientation matrix and spin vector. */
Fk5hip(&r5h, &s5h)
/* Make spin units per day instead of per year. */
for i = 0; i < 3; i++ {
s5h[i] /= 365.25
}
/* Orient the FK5 position into the Hipparcos system. */
Rxp(r5h, pv5[0], &pvh[0])
/* Apply spin to the position giving an extra space motion component. */
Pxp(pv5[0], s5h, &wxp)
/* Add this component to the FK5 space motion. */
Ppp(wxp, pv5[1], &vv)
/* Orient the FK5 space motion into the Hipparcos system. */
Rxp(r5h, vv, &pvh[1])
/* Hipparcos pv-vector to spherical. */
Pvstar(pvh, rh, dh, drh, ddh, pxh, rvh)
}
/*
Fk54z Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero proper motion in FK5 system and zero parallax
Given:
r2000,d2000 float64 J2000.0 FK5 RA,Dec (rad)
bepoch float64 Besselian epoch (e.g. 1950.0)
Returned:
r1950,d1950 float64 B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
dr1950,dd1950 float64 B1950.0 FK4 proper motions (rad/trop.yr)
Notes:
1. In contrast to the Fk524 function, here the FK5 proper
motions, the parallax and the radial velocity are presumed zero.
2. This function converts a star position from the IAU 1976 FK5
(Fricke) system to the former FK4 (Bessel-Newcomb) system, for
cases such as distant radio sources where it is presumed there is
zero parallax and no proper motion. Because of the E-terms of
aberration, such objects have (in general) non-zero proper motion
in FK4, and the present function returns those fictitious proper
motions.
3. Conversion from J2000.0 FK5 to B1950.0 FK4 only is provided for.
Conversions involving other equinoxes would require additional
treatment for precession.
4. The position returned by this function is in the B1950.0 FK4
reference system but at Besselian epoch BEPOCH. For comparison
with catalogs the BEPOCH argument will frequently be 1950.0. (In
this context the distinction between Besselian and Julian epoch
is insignificant.)
5. The RA component of the returned (fictitious) proper motion is
dRA/dt rather than cos(Dec)*dRA/dt.
Called:
Anp normalize angle into range 0 to 2pi
C2s p-vector to spherical
Fk524 FK4 to FK5
S2c spherical to p-vector
*/
func Fk54z(r2000, d2000, bepoch float64, r1950, d1950 *float64, dr1950, dd1950 *float64) {
var r, d, pr, pd, px, rv, w float64
var p, v [3]float64
var i int
/* FK5 equinox J2000.0 to FK4 equinox B1950.0. */
Fk524(r2000, d2000, 0.0, 0.0, 0.0, 0.0,
&r, &d, &pr, &pd, &px, &rv)
/* Spherical to Cartesian. */
S2c(r, d, &p)
/* Fictitious proper motion (radians per year). */
v[0] = -pr*p[1] - pd*cos(r)*sin(d)
v[1] = pr*p[0] - pd*sin(r)*sin(d)
v[2] = pd * cos(d)
/* Apply the motion. */
w = bepoch - 1950.0
for i = 0; i < 3; i++ {
p[i] += w * v[i]
}
/* Cartesian to spherical. */
C2s(p, &w, d1950)
*r1950 = Anp(w)
/* Fictitious proper motion. */
*dr1950 = pr
*dd1950 = pd
}
/*
Fk5hip FK5 orientation and spin with respect to Hipparcos
Returned:
r5h [3][3]float64 r-matrix: FK5 rotation wrt Hipparcos (Note 2)
s5h [3]float64 r-vector: FK5 spin wrt Hipparcos (Note 3)
Notes:
1. This function models the FK5 to Hipparcos transformation as a
pure rotation and spin; zonal errors in the FK5 catalogue are
not taken into account.
2. The r-matrix r5h operates in the sense:
P_Hipparcos = r5h x P_FK5
where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is
the equivalent Hipparcos p-vector.
3. The r-vector s5h represents the time derivative of the FK5 to
Hipparcos rotation. The units are radians per year (Julian,
TDB).
Called:
Rv2m r-vector to r-matrix
Reference:
F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).
*/
func Fk5hip(r5h *[3][3]float64, s5h *[3]float64) {
var v [3]float64
/* FK5 wrt Hipparcos orientation and spin (radians, radians/year) */
var epx, epy, epz float64
var omx, omy, omz float64
epx = -19.9e-3 * DAS2R
epy = -9.1e-3 * DAS2R
epz = 22.9e-3 * DAS2R
omx = -0.30e-3 * DAS2R
omy = 0.60e-3 * DAS2R
omz = 0.70e-3 * DAS2R
/* FK5 to Hipparcos orientation expressed as an r-vector. */
v[0] = epx
v[1] = epy
v[2] = epz
/* Re-express as an r-matrix. */
Rv2m(v, r5h)
/* Hipparcos wrt FK5 spin expressed as an r-vector. */
s5h[0] = omx
s5h[1] = omy
s5h[2] = omz
}
/*
Fk5hz FK5 to Hipparcos assuming zero Hipparcos proper motion
Transform an FK5 (J2000.0) star position into the system of the
Hipparcos catalogue, assuming zero Hipparcos proper motion.
Given:
r5 float64 FK5 RA (radians), equinox J2000.0, at date
d5 float64 FK5 Dec (radians), equinox J2000.0, at date
date1,date2 float64 TDB date (Notes 1,2)
Returned:
rh float64 Hipparcos RA (radians)
dh float64 Hipparcos Dec (radians)
Notes:
1. This function converts a star position from the FK5 system to
the Hipparcos system, in such a way that the Hipparcos proper
motion is zero. Because such a star has, in general, a non-zero
proper motion in the FK5 system, the function requires the date
at which the position in the FK5 system was determined.
2. The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
3. The FK5 to Hipparcos transformation is modeled as a pure
rotation and spin; zonal errors in the FK5 catalogue are not
taken into account.
4. The position returned by this function is in the Hipparcos
reference system but at date date1+date2.
5. See also Fk52h, H2fk5, Hfk5z.
Called:
S2c spherical coordinates to unit vector
Fk5hip FK5 to Hipparcos rotation and spin
Sxp multiply p-vector by scalar
Rv2m r-vector to r-matrix
Trxp product of transpose of r-matrix and p-vector
Pxp vector product of two p-vectors
C2s p-vector to spherical
Anp normalize angle into range 0 to 2pi
Reference:
F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
*/
func Fk5hz(r5, d5 float64, date1, date2 float64, rh, dh *float64) {
var t, w float64
var p5e, s5h, vst, p5, ph [3]float64
var r5h, rst [3][3]float64
/* Interval from given date to fundamental epoch J2000.0 (JY). */
t = -((date1 - DJ00) + date2) / DJY
/* FK5 barycentric position vector. */
S2c(r5, d5, &p5e)
/* FK5 to Hipparcos orientation matrix and spin vector. */
Fk5hip(&r5h, &s5h)
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
Sxp(t, s5h, &vst)
/* Express the accumulated spin as a rotation matrix. */
Rv2m(vst, &rst)
/* Derotate the vector's FK5 axes back to date. */
Trxp(rst, p5e, &p5)
/* Rotate the vector into the Hipparcos system. */
Rxp(r5h, p5, &ph)
/* Hipparcos vector to spherical. */
C2s(ph, &w, dh)
*rh = Anp(w)
}
/*
H2fk5 Transform Hipparcos star data into the FK5 (J2000.0) frame
Given (all Hipparcos, epoch J2000.0):
rh float64 RA (radians)
dh float64 Dec (radians)
drh float64 proper motion in RA (dRA/dt, rad/Jyear)
ddh float64 proper motion in Dec (dDec/dt, rad/Jyear)
pxh float64 parallax (arcsec)
rvh float64 radial velocity (km/s, positive = receding)
Returned (all FK5, equinox J2000.0, epoch J2000.0):
r5 float64 RA (radians)
d5 float64 Dec (radians)
dr5 float64 proper motion in RA (dRA/dt, rad/Jyear)
dd5 float64 proper motion in Dec (dDec/dt, rad/Jyear)
px5 float64 parallax (arcsec)
rv5 float64 radial velocity (km/s, positive = receding)
Notes:
1. This function transforms Hipparcos star positions and proper
motions into FK5 J2000.0.
2. The proper motions in RA are dRA/dt rather than
cos(Dec)*dRA/dt, and are per year rather than per century.
3. The FK5 to Hipparcos transformation is modeled as a pure
rotation and spin; zonal errors in the FK5 catalog are not
taken into account.
4. See also Fk52h, Fk5hz, Hfk5z.
Called:
Starpv star catalog data to space motion pv-vector
Fk5hip FK5 to Hipparcos rotation and spin
Rv2m r-vector to r-matrix
Rxp product of r-matrix and p-vector
Trxp product of transpose of r-matrix and p-vector
Pxp vector product of two p-vectors
Pmp p-vector minus p-vector
Pvstar space motion pv-vector to star catalog data
Reference:
F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).
*/
func H2fk5(rh, dh float64, drh, ddh, pxh, rvh float64,
r5, d5 *float64, dr5, dd5, px5, rv5 *float64) {
var i int
var pvh, pv5 [2][3]float64
var r5h [3][3]float64
var s5h, sh, wxp, vv [3]float64
/* Hipparcos barycentric position/velocity pv-vector (normalized). */
Starpv(rh, dh, drh, ddh, pxh, rvh, &pvh)
/* FK5 to Hipparcos orientation matrix and spin vector. */
Fk5hip(&r5h, &s5h)
/* Make spin units per day instead of per year. */
for i = 0; i < 3; i++ {
s5h[i] /= 365.25
}
/* Orient the spin into the Hipparcos system. */
Rxp(r5h, s5h, &sh)
/* De-orient the Hipparcos position into the FK5 system. */
Trxp(r5h, pvh[0], &pv5[0])
/* Apply spin to the position giving an extra space motion component. */
Pxp(pvh[0], sh, &wxp)
/* Subtract this component from the Hipparcos space motion. */
Pmp(pvh[1], wxp, &vv)
/* De-orient the Hipparcos space motion into the FK5 system. */
Trxp(r5h, vv, &pv5[1])
/* FK5 pv-vector to spherical. */
Pvstar(pv5, r5, d5, dr5, dd5, px5, rv5)
}
/*
Hfk5z Hipparcos to FK5 assuming zero Hipparcos proper motion
Transform a Hipparcos star position into FK5 J2000.0, assuming
zero Hipparcos proper motion.
Given:
rh float64 Hipparcos RA (radians)
dh float64 Hipparcos Dec (radians)
date1,date2 float64 TDB date (Note 1)
Returned (all FK5, equinox J2000.0, date date1+date2):
r5 float64 RA (radians)
d5 float64 Dec (radians)
dr5 float64 FK5 RA proper motion (rad/year, Note 4)
dd5 float64 Dec proper motion (rad/year, Note 4)
Notes:
1. The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
3. The FK5 to Hipparcos transformation is modeled as a pure rotation
and spin; zonal errors in the FK5 catalogue are not taken into
account.
4. It was the intention that Hipparcos should be a close
approximation to an inertial frame, so that distant objects have
zero proper motion; such objects have (in general) non-zero
proper motion in FK5, and this function returns those fictitious
proper motions.
5. The position returned by this function is in the FK5 J2000.0
reference system but at date date1+date2.
6. See also Fk52h, H2fk5, Fk5hz.
Called:
S2c spherical coordinates to unit vector
Fk5hip FK5 to Hipparcos rotation and spin
Rxp product of r-matrix and p-vector
Sxp multiply p-vector by scalar
Rxr product of two r-matrices
Trxp product of transpose of r-matrix and p-vector
Pxp vector product of two p-vectors
Pv2s pv-vector to spherical
Anp normalize angle into range 0 to 2pi
Reference:
F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
*/
func Hfk5z(rh, dh float64, date1, date2 float64, r5, d5, dr5, dd5 *float64) {
var t, w, r, v float64
var ph, s5h, sh, vst, vv [3]float64
var pv5e [2][3]float64
var r5h, rst, r5ht [3][3]float64
/* Time interval from fundamental epoch J2000.0 to given date (JY). */
t = ((date1 - DJ00) + date2) / DJY
/* Hipparcos barycentric position vector (normalized). */
S2c(rh, dh, &ph)
/* FK5 to Hipparcos orientation matrix and spin vector. */
Fk5hip(&r5h, &s5h)
/* Rotate the spin into the Hipparcos system. */
Rxp(r5h, s5h, &sh)
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
Sxp(t, s5h, &vst)
/* Express the accumulated spin as a rotation matrix. */
Rv2m(vst, &rst)
/* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
Rxr(r5h, rst, &r5ht)
/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
Trxp(r5ht, ph, &pv5e[0])
/* Apply spin to the position giving a space motion. */
Pxp(sh, ph, &vv)
/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
Trxp(r5ht, vv, &pv5e[1])
/* FK5 position/velocity pv-vector to spherical. */
Pv2s(pv5e, &w, d5, &r, dr5, dd5, &v)
*r5 = Anp(w)
}
gofa-1.19.1/coord.go 0000664 0000000 0000000 00000113122 14535740236 0014165 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Coord
// Galactic Coordinates
/*
Icrs2g Transformation from ICRS to Galactic Coordinates.
Given:
dr float64 ICRS right ascension (radians)
dd float64 ICRS declination (radians)
Returned:
dl float64 galactic longitude (radians)
db float64 galactic latitude (radians)
Notes:
1) The IAU 1958 system of Galactic coordinates was defined with
respect to the now obsolete reference system FK4 B1950.0. When
interpreting the system in a modern context, several factors have
to be taken into account:
. The inclusion in FK4 positions of the E-terms of aberration.
. The distortion of the FK4 proper motion system by differential
Galactic rotation.
. The use of the B1950.0 equinox rather than the now-standard
J2000.0.
. The frame bias between ICRS and the J2000.0 mean place system.
The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
matrix that transforms directly between ICRS and Galactic
coordinates with the above factors taken into account. The
matrix is derived from three angles, namely the ICRS coordinates
of the Galactic pole and the longitude of the ascending node of
the galactic equator on the ICRS equator. They are given in
degrees to five decimal places and for canonical purposes are
regarded as exact. In the Hipparcos Catalogue the matrix
elements are given to 10 decimal places (about 20 microarcsec).
In the present SOFA function the matrix elements have been
recomputed from the canonical three angles and are given to 30
decimal places.
2) The inverse transformation is performed by the function G2icrs.
Called:
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
S2c spherical coordinates to unit vector
Rxp product of r-matrix and p-vector
C2s p-vector to spherical
Reference:
Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
catalogues. Astrometric and photometric star catalogues
derived from the ESA Hipparcos Space Astrometry Mission. ESA
Publications Division, Noordwijk, Netherlands.
*/
func Icrs2g(dr, dd float64, dl, db *float64) {
var v1, v2 [3]float64
/*
L2,B2 system of galactic coordinates in the form presented in the
Hipparcos Catalogue. In degrees:
P = 192.85948 right ascension of the Galactic north pole in ICRS
Q = 27.12825 declination of the Galactic north pole in ICRS
R = 32.93192 Galactic longitude of the ascending node of
the Galactic equator on the ICRS equator
ICRS to galactic rotation matrix, obtained by computing
R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
*/
r := [3][3]float64{
{-0.054875560416215368492398900454, -0.873437090234885048760383168409, -0.483835015548713226831774175116},
{+0.494109427875583673525222371358, -0.444829629960011178146614061616, +0.746982244497218890527388004556},
{-0.867666149019004701181616534570, -0.198076373431201528180486091412, +0.455983776175066922272100478348},
}
/* Spherical to Cartesian. */
S2c(dr, dd, &v1)
/* ICRS to Galactic. */
Rxp(r, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, dl, db)
/* Express in conventional ranges. */
*dl = Anp(*dl)
*db = Anpm(*db)
}
/*
G2icrsTransformation from Galactic Coordinates to ICRS.
Given:
dl float64 galactic longitude (radians)
db float64 galactic latitude (radians)
Returned:
dr float64 ICRS right ascension (radians)
dd float64 ICRS declination (radians)
Notes:
1) The IAU 1958 system of Galactic coordinates was defined with
respect to the now obsolete reference system FK4 B1950.0. When
interpreting the system in a modern context, several factors have
to be taken into account:
. The inclusion in FK4 positions of the E-terms of aberration.
. The distortion of the FK4 proper motion system by differential
Galactic rotation.
. The use of the B1950.0 equinox rather than the now-standard
J2000.0.
. The frame bias between ICRS and the J2000.0 mean place system.
The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
matrix that transforms directly between ICRS and Galactic
coordinates with the above factors taken into account. The
matrix is derived from three angles, namely the ICRS coordinates
of the Galactic pole and the longitude of the ascending node of
the galactic equator on the ICRS equator. They are given in
degrees to five decimal places and for canonical purposes are
regarded as exact. In the Hipparcos Catalogue the matrix
elements are given to 10 decimal places (about 20 microarcsec).
In the present SOFA function the matrix elements have been
recomputed from the canonical three angles and are given to 30
decimal places.
2) The inverse transformation is performed by the function Icrs2g.
Called:
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
S2c spherical coordinates to unit vector
Trxp product of transpose of r-matrix and p-vector
C2s p-vector to spherical
Reference:
Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
catalogues. Astrometric and photometric star catalogues
derived from the ESA Hipparcos Space Astrometry Mission. ESA
Publications Division, Noordwijk, Netherlands.
*/
func G2icrs(dl, db float64, dr, dd *float64) {
var v1, v2 [3]float64
/*
L2,B2 system of galactic coordinates in the form presented in the
Hipparcos Catalogue. In degrees:
P = 192.85948 right ascension of the Galactic north pole in ICRS
Q = 27.12825 declination of the Galactic north pole in ICRS
R = 32.93192 Galactic longitude of the ascending node of
the Galactic equator on the ICRS equator
ICRS to galactic rotation matrix, obtained by computing
R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
*/
r := [3][3]float64{
{-0.054875560416215368492398900454, -0.873437090234885048760383168409, -0.483835015548713226831774175116},
{+0.494109427875583673525222371358, -0.444829629960011178146614061616, +0.746982244497218890527388004556},
{-0.867666149019004701181616534570, -0.198076373431201528180486091412, +0.455983776175066922272100478348},
}
/* Spherical to Cartesian. */
S2c(dl, db, &v1)
/* Galactic to ICRS. */
Trxp(r, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, dr, dd)
/* Express in conventional ranges. */
*dr = Anp(*dr)
*dd = Anpm(*dd)
}
/*
Ae2hd Horizon to equatorial coordinates, transform azimuth and altitude to hour angle and declination.
Given:
az float64 azimuth
el float64 altitude (informally, elevation)
phi float64 site latitude
Returned:
ha float64 hour angle (local)
dec float64 declination
Notes:
1) All the arguments are angles in radians.
2) The sign convention for azimuth is north zero, east +pi/2.
3) HA is returned in the range +/-pi. Declination is returned in
the range +/-pi/2.
4) The latitude phi is pi/2 minus the angle between the Earth's
rotation axis and the adopted zenith. In many applications it
will be sufficient to use the published geodetic latitude of the
site. In very precise (sub-arcsecond) applications, phi can be
corrected for polar motion.
5) The azimuth az must be with respect to the rotational north pole,
as opposed to the ITRS pole, and an azimuth with respect to north
on a map of the Earth's surface will need to be adjusted for
polar motion if sub-arcsecond accuracy is required.
6) Should the user wish to work with respect to the astronomical
zenith rather than the geodetic zenith, phi will need to be
adjusted for deflection of the vertical (often tens of
arcseconds), and the zero point of ha will also be affected.
7) The transformation is the same as Ve = Ry(phi-pi/2)*Rz(pi)*Vh,
where Ve and Vh are lefthanded unit vectors in the (ha,dec) and
(az,el) systems respectively and Rz and Ry are rotations about
first the z-axis and then the y-axis. (n.b. Rz(pi) simply
reverses the signs of the x and y components.) For efficiency,
the algorithm is written out rather than calling other utility
functions. For applications that require even greater
efficiency, additional savings are possible if constant terms
such as functions of latitude are computed once and for all.
8) Again for efficiency, no range checking of arguments is carried
out.
*/
func Ae2hd(az, el, phi float64, ha, dec *float64) {
var sa, ca, se, ce, sp, cp, x, y, z, r float64
/* Useful trig functions. */
sa = sin(az)
ca = cos(az)
se = sin(el)
ce = cos(el)
sp = sin(phi)
cp = cos(phi)
/* HA,Dec unit vector. */
x = -ca*ce*sp + se*cp
y = -sa * ce
z = ca*ce*cp + se*sp
/* To spherical. */
r = sqrt(x*x + y*y)
if r != 0.0 {
*ha = atan2(y, x)
} else {
*ha = 0.0
}
*dec = atan2(z, r)
}
/*
Hd2ae Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude.
Given:
ha float64 hour angle (local)
dec float64 declination
phi float64 site latitude
Returned:
az float64 azimuth
el float64 altitude (informally, elevation)
Notes:
1) All the arguments are angles in radians.
2) Azimuth is returned in the range 0-2pi; north is zero, and east
is +pi/2. Altitude is returned in the range +/- pi/2.
3) The latitude phi is pi/2 minus the angle between the Earth's
rotation axis and the adopted zenith. In many applications it
will be sufficient to use the published geodetic latitude of the
site. In very precise (sub-arcsecond) applications, phi can be
corrected for polar motion.
4) The returned azimuth az is with respect to the rotational north
pole, as opposed to the ITRS pole, and for sub-arcsecond
accuracy will need to be adjusted for polar motion if it is to
be with respect to north on a map of the Earth's surface.
5) Should the user wish to work with respect to the astronomical
zenith rather than the geodetic zenith, phi will need to be
adjusted for deflection of the vertical (often tens of
arcseconds), and the zero point of the hour angle ha will also
be affected.
6) The transformation is the same as Vh = Rz(pi)*Ry(pi/2-phi)*Ve,
where Vh and Ve are lefthanded unit vectors in the (az,el) and
(ha,dec) systems respectively and Ry and Rz are rotations about
first the y-axis and then the z-axis. (n.b. Rz(pi) simply
reverses the signs of the x and y components.) For efficiency,
the algorithm is written out rather than calling other utility
functions. For applications that require even greater
efficiency, additional savings are possible if constant terms
such as functions of latitude are computed once and for all.
7) Again for efficiency, no range checking of arguments is carried
out.
*/
func Hd2ae(ha, dec, phi float64, az, el *float64) {
var sh, ch, sd, cd, sp, cp, x, y, z, r, a float64
/* Useful trig functions. */
sh = sin(ha)
ch = cos(ha)
sd = sin(dec)
cd = cos(dec)
sp = sin(phi)
cp = cos(phi)
/* Az,Alt unit vector. */
x = -ch*cd*sp + sd*cp
y = -sh * cd
z = ch*cd*cp + sd*sp
/* To spherical. */
r = sqrt(x*x + y*y)
if r != 0.0 {
a = atan2(y, x)
} else {
a = 0.0
}
if a < 0.0 {
*az = a + D2PI
} else {
*az = a
}
*el = atan2(z, r)
}
/*
Hd2pa Parallactic angle for a given hour angle and declination.
Given:
ha float64 hour angle
dec float64 declination
phi float64 site latitude
Returned (function value):
float64 parallactic angle
Notes:
1) All the arguments are angles in radians.
2) The parallactic angle at a point in the sky is the position
angle of the vertical, i.e. the angle between the directions to
the north celestial pole and to the zenith respectively.
3) The result is returned in the range -pi to +pi.
4) At the pole itself a zero result is returned.
5) The latitude phi is pi/2 minus the angle between the Earth's
rotation axis and the adopted zenith. In many applications it
will be sufficient to use the published geodetic latitude of the
site. In very precise (sub-arcsecond) applications, phi can be
corrected for polar motion.
6) Should the user wish to work with respect to the astronomical
zenith rather than the geodetic zenith, phi will need to be
adjusted for deflection of the vertical (often tens of
arcseconds), and the zero point of the hour angle ha will also
be affected.
Reference:
Smart, W.M., "Spherical Astronomy", Cambridge University Press,
6th edition (Green, 1977), p49.
*/
func Hd2pa(ha, dec, phi float64) float64 {
var cp, cqsz, sqsz float64
cp = cos(phi)
sqsz = cp * sin(ha)
cqsz = sin(phi)*cos(dec) - cp*sin(dec)*cos(ha)
if sqsz != 0.0 || cqsz != 0.0 {
return atan2(sqsz, cqsz)
}
return 0.0
}
/*
Ecm06 ICRS equatorial to ecliptic rotation matrix, IAU 2006.
Given:
date1,date2 float64 TT as a 2-part Julian date (Note 1)
Returned:
rm [3][3]float64 ICRS to ecliptic rotation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix is in the sense
E_ep = rm x P_ICRS,
where P_ICRS is a vector with respect to ICRS right ascension
and declination axes and E_ep is the same vector with respect to
the (inertial) ecliptic and equinox of date.
3) P_ICRS is a free vector, merely a direction, typically of unit
magnitude, and not bound to any particular spatial origin, such
as the Earth, Sun or SSB. No assumptions are made about whether
it represents starlight and embodies astrometric effects such as
parallax or aberration. The transformation is approximately that
between mean J2000.0 right ascension and declination and ecliptic
longitude and latitude, with only frame bias (always less than
25 mas) to disturb this classical picture.
Called:
Obl06 mean obliquity, IAU 2006
Pmat06 PB matrix, IAU 2006
Ir initialize r-matrix to identity
Rx rotate around X-axis
Rxr product of two r-matrices
*/
func Ecm06(date1, date2 float64, rm *[3][3]float64) {
var ob float64
var bp, e [3][3]float64
/* Obliquity, IAU 2006. */
ob = Obl06(date1, date2)
/* Precession-bias matrix, IAU 2006. */
Pmat06(date1, date2, &bp)
/* Equatorial of date to ecliptic matrix. */
Ir(&e)
Rx(ob, &e)
/* ICRS to ecliptic coordinates rotation matrix, IAU 2006. */
Rxr(e, bp, rm)
}
/*
Eqec06 Transformation from ICRS equatorial coordinates to ecliptic coordinates
(mean equinox and ecliptic of date) using IAU 2006 precession model.
Given:
date1,date2 float64 TT as a 2-part Julian date (Note 1)
dr,dd float64 ICRS right ascension and declination (radians)
Returned:
dl,db float64 ecliptic longitude and latitude (radians)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) No assumptions are made about whether the coordinates represent
starlight and embody astrometric effects such as parallax or
aberration.
3) The transformation is approximately that from mean J2000.0 right
ascension and declination to ecliptic longitude and latitude
(mean equinox and ecliptic of date), with only frame bias (always
less than 25 mas) to disturb this classical picture.
Called:
S2c spherical coordinates to unit vector
Ecm06 J2000.0 to ecliptic rotation matrix, IAU 2006
Rxp product of r-matrix and p-vector
C2s unit vector to spherical coordinates
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
*/
func Eqec06(date1, date2 float64, dr, dd float64, dl, db *float64) {
var rm [3][3]float64
var v1, v2 [3]float64
var a, b float64
/* Spherical to Cartesian. */
S2c(dr, dd, &v1)
/* Rotation matrix, ICRS equatorial to ecliptic. */
Ecm06(date1, date2, &rm)
/* The transformation from ICRS to ecliptic. */
Rxp(rm, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, &a, &b)
/* Express in conventional ranges. */
*dl = Anp(a)
*db = Anpm(b)
}
/*
Eceq06 Transformation from ecliptic coordinates (mean equinox and ecliptic
of date) to ICRS RA,Dec, using the IAU 2006 precession model.
Given:
date1,date2 float64 TT as a 2-part Julian date (Note 1)
dl,db float64 ecliptic longitude and latitude (radians)
Returned:
dr,dd float64 ICRS right ascension and declination (radians)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) No assumptions are made about whether the coordinates represent
starlight and embody astrometric effects such as parallax or
aberration.
3) The transformation is approximately that from ecliptic longitude
and latitude (mean equinox and ecliptic of date) to mean J2000.0
right ascension and declination, with only frame bias (always
less than 25 mas) to disturb this classical picture.
Called:
S2c spherical coordinates to unit vector
Ecm06 J2000.0 to ecliptic rotation matrix, IAU 2006
Trxp product of transpose of r-matrix and p-vector
C2s unit vector to spherical coordinates
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
*/
func Eceq06(date1, date2 float64, dl, db float64, dr, dd *float64) {
var rm [3][3]float64
var v1, v2 [3]float64
var a, b float64
/* Spherical to Cartesian. */
S2c(dl, db, &v1)
/* Rotation matrix, ICRS equatorial to ecliptic. */
Ecm06(date1, date2, &rm)
/* The transformation from ecliptic to ICRS. */
Trxp(rm, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, &a, &b)
/* Express in conventional ranges. */
*dr = Anp(a)
*dd = Anpm(b)
}
/*
Ltecm ICRS equatorial to ecliptic rotation matrix, long-term.
Given:
epj float64 Julian epoch (TT)
Returned:
rm [3][3]float64 ICRS to ecliptic rotation matrix
Notes:
1) The matrix is in the sense
E_ep = rm x P_ICRS,
where P_ICRS is a vector with respect to ICRS right ascension
and declination axes and E_ep is the same vector with respect to
the (inertial) ecliptic and equinox of epoch epj.
2) P_ICRS is a free vector, merely a direction, typically of unit
magnitude, and not bound to any particular spatial origin, such
as the Earth, Sun or SSB. No assumptions are made about whether
it represents starlight and embodies astrometric effects such as
parallax or aberration. The transformation is approximately that
between mean J2000.0 right ascension and declination and ecliptic
longitude and latitude, with only frame bias (always less than
25 mas) to disturb this classical picture.
3) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
Called:
Ltpequ equator pole, long term
Ltpecl ecliptic pole, long term
Pxp vector product
Pn normalize vector
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Ltecm(epj float64, rm *[3][3]float64) {
/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
dx := -0.016617 * DAS2R
de := -0.0068192 * DAS2R
dr := -0.0146 * DAS2R
var p, z, w, x, y [3]float64
var s float64
/* Equator pole. */
Ltpequ(epj, &p)
/* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */
Ltpecl(epj, &z)
/* Equinox (top row of matrix). */
Pxp(p, z, &w)
Pn(w, &s, &x)
/* Middle row of matrix. */
Pxp(z, x, &y)
/* Combine with frame bias. */
rm[0][0] = x[0] - x[1]*dr + x[2]*dx
rm[0][1] = x[0]*dr + x[1] + x[2]*de
rm[0][2] = -x[0]*dx - x[1]*de + x[2]
rm[1][0] = y[0] - y[1]*dr + y[2]*dx
rm[1][1] = y[0]*dr + y[1] + y[2]*de
rm[1][2] = -y[0]*dx - y[1]*de + y[2]
rm[2][0] = z[0] - z[1]*dr + z[2]*dx
rm[2][1] = z[0]*dr + z[1] + z[2]*de
rm[2][2] = -z[0]*dx - z[1]*de + z[2]
}
/*
Lteqec Transformation from ICRS equatorial coordinates to ecliptic coordinates
(mean equinox and ecliptic of date) using a long-term precession model.
Given:
epj float64 Julian epoch (TT)
dr,dd float64 ICRS right ascension and declination (radians)
Returned:
dl,db float64 ecliptic longitude and latitude (radians)
Notes:
1) No assumptions are made about whether the coordinates represent
starlight and embody astrometric effects such as parallax or
aberration.
2) The transformation is approximately that from mean J2000.0 right
ascension and declination to ecliptic longitude and latitude
(mean equinox and ecliptic of date), with only frame bias (always
less than 25 mas) to disturb this classical picture.
3) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
Called:
S2c spherical coordinates to unit vector
Ltecm J2000.0 to ecliptic rotation matrix, long term
Rxp product of r-matrix and p-vector
C2s unit vector to spherical coordinates
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Lteqec(epj float64, dr, dd float64, dl, db *float64) {
var rm [3][3]float64
var v1, v2 [3]float64
var a, b float64
/* Spherical to Cartesian. */
S2c(dr, dd, &v1)
/* Rotation matrix, ICRS equatorial to ecliptic. */
Ltecm(epj, &rm)
/* The transformation from ICRS to ecliptic. */
Rxp(rm, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, &a, &b)
/* Express in conventional ranges. */
*dl = Anp(a)
*db = Anpm(b)
}
/*
Lteceq Transformation from ecliptic coordinates (mean equinox and ecliptic
of date) to ICRS RA,Dec, using a long-term precession model.
Given:
epj float64 Julian epoch (TT)
dl,db float64 ecliptic longitude and latitude (radians)
Returned:
dr,dd float64 ICRS right ascension and declination (radians)
Notes:
1) No assumptions are made about whether the coordinates represent
starlight and embody astrometric effects such as parallax or
aberration.
2) The transformation is approximately that from ecliptic longitude
and latitude (mean equinox and ecliptic of date) to mean J2000.0
right ascension and declination, with only frame bias (always
less than 25 mas) to disturb this classical picture.
3) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
Called:
S2c spherical coordinates to unit vector
Ltecm J2000.0 to ecliptic rotation matrix, long term
Trxp product of transpose of r-matrix and p-vector
C2s unit vector to spherical coordinates
Anp normalize angle into range 0 to 2pi
Anpm normalize angle into range +/- pi
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Lteceq(epj float64, dl, db float64, dr, dd *float64) {
var rm [3][3]float64
var v1, v2 [3]float64
var a, b float64
/* Spherical to Cartesian. */
S2c(dl, db, &v1)
/* Rotation matrix, ICRS equatorial to ecliptic. */
Ltecm(epj, &rm)
/* The transformation from ecliptic to ICRS. */
Trxp(rm, v1, &v2)
/* Cartesian to spherical. */
C2s(v2, &a, &b)
/* Express in conventional ranges. */
*dr = Anp(a)
*dd = Anpm(b)
}
/*
Eform a,f for a nominated Earth reference ellipsoid
Given:
n int ellipsoid identifier (Note 1)
Returned:
a float64 equatorial radius (meters, Note 2)
f float64 flattening (Note 2)
Returned (function value):
int status: 0 = OK
-1 = illegal identifier (Note 3)
Notes:
1) The identifier n is a number that specifies the choice of
reference ellipsoid. The following are supported:
n ellipsoid
1 WGS84
2 GRS80
3 WGS72
The n value has no significance outside the SOFA software. For
convenience, symbols WGS84 etc. are defined in sofam.h.
2) The ellipsoid parameters are returned in the form of equatorial
radius in meters (a) and flattening (f). The latter is a number
around 0.00335, i.e. around 1/298.
3) For the case where an unsupported n value is supplied, zero a and
f are returned, as well as error status.
References:
Department of Defense World Geodetic System 1984, National
Imagery and Mapping Agency Technical Report 8350.2, Third
Edition, p3-2.
Moritz, H., Bull. Geodesique 66-2, 187 (1992).
The Department of Defense World Geodetic System 1972, World
Geodetic System Committee, May 1974.
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
p220.
*/
func Eform(n int, a, f *float64) int {
/* Look up a and f for the specified reference ellipsoid. */
switch n {
case WGS84:
*a = 6378137.0
*f = 1.0 / 298.257223563
break
case GRS80:
*a = 6378137.0
*f = 1.0 / 298.257222101
break
case WGS72:
*a = 6378135.0
*f = 1.0 / 298.26
break
default:
/* Invalid identifier. */
*a = 0.0
*f = 0.0
return -1
}
/* OK status. */
return 0
}
/*
Gc2gd Transform geocentric coordinates to geodetic using the specified
reference ellipsoid.
Given:
n int ellipsoid identifier (Note 1)
xyz [3]float64 geocentric vector (Note 2)
Returned:
elong float64 longitude (radians, east +ve, Note 3)
phi float64 latitude (geodetic, radians, Note 3)
height float64 height above ellipsoid (geodetic, Notes 2,3)
Returned (function value):
int status: 0 = OK
-1 = illegal identifier (Note 3)
-2 = internal error (Note 3)
Notes:
1) The identifier n is a number that specifies the choice of
reference ellipsoid. The following are supported:
n ellipsoid
1 WGS84
2 GRS80
3 WGS72
The n value has no significance outside the SOFA software. For
convenience, symbols WGS84 etc. are defined in sofam.h.
2) The geocentric vector (xyz, given) and height (height, returned)
are in meters.
3) An error status -1 means that the identifier n is illegal. An
error status -2 is theoretically impossible. In all error cases,
all three results are set to -1e9.
4) The inverse transformation is performed in the function iauGd2gc.
Called:
Eform Earth reference ellipsoids
Gc2gde geocentric to geodetic transformation, general
*/
func Gc2gd(n int, xyz [3]float64, elong, phi, height *float64) int {
var j int
var a, f float64
/* Obtain reference ellipsoid parameters. */
j = Eform(n, &a, &f)
/* If OK, transform x,y,z to longitude, geodetic latitude, height. */
if j == 0 {
j = Gc2gde(a, f, xyz, elong, phi, height)
if j < 0 {
j = -2
}
}
/* Deal with any errors. */
if j < 0 {
*elong = -1e9
*phi = -1e9
*height = -1e9
}
/* Return the status. */
return j
}
/*
Gc2gde Transform geocentric coordinates to geodetic for a reference
ellipsoid of specified form.
Given:
a float64 equatorial radius (Notes 2,4)
f float64 flattening (Note 3)
xyz [3]float64 geocentric vector (Note 4)
Returned:
elong float64 longitude (radians, east +ve)
phi float64 latitude (geodetic, radians)
height float64 height above ellipsoid (geodetic, Note 4)
Returned (function value):
int status: 0 = OK
-1 = illegal f
-2 = illegal a
Notes:
1) This function is based on the GCONV2H Fortran subroutine by
Toshio Fukushima (see reference).
2) The equatorial radius, a, can be in any units, but meters is
the conventional choice.
3) The flattening, f, is (for the Earth) a value around 0.00335,
i.e. around 1/298.
4) The equatorial radius, a, and the geocentric vector, xyz,
must be given in the same units, and determine the units of
the returned height, height.
5) If an error occurs (status < 0), elong, phi and height are
unchanged.
6) The inverse transformation is performed in the function
iauGd2gce.
7) The transformation for a standard ellipsoid (such as WGS84) can
more conveniently be performed by calling iauGc2gd, which uses a
numerical code to identify the required A and F values.
Reference:
Fukushima, T., "Transformation from Cartesian to geodetic
coordinates accelerated by Halley's method", J.Geodesy (2006)
79: 689-693
*/
func Gc2gde(a, f float64, xyz [3]float64, elong, phi, height *float64) int {
var aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
cc, s12, cc2 float64
/* ------------- */
/* Preliminaries */
/* ------------- */
/* Validate ellipsoid parameters. */
if f < 0.0 || f >= 1.0 {
return -1
}
if a <= 0.0 {
return -2
}
/* Functions of ellipsoid parameters (with further validation of f). */
aeps2 = a * a * 1e-32
e2 = (2.0 - f) * f
e4t = e2 * e2 * 1.5
ec2 = 1.0 - e2
if ec2 <= 0.0 {
return -1
}
ec = sqrt(ec2)
b = a * ec
/* Cartesian components. */
x = xyz[0]
y = xyz[1]
z = xyz[2]
/* Distance from polar axis squared. */
p2 = x*x + y*y
/* Longitude. */
// *elong = p2 > 0.0 ? atan2(y, x) : 0.0;
if p2 > 0.0 {
*elong = atan2(y, x)
} else {
*elong = 0.0
}
/* Unsigned z-coordinate. */
absz = fabs(z)
/* Proceed unless polar case. */
if p2 > aeps2 {
/* Distance from polar axis. */
p = sqrt(p2)
/* Normalization. */
s0 = absz / a
pn = p / a
zc = ec * s0
/* Prepare Newton correction factors. */
c0 = ec * pn
c02 = c0 * c0
c03 = c02 * c0
s02 = s0 * s0
s03 = s02 * s0
a02 = c02 + s02
a0 = sqrt(a02)
a03 = a02 * a0
d0 = zc*a03 + e2*s03
f0 = pn*a03 - e2*c03
/* Prepare Halley correction factor. */
b0 = e4t * s02 * c02 * pn * (a0 - ec)
s1 = d0*f0 - b0*s0
cc = ec * (f0*f0 - b0*c0)
/* Evaluate latitude and height. */
*phi = atan(s1 / cc)
s12 = s1 * s1
cc2 = cc * cc
*height = (p*cc + absz*s1 - a*sqrt(ec2*s12+cc2)) / sqrt(s12+cc2)
} else {
/* Exception: pole. */
*phi = DPI / 2.0
*height = absz - b
}
/* Restore sign of latitude. */
if z < 0 {
*phi = -*phi
}
/* OK status. */
return 0
}
/*
Gd2gc Transform geodetic coordinates to geocentric using the specified
reference ellipsoid.
Given:
n int ellipsoid identifier (Note 1)
elong float64 longitude (radians, east +ve)
phi float64 latitude (geodetic, radians, Note 3)
height float64 height above ellipsoid (geodetic, Notes 2,3)
Returned:
xyz [3]float64 geocentric vector (Note 2)
Returned (function value):
int status: 0 = OK
-1 = illegal identifier (Note 3)
-2 = illegal case (Note 3)
Notes:
1) The identifier n is a number that specifies the choice of
reference ellipsoid. The following are supported:
n ellipsoid
1 WGS84
2 GRS80
3 WGS72
The n value has no significance outside the SOFA software. For
convenience, symbols WGS84 etc. are defined in sofam.h.
2) The height (height, given) and the geocentric vector (xyz,
returned) are in meters.
3) No validation is performed on the arguments elong, phi and
height. An error status -1 means that the identifier n is
illegal. An error status -2 protects against cases that would
lead to arithmetic exceptions. In all error cases, xyz is set
to zeros.
4) The inverse transformation is performed in the function iauGc2gd.
Called:
Eform Earth reference ellipsoids
Gd2gce geodetic to geocentric transformation, general
Zp zero p-vector
*/
func Gd2gc(n int, elong, phi, height float64, xyz *[3]float64) int {
var j int
var a, f float64
/* Obtain reference ellipsoid parameters. */
j = Eform(n, &a, &f)
/* If OK, transform longitude, geodetic latitude, height to x,y,z. */
if j == 0 {
j = Gd2gce(a, f, elong, phi, height, xyz)
if j != 0 {
j = -2
}
}
/* Deal with any errors. */
if j != 0 {
Zp(xyz)
}
/* Return the status. */
return j
}
/*
Gd2gce Transform geodetic coordinates to geocentric for a reference
ellipsoid of specified form.
Given:
a float64 equatorial radius (Notes 1,4)
f float64 flattening (Notes 2,4)
elong float64 longitude (radians, east +ve)
phi float64 latitude (geodetic, radians, Note 4)
height float64 height above ellipsoid (geodetic, Notes 3,4)
Returned:
xyz [3]float64 geocentric vector (Note 3)
Returned (function value):
int status: 0 = OK
-1 = illegal case (Note 4)
Notes:
1) The equatorial radius, a, can be in any units, but meters is
the conventional choice.
2) The flattening, f, is (for the Earth) a value around 0.00335,
i.e. around 1/298.
3) The equatorial radius, a, and the height, height, must be
given in the same units, and determine the units of the
returned geocentric vector, xyz.
4) No validation is performed on individual arguments. The error
status -1 protects against (unrealistic) cases that would lead
to arithmetic exceptions. If an error occurs, xyz is unchanged.
5) The inverse transformation is performed in the function
iauGc2gde.
6) The transformation for a standard ellipsoid (such as WGS84) can
more conveniently be performed by calling iauGd2gc, which uses a
numerical code to identify the required a and f values.
References:
Green, R.M., Spherical Astronomy, Cambridge University Press,
(1985) Section 4.5, p96.
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 4.22, p202.
*/
func Gd2gce(a, f float64, elong, phi, height float64, xyz *[3]float64) int {
var sp, cp, w, d, ac, as, r float64
/* Functions of geodetic latitude. */
sp = sin(phi)
cp = cos(phi)
w = 1.0 - f
w = w * w
d = cp*cp + w*sp*sp
if d <= 0.0 {
return -1
}
ac = a / sqrt(d)
as = w * ac
/* Geocentric vector. */
r = (ac + height) * cp
xyz[0] = r * cos(elong)
xyz[1] = r * sin(elong)
xyz[2] = (as + height) * sp
/* Success. */
return 0
}
gofa-1.19.1/ephem.go 0000664 0000000 0000000 00000507075 14535740236 0014173 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Ephemeride
/*
Epv00 Earth position and velocity, heliocentric and barycentric, with
respect to the Barycentric Celestial Reference System.
Given:
date1,date2 float64 TDB date (Note 1)
Returned:
pvh [2][3]float64 heliocentric Earth position/velocity
pvb [2][3]float64 barycentric Earth position/velocity
Returned (function value):
int status: 0 = OK
+1 = warning: date outside the range 1900-2100 AD
Notes:
1) The TDB date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TDB)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. However,
the accuracy of the result is more likely to be limited by the
algorithm itself than the way the date has been expressed.
n.b. TT can be used instead of TDB in most applications.
2) On return, the arrays pvh and pvb contain the following:
pvh[0][0] x }
pvh[0][1] y } heliocentric position, au
pvh[0][2] z }
pvh[1][0] xdot }
pvh[1][1] ydot } heliocentric velocity, au/d
pvh[1][2] zdot }
pvb[0][0] x }
pvb[0][1] y } barycentric position, au
pvb[0][2] z }
pvb[1][0] xdot }
pvb[1][1] ydot } barycentric velocity, au/d
pvb[1][2] zdot }
The vectors are with respect to the Barycentric Celestial
Reference System. The time unit is one day in TDB.
3) The function is a SIMPLIFIED SOLUTION from the planetary theory
VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
Fortran code supplied by P. Bretagnon (private comm., 2000).
4) Comparisons over the time span 1900-2100 with this simplified
solution and the JPL DE405 ephemeris give the following results:
RMS max
Heliocentric:
position error 3.7 11.2 km
velocity error 1.4 5.0 mm/s
Barycentric:
position error 4.6 13.4 km
velocity error 1.4 4.9 mm/s
Comparisons with the JPL DE406 ephemeris show that by 1800 and
2200 the position errors are approximately double their 1900-2100
size. By 1500 and 2500 the deterioration is a factor of 10 and
by 1000 and 3000 a factor of 60. The velocity accuracy falls off
at about half that rate.
5) It is permissible to use the same array for pvh and pvb, which
will receive the barycentric values.
*/
func Epv00(date1, date2 float64, pvh, pvb *[2][3]float64) int {
/*
Matrix elements for orienting the analytical model to DE405.
The corresponding Euler angles are:
d ' "
1st rotation - 23 26 21.4091 about the x-axis (obliquity)
2nd rotation + 0.0475 about the z-axis (RA offset)
These were obtained empirically, by comparisons with DE405 over
1900-2100.
*/
const (
am12 = 0.000000211284
am13 = -0.000000091603
am21 = -0.000000230286
am22 = 0.917482137087
am23 = -0.397776982902
am32 = 0.397776982902
am33 = 0.917482137087
)
/*
----------------------
Ephemeris Coefficients
----------------------
The ephemeris consists of harmonic terms for predicting (i) the Sun
to Earth vector and (ii) the Solar-System-barycenter to Sun vector
respectively. The coefficients are stored in arrays which, although
1-demensional, contain groups of three. Each triplet of
coefficients is the amplitude, phase and frequency for one term in
the model, and each array contains the number of terms called for by
the model.
There are eighteen such arrays, named as follows:
array model power of T component
e0x Sun-to-Earth 0 x
e0y Sun-to-Earth 0 y
e0z Sun-to-Earth 0 z
e1x Sun-to-Earth 1 x
e1y Sun-to-Earth 1 y
e1z Sun-to-Earth 1 z
e2x Sun-to-Earth 2 x
e2y Sun-to-Earth 2 y
e2z Sun-to-Earth 2 z
s0x SSB-to-Sun 0 x
s0y SSB-to-Sun 0 y
s0z SSB-to-Sun 0 z
s1x SSB-to-Sun 1 x
s1y SSB-to-Sun 1 y
s1z SSB-to-Sun 1 z
s2x SSB-to-Sun 2 x
s2y SSB-to-Sun 2 y
s2z SSB-to-Sun 2 z
*/
/* Sun-to-Earth, T^0, X */
e0x := []float64{
0.9998292878132e+00, 0.1753485171504e+01, 0.6283075850446e+01,
0.8352579567414e-02, 0.1710344404582e+01, 0.1256615170089e+02,
0.5611445335148e-02, 0.0000000000000e+00, 0.0000000000000e+00,
0.1046664295572e-03, 0.1667225416770e+01, 0.1884922755134e+02,
0.3110842534677e-04, 0.6687513390251e+00, 0.8399684731857e+02,
0.2552413503550e-04, 0.5830637358413e+00, 0.5296909721118e+00,
0.2137207845781e-04, 0.1092330954011e+01, 0.1577343543434e+01,
0.1680240182951e-04, 0.4955366134987e+00, 0.6279552690824e+01,
0.1679012370795e-04, 0.6153014091901e+01, 0.6286599010068e+01,
0.1445526946777e-04, 0.3472744100492e+01, 0.2352866153506e+01,
0.1091038246184e-04, 0.3689845786119e+01, 0.5223693906222e+01,
0.9344399733932e-05, 0.6073934645672e+01, 0.1203646072878e+02,
0.8993182910652e-05, 0.3175705249069e+01, 0.1021328554739e+02,
0.5665546034116e-05, 0.2152484672246e+01, 0.1059381944224e+01,
0.6844146703035e-05, 0.1306964099750e+01, 0.5753384878334e+01,
0.7346610905565e-05, 0.4354980070466e+01, 0.3981490189893e+00,
0.6815396474414e-05, 0.2218229211267e+01, 0.4705732307012e+01,
0.6112787253053e-05, 0.5384788425458e+01, 0.6812766822558e+01,
0.4518120711239e-05, 0.6087604012291e+01, 0.5884926831456e+01,
0.4521963430706e-05, 0.1279424524906e+01, 0.6256777527156e+01,
0.4497426764085e-05, 0.5369129144266e+01, 0.6309374173736e+01,
0.4062190566959e-05, 0.5436473303367e+00, 0.6681224869435e+01,
0.5412193480192e-05, 0.7867838528395e+00, 0.7755226100720e+00,
0.5469839049386e-05, 0.1461440311134e+01, 0.1414349524433e+02,
0.5205264083477e-05, 0.4432944696116e+01, 0.7860419393880e+01,
0.2149759935455e-05, 0.4502237496846e+01, 0.1150676975667e+02,
0.2279109618501e-05, 0.1239441308815e+01, 0.7058598460518e+01,
0.2259282939683e-05, 0.3272430985331e+01, 0.4694002934110e+01,
0.2558950271319e-05, 0.2265471086404e+01, 0.1216800268190e+02,
0.2561581447555e-05, 0.1454740653245e+01, 0.7099330490126e+00,
0.1781441115440e-05, 0.2962068630206e+01, 0.7962980379786e+00,
0.1612005874644e-05, 0.1473255041006e+01, 0.5486777812467e+01,
0.1818630667105e-05, 0.3743903293447e+00, 0.6283008715021e+01,
0.1818601377529e-05, 0.6274174354554e+01, 0.6283142985870e+01,
0.1554475925257e-05, 0.1624110906816e+01, 0.2513230340178e+02,
0.2090948029241e-05, 0.5852052276256e+01, 0.1179062909082e+02,
0.2000176345460e-05, 0.4072093298513e+01, 0.1778984560711e+02,
0.1289535917759e-05, 0.5217019331069e+01, 0.7079373888424e+01,
0.1281135307881e-05, 0.4802054538934e+01, 0.3738761453707e+01,
0.1518229005692e-05, 0.8691914742502e+00, 0.2132990797783e+00,
0.9450128579027e-06, 0.4601859529950e+01, 0.1097707878456e+02,
0.7781119494996e-06, 0.1844352816694e+01, 0.8827390247185e+01,
0.7733407759912e-06, 0.3582790154750e+01, 0.5507553240374e+01,
0.7350644318120e-06, 0.2695277788230e+01, 0.1589072916335e+01,
0.6535928827023e-06, 0.3651327986142e+01, 0.1176985366291e+02,
0.6324624183656e-06, 0.2241302375862e+01, 0.6262300422539e+01,
0.6298565300557e-06, 0.4407122406081e+01, 0.6303851278352e+01,
0.8587037089179e-06, 0.3024307223119e+01, 0.1672837615881e+03,
0.8299954491035e-06, 0.6192539428237e+01, 0.3340612434717e+01,
0.6311263503401e-06, 0.2014758795416e+01, 0.7113454667900e-02,
0.6005646745452e-06, 0.3399500503397e+01, 0.4136910472696e+01,
0.7917715109929e-06, 0.2493386877837e+01, 0.6069776770667e+01,
0.7556958099685e-06, 0.4159491740143e+01, 0.6496374930224e+01,
0.6773228244949e-06, 0.4034162934230e+01, 0.9437762937313e+01,
0.5370708577847e-06, 0.1562219163734e+01, 0.1194447056968e+01,
0.5710804266203e-06, 0.2662730803386e+01, 0.6282095334605e+01,
0.5709824583726e-06, 0.3985828430833e+01, 0.6284056366286e+01,
0.5143950896447e-06, 0.1308144688689e+01, 0.6290189305114e+01,
0.5088010604546e-06, 0.5352817214804e+01, 0.6275962395778e+01,
0.4960369085172e-06, 0.2644267922349e+01, 0.6127655567643e+01,
0.4803137891183e-06, 0.4008844192080e+01, 0.6438496133249e+01,
0.5731747768225e-06, 0.3794550174597e+01, 0.3154687086868e+01,
0.4735947960579e-06, 0.6107118308982e+01, 0.3128388763578e+01,
0.4808348796625e-06, 0.4771458618163e+01, 0.8018209333619e+00,
0.4115073743137e-06, 0.3327111335159e+01, 0.8429241228195e+01,
0.5230575889287e-06, 0.5305708551694e+01, 0.1336797263425e+02,
0.5133977889215e-06, 0.5784230738814e+01, 0.1235285262111e+02,
0.5065815825327e-06, 0.2052064793679e+01, 0.1185621865188e+02,
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0.7737289283765e-08, 0.3784727847451e+01, 0.7834121070590e+01,
0.9260204034710e-08, 0.2223352487601e+01, 0.2787043132925e+01,
0.7320252888486e-08, 0.1288694636874e+01, 0.6282655592598e+01,
0.7319785780946e-08, 0.5359869567774e+01, 0.6283496108294e+01,
0.7147219933778e-08, 0.5516616675856e+01, 0.1725663147538e+02,
0.7946502829878e-08, 0.2630459984567e+01, 0.1241073141809e+02,
0.9001711808932e-08, 0.2849815827227e+01, 0.6281591679874e+01,
0.8994041507257e-08, 0.3795244450750e+01, 0.6284560021018e+01,
0.8298582787358e-08, 0.5236413127363e+00, 0.1241658836951e+02,
0.8526596520710e-08, 0.4794605424426e+01, 0.1098419223922e+02,
0.8209822103197e-08, 0.1578752370328e+01, 0.1096996532989e+02,
0.6357049861094e-08, 0.5708926113761e+01, 0.1596186371003e+01,
0.7370473179049e-08, 0.3842402530241e+01, 0.4061219149443e+01,
0.7232154664726e-08, 0.3067548981535e+01, 0.1610006857377e+03,
0.6328765494903e-08, 0.1313930030069e+01, 0.1193336791622e+02,
0.8030064908595e-08, 0.3488500408886e+01, 0.8460828644453e+00,
0.6275464259232e-08, 0.1532061626198e+01, 0.8531963191132e+00,
0.7051897446325e-08, 0.3285859929993e+01, 0.5849364236221e+01,
0.6161593705428e-08, 0.1477341999464e+01, 0.5573142801433e+01,
0.7754683957278e-08, 0.1586118663096e+01, 0.8662240327241e+01,
0.5889928990701e-08, 0.1304887868803e+01, 0.1232342296471e+02,
0.5705756047075e-08, 0.4555333589350e+01, 0.1258692712880e+02,
0.5964178808332e-08, 0.3001762842062e+01, 0.5333900173445e+01,
0.6712446027467e-08, 0.4886780007595e+01, 0.1171295538178e+02,
0.5941809275464e-08, 0.4701509603824e+01, 0.9779108567966e+01,
0.5466993627395e-08, 0.4588357817278e+01, 0.1884211409667e+02,
0.6340512090980e-08, 0.1164543038893e+01, 0.5217580628120e+02,
0.6325505710045e-08, 0.3919171259645e+01, 0.1041998632314e+02,
0.6164789509685e-08, 0.2143828253542e+01, 0.6151533897323e+01,
0.5263330812430e-08, 0.6066564434241e+01, 0.1885275071096e+02,
0.5597087780221e-08, 0.2926316429472e+01, 0.4337116142245e+00,
0.5396556236817e-08, 0.3244303591505e+01, 0.6286362197481e+01,
0.5396615148223e-08, 0.3404304703662e+01, 0.6279789503410e+01,
0.7091832443341e-08, 0.8532377803192e+00, 0.4907302013889e+01,
0.6572352589782e-08, 0.4901966774419e+01, 0.1176433076753e+02,
0.5960236060795e-08, 0.1874672315797e+01, 0.1422690933580e-01,
0.5125480043511e-08, 0.3735726064334e+01, 0.1245594543367e+02,
0.5928241866410e-08, 0.4502033899935e+01, 0.6414617803568e+01,
0.5249600357424e-08, 0.4372334799878e+01, 0.1151388321134e+02,
0.6059171276087e-08, 0.2581617302908e+01, 0.6062663316000e+01,
0.5295235081662e-08, 0.2974811513158e+01, 0.3496032717521e+01,
0.5820561875933e-08, 0.1796073748244e+00, 0.2838593341516e+00,
0.4754696606440e-08, 0.1981998136973e+01, 0.3104930017775e+01,
0.6385053548955e-08, 0.2559174171605e+00, 0.6133512519065e+01,
0.6589828273941e-08, 0.2750967106776e+01, 0.4087944051283e+02,
0.5383376567189e-08, 0.6325947523578e+00, 0.2248384854122e+02,
0.5928941683538e-08, 0.1672304519067e+01, 0.1581959461667e+01,
0.4816060709794e-08, 0.3512566172575e+01, 0.9388005868221e+01,
0.6003381586512e-08, 0.5610932219189e+01, 0.5326786718777e+01,
0.5504225393105e-08, 0.4037501131256e+01, 0.6503488384892e+01,
0.5353772620129e-08, 0.6122774968240e+01, 0.1735668374386e+03,
0.5786253768544e-08, 0.5527984999515e+01, 0.1350651127443e+00,
0.5065706702002e-08, 0.9980765573624e+00, 0.1248988586463e+02,
0.5972838885276e-08, 0.6044489493203e+01, 0.2673594526851e+02,
0.5323585877961e-08, 0.3924265998147e+01, 0.4171425416666e+01,
0.5210772682858e-08, 0.6220111376901e+01, 0.2460261242967e+02,
0.4726549040535e-08, 0.3716043206862e+01, 0.7232251527446e+01,
0.6029425105059e-08, 0.8548704071116e+00, 0.3227113045244e+03,
0.4481542826513e-08, 0.1426925072829e+01, 0.5547199253223e+01,
0.5836024505068e-08, 0.7135651752625e-01, 0.7285056171570e+02,
0.4137046613272e-08, 0.5330767643283e+01, 0.1087398597200e+02,
0.5171977473924e-08, 0.4494262335353e+00, 0.1884570439172e+02,
0.5694429833732e-08, 0.2952369582215e+01, 0.9723862754494e+02,
0.4009158925298e-08, 0.3500003416535e+01, 0.6244942932314e+01,
0.4784939596873e-08, 0.6196709413181e+01, 0.2929661536378e+02,
0.3983725022610e-08, 0.5103690031897e+01, 0.4274518229222e+01,
0.3870535232462e-08, 0.3187569587401e+01, 0.6321208768577e+01,
0.5140501213951e-08, 0.1668924357457e+01, 0.1232032006293e+02,
0.3849034819355e-08, 0.4445722510309e+01, 0.1726726808967e+02,
0.4002383075060e-08, 0.5226224152423e+01, 0.7018952447668e+01,
0.3890719543549e-08, 0.4371166550274e+01, 0.1491901785440e+02,
0.4887084607881e-08, 0.5973556689693e+01, 0.1478866649112e+01,
0.3739939287592e-08, 0.2089084714600e+01, 0.6922973089781e+01,
0.5031925918209e-08, 0.4658371936827e+01, 0.1715706182245e+02,
0.4387748764954e-08, 0.4825580552819e+01, 0.2331413144044e+03,
0.4147398098865e-08, 0.3739003524998e+01, 0.1376059875786e+02,
0.3719089993586e-08, 0.1148941386536e+01, 0.6297302759782e+01,
0.3934238461056e-08, 0.1559893008343e+01, 0.7872148766781e+01,
0.3672471375622e-08, 0.5516145383612e+01, 0.6268848941110e+01,
0.3768911277583e-08, 0.6116053700563e+01, 0.4157198507331e+01,
0.4033388417295e-08, 0.5076821746017e+01, 0.1567108171867e+02,
0.3764194617832e-08, 0.8164676232075e+00, 0.3185192151914e+01,
0.4840628226284e-08, 0.1360479453671e+01, 0.1252801878276e+02,
0.4949443923785e-08, 0.2725622229926e+01, 0.1617106187867e+03,
0.4117393089971e-08, 0.6054459628492e+00, 0.5642198095270e+01,
0.3925754020428e-08, 0.8570462135210e+00, 0.2139354194808e+02,
0.3630551757923e-08, 0.3552067338279e+01, 0.6294805223347e+01,
0.3627274802357e-08, 0.3096565085313e+01, 0.6271346477544e+01,
0.3806143885093e-08, 0.6367751709777e+00, 0.1725304118033e+02,
0.4433254641565e-08, 0.4848461503937e+01, 0.7445550607224e+01,
0.3712319846576e-08, 0.1331950643655e+01, 0.4194847048887e+00,
0.3849847534783e-08, 0.4958368297746e+00, 0.9562891316684e+00,
0.3483955430165e-08, 0.2237215515707e+01, 0.1161697602389e+02,
0.3961912730982e-08, 0.3332402188575e+01, 0.2277943724828e+02,
0.3419978244481e-08, 0.5785600576016e+01, 0.1362553364512e+02,
0.3329417758177e-08, 0.9812676559709e-01, 0.1685848245639e+02,
0.4207206893193e-08, 0.9494780468236e+00, 0.2986433403208e+02,
0.3268548976410e-08, 0.1739332095686e+00, 0.5749861718712e+01,
0.3321880082685e-08, 0.1423354800666e+01, 0.6279143387820e+01,
0.4503173010852e-08, 0.2314972675293e+00, 0.1385561574497e+01,
0.4316599090954e-08, 0.1012646782616e+00, 0.4176041334900e+01,
0.3283493323850e-08, 0.5233306881265e+01, 0.6287008313071e+01,
0.3164033542343e-08, 0.4005597257511e+01, 0.2099539292909e+02,
0.4159720956725e-08, 0.5365676242020e+01, 0.5905702259363e+01,
0.3565176892217e-08, 0.4284440620612e+01, 0.3932462625300e-02,
0.3514440950221e-08, 0.4270562636575e+01, 0.7335344340001e+01,
0.3540596871909e-08, 0.5953553201060e+01, 0.1234573916645e+02,
0.2960769905118e-08, 0.1115180417718e+01, 0.2670964694522e+02,
0.2962213739684e-08, 0.3863811918186e+01, 0.6408777551755e+00,
0.3883556700251e-08, 0.1268617928302e+01, 0.6660449441528e+01,
0.2919225516346e-08, 0.4908605223265e+01, 0.1375773836557e+01,
0.3115158863370e-08, 0.3744519976885e+01, 0.3802769619140e-01,
0.4099438144212e-08, 0.4173244670532e+01, 0.4480965020977e+02,
0.2899531858964e-08, 0.5910601428850e+01, 0.2059724391010e+02,
0.3289733429855e-08, 0.2488050078239e+01, 0.1081813534213e+02,
0.3933075612875e-08, 0.1122363652883e+01, 0.3773735910827e+00,
0.3021403764467e-08, 0.4951973724904e+01, 0.2982630633589e+02,
0.2798598949757e-08, 0.5117057845513e+01, 0.1937891852345e+02,
0.3397421302707e-08, 0.6104159180476e+01, 0.6923953605621e+01,
0.3720398002179e-08, 0.1184933429829e+01, 0.3066615496545e+02,
0.3598484186267e-08, 0.3505282086105e+01, 0.6147450479709e+01,
0.3694594027310e-08, 0.2286651088141e+01, 0.2636725487657e+01,
0.2680444152969e-08, 0.1871816775482e+00, 0.6816289982179e+01,
0.3497574865641e-08, 0.3143251755431e+01, 0.6418701221183e+01,
0.3130274129494e-08, 0.2462167316018e+01, 0.1235996607578e+02,
0.3241119069551e-08, 0.4256374004686e+01, 0.1652265972112e+02,
0.2601960842061e-08, 0.4970362941425e+01, 0.1045450126711e+02,
0.2690601527504e-08, 0.2372657824898e+01, 0.3163918923335e+00,
0.2908688152664e-08, 0.4232652627721e+01, 0.2828699048865e+02,
0.3120456131875e-08, 0.3925747001137e+00, 0.2195415756911e+02,
0.3148855423384e-08, 0.3093478330445e+01, 0.1172006883645e+02,
0.3051044261017e-08, 0.5560948248212e+01, 0.6055599646783e+01,
0.2826006876660e-08, 0.5072790310072e+01, 0.5120601093667e+01,
0.3100034191711e-08, 0.4998530231096e+01, 0.1799603123222e+02,
0.2398771640101e-08, 0.2561739802176e+01, 0.6255674361143e+01,
0.2384002842728e-08, 0.4087420284111e+01, 0.6310477339748e+01,
0.2842146517568e-08, 0.2515048217955e+01, 0.5469525544182e+01,
0.2847674371340e-08, 0.5235326497443e+01, 0.1034429499989e+02,
0.2903722140764e-08, 0.1088200795797e+01, 0.6510552054109e+01,
0.3187610710605e-08, 0.4710624424816e+01, 0.1693792562116e+03,
0.3048869992813e-08, 0.2857975896445e+00, 0.8390110365991e+01,
0.2860216950984e-08, 0.2241619020815e+01, 0.2243449970715e+00,
0.2701117683113e-08, 0.6651573305272e-01, 0.6129297044991e+01,
0.2509891590152e-08, 0.1285135324585e+01, 0.1044027435778e+02,
0.2623200252223e-08, 0.2981229834530e+00, 0.6436854655901e+01,
0.2622541669202e-08, 0.6122470726189e+01, 0.9380959548977e+01,
0.2818435667099e-08, 0.4251087148947e+01, 0.5934151399930e+01,
0.2365196797465e-08, 0.3465070460790e+01, 0.2470570524223e+02,
0.2358704646143e-08, 0.5791603815350e+01, 0.8671969964381e+01,
0.2388299481390e-08, 0.4142483772941e+01, 0.7096626156709e+01,
0.1996041217224e-08, 0.2101901889496e+01, 0.1727188400790e+02,
0.2687593060336e-08, 0.1526689456959e+01, 0.7075506709219e+02,
0.2618913670810e-08, 0.2397684236095e+01, 0.6632000300961e+01,
0.2571523050364e-08, 0.5751929456787e+00, 0.6206810014183e+01,
0.2582135006946e-08, 0.5595464352926e+01, 0.4873985990671e+02,
0.2372530190361e-08, 0.5092689490655e+01, 0.1590676413561e+02,
0.2357178484712e-08, 0.4444363527851e+01, 0.3097883698531e+01,
0.2451590394723e-08, 0.3108251687661e+01, 0.6612329252343e+00,
0.2370045949608e-08, 0.2608133861079e+01, 0.3459636466239e+02,
0.2268997267358e-08, 0.3639717753384e+01, 0.2844914056730e-01,
0.1731432137906e-08, 0.1741898445707e+00, 0.2019909489111e+02,
0.1629869741622e-08, 0.3902225646724e+01, 0.3035599730800e+02,
0.2206215801974e-08, 0.4971131250731e+01, 0.6281667977667e+01,
0.2205469554680e-08, 0.1677462357110e+01, 0.6284483723224e+01,
0.2148792362509e-08, 0.4236259604006e+01, 0.1980482729015e+02,
0.1873733657847e-08, 0.5926814998687e+01, 0.2876692439167e+02,
0.2026573758959e-08, 0.4349643351962e+01, 0.2449240616245e+02,
0.1807770325110e-08, 0.5700940482701e+01, 0.2045286941806e+02,
0.1881174408581e-08, 0.6601286363430e+00, 0.2358125818164e+02,
0.1368023671690e-08, 0.2211098592752e+01, 0.2473415438279e+02,
0.1720017916280e-08, 0.4942488551129e+01, 0.1679593901136e+03,
0.1702427665131e-08, 0.1452233856386e+01, 0.3338575901272e+03,
0.1414032510054e-08, 0.5525357721439e+01, 0.1624205518357e+03,
0.1652626045364e-08, 0.4108794283624e+01, 0.8956999012000e+02,
0.1642957769686e-08, 0.7344335209984e+00, 0.5267006960365e+02,
0.1614952403624e-08, 0.3541213951363e+01, 0.3332657872986e+02,
0.1535988291188e-08, 0.4031094072151e+01, 0.3852657435933e+02,
0.1593193738177e-08, 0.4185136203609e+01, 0.2282781046519e+03,
0.1074569126382e-08, 0.1720485636868e+01, 0.8397383534231e+02,
0.1074408214509e-08, 0.2758613420318e+01, 0.8401985929482e+02,
0.9700199670465e-09, 0.4216686842097e+01, 0.7826370942180e+02,
0.1258433517061e-08, 0.2575068876639e+00, 0.3115650189215e+03,
0.1240303229539e-08, 0.4800844956756e+00, 0.1784300471910e+03,
0.9018345948127e-09, 0.3896756361552e+00, 0.5886454391678e+02,
0.1135301432805e-08, 0.3700805023550e+00, 0.7842370451713e+02,
0.9215887951370e-09, 0.4364579276638e+01, 0.1014262087719e+03,
0.1055401054147e-08, 0.2156564222111e+01, 0.5660027930059e+02,
0.1008725979831e-08, 0.5454015785234e+01, 0.4245678405627e+02,
0.7217398104321e-09, 0.1597772562175e+01, 0.2457074661053e+03,
0.6912033134447e-09, 0.5824090621461e+01, 0.1679936946371e+03,
0.6833881523549e-09, 0.3578778482835e+01, 0.6053048899753e+02,
0.4887304205142e-09, 0.3724362812423e+01, 0.9656299901946e+02,
0.5173709754788e-09, 0.5422427507933e+01, 0.2442876000072e+03,
0.4671353097145e-09, 0.2396106924439e+01, 0.1435713242844e+03,
0.5652608439480e-09, 0.2804028838685e+01, 0.8365903305582e+02,
0.5604061331253e-09, 0.1638816006247e+01, 0.8433466158131e+02,
0.4712723365400e-09, 0.8979003224474e+00, 0.3164282286739e+03,
0.4909967465112e-09, 0.3210426725516e+01, 0.4059982187939e+03,
0.4771358267658e-09, 0.5308027211629e+01, 0.1805255418145e+03,
0.3943451445989e-09, 0.2195145341074e+01, 0.2568537517081e+03,
0.3952109120244e-09, 0.5081189491586e+01, 0.2449975330562e+03,
0.3788134594789e-09, 0.4345171264441e+01, 0.1568131045107e+03,
0.3738330190479e-09, 0.2613062847997e+01, 0.3948519331910e+03,
0.3099866678136e-09, 0.2846760817689e+01, 0.1547176098872e+03,
0.2002962716768e-09, 0.4921360989412e+01, 0.2268582385539e+03,
0.2198291338754e-09, 0.1130360117454e+00, 0.1658638954901e+03,
0.1491958330784e-09, 0.4228195232278e+01, 0.2219950288015e+03,
0.1475384076173e-09, 0.3005721811604e+00, 0.3052819430710e+03,
0.1661626624624e-09, 0.7830125621203e+00, 0.2526661704812e+03,
0.9015823460025e-10, 0.3807792942715e+01, 0.4171445043968e+03}
/* Sun-to-Earth, T^0, Y */
e0y := []float64{
0.9998921098898e+00, 0.1826583913846e+00, 0.6283075850446e+01,
-0.2442700893735e-01, 0.0000000000000e+00, 0.0000000000000e+00,
0.8352929742915e-02, 0.1395277998680e+00, 0.1256615170089e+02,
0.1046697300177e-03, 0.9641423109763e-01, 0.1884922755134e+02,
0.3110841876663e-04, 0.5381140401712e+01, 0.8399684731857e+02,
0.2570269094593e-04, 0.5301016407128e+01, 0.5296909721118e+00,
0.2147389623610e-04, 0.2662510869850e+01, 0.1577343543434e+01,
0.1680344384050e-04, 0.5207904119704e+01, 0.6279552690824e+01,
0.1679117312193e-04, 0.4582187486968e+01, 0.6286599010068e+01,
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0.1629683015329e-08, 0.2331362582487e+01, 0.3035599730800e+02,
0.2206492862426e-08, 0.3400274026992e+01, 0.6281667977667e+01,
0.2205746568257e-08, 0.1066051230724e+00, 0.6284483723224e+01,
0.2026310767991e-08, 0.2779066487979e+01, 0.2449240616245e+02,
0.1762977622163e-08, 0.9951450691840e+00, 0.2045286941806e+02,
0.1368535049606e-08, 0.6402447365817e+00, 0.2473415438279e+02,
0.1720598775450e-08, 0.2303524214705e+00, 0.1679593901136e+03,
0.1702429015449e-08, 0.6164622655048e+01, 0.3338575901272e+03,
0.1414033197685e-08, 0.3954561185580e+01, 0.1624205518357e+03,
0.1573768958043e-08, 0.2028286308984e+01, 0.3144167757552e+02,
0.1650705184447e-08, 0.2304040666128e+01, 0.5267006960365e+02,
0.1651087618855e-08, 0.2538461057280e+01, 0.8956999012000e+02,
0.1616409518983e-08, 0.5111054348152e+01, 0.3332657872986e+02,
0.1537175173581e-08, 0.5601130666603e+01, 0.3852657435933e+02,
0.1593191980553e-08, 0.2614340453411e+01, 0.2282781046519e+03,
0.1499480170643e-08, 0.3624721577264e+01, 0.2823723341956e+02,
0.1493807843235e-08, 0.4214569879008e+01, 0.2876692439167e+02,
0.1074571199328e-08, 0.1496911744704e+00, 0.8397383534231e+02,
0.1074406983417e-08, 0.1187817671922e+01, 0.8401985929482e+02,
0.9757576855851e-09, 0.2655703035858e+01, 0.7826370942180e+02,
0.1258432887565e-08, 0.4969896184844e+01, 0.3115650189215e+03,
0.1240336343282e-08, 0.5192460776926e+01, 0.1784300471910e+03,
0.9016107005164e-09, 0.1960356923057e+01, 0.5886454391678e+02,
0.1135392360918e-08, 0.5082427809068e+01, 0.7842370451713e+02,
0.9216046089565e-09, 0.2793775037273e+01, 0.1014262087719e+03,
0.1061276615030e-08, 0.3726144311409e+01, 0.5660027930059e+02,
0.1010110596263e-08, 0.7404080708937e+00, 0.4245678405627e+02,
0.7217424756199e-09, 0.2697449980577e-01, 0.2457074661053e+03,
0.6912003846756e-09, 0.4253296276335e+01, 0.1679936946371e+03,
0.6871814664847e-09, 0.5148072412354e+01, 0.6053048899753e+02,
0.4887158016343e-09, 0.2153581148294e+01, 0.9656299901946e+02,
0.5161802866314e-09, 0.3852750634351e+01, 0.2442876000072e+03,
0.5652599559057e-09, 0.1233233356270e+01, 0.8365903305582e+02,
0.4710812608586e-09, 0.5610486976767e+01, 0.3164282286739e+03,
0.4909977500324e-09, 0.1639629524123e+01, 0.4059982187939e+03,
0.4772641839378e-09, 0.3737100368583e+01, 0.1805255418145e+03,
0.4487562567153e-09, 0.1158417054478e+00, 0.8433466158131e+02,
0.3943441230497e-09, 0.6243502862796e+00, 0.2568537517081e+03,
0.3952236913598e-09, 0.3510377382385e+01, 0.2449975330562e+03,
0.3788898363417e-09, 0.5916128302299e+01, 0.1568131045107e+03,
0.3738329328831e-09, 0.1042266763456e+01, 0.3948519331910e+03,
0.2451199165151e-09, 0.1166788435700e+01, 0.1435713242844e+03,
0.2436734402904e-09, 0.3254726114901e+01, 0.2268582385539e+03,
0.2213605274325e-09, 0.1687210598530e+01, 0.1658638954901e+03,
0.1491521204829e-09, 0.2657541786794e+01, 0.2219950288015e+03,
0.1474995329744e-09, 0.5013089805819e+01, 0.3052819430710e+03,
0.1661939475656e-09, 0.5495315428418e+01, 0.2526661704812e+03,
0.9015946748003e-10, 0.2236989966505e+01, 0.4171445043968e+03}
/* Sun-to-Earth, T^0, Z */
e0z := []float64{
0.2796207639075e-05, 0.3198701560209e+01, 0.8433466158131e+02,
0.1016042198142e-05, 0.5422360395913e+01, 0.5507553240374e+01,
0.8044305033647e-06, 0.3880222866652e+01, 0.5223693906222e+01,
0.4385347909274e-06, 0.3704369937468e+01, 0.2352866153506e+01,
0.3186156414906e-06, 0.3999639363235e+01, 0.1577343543434e+01,
0.2272412285792e-06, 0.3984738315952e+01, 0.1047747311755e+01,
0.1645620103007e-06, 0.3565412516841e+01, 0.5856477690889e+01,
0.1815836921166e-06, 0.4984507059020e+01, 0.6283075850446e+01,
0.1447461676364e-06, 0.3702753570108e+01, 0.9437762937313e+01,
0.1430760876382e-06, 0.3409658712357e+01, 0.1021328554739e+02,
0.1120445753226e-06, 0.4829561570246e+01, 0.1414349524433e+02,
0.1090232840797e-06, 0.2080729178066e+01, 0.6812766822558e+01,
0.9715727346551e-07, 0.3476295881948e+01, 0.4694002934110e+01,
0.1036267136217e-06, 0.4056639536648e+01, 0.7109288135493e+02,
0.8752665271340e-07, 0.4448159519911e+01, 0.5753384878334e+01,
0.8331864956004e-07, 0.4991704044208e+01, 0.7084896783808e+01,
0.6901658670245e-07, 0.4325358994219e+01, 0.6275962395778e+01,
0.9144536848998e-07, 0.1141826375363e+01, 0.6620890113188e+01,
0.7205085037435e-07, 0.3624344170143e+01, 0.5296909721118e+00,
0.7697874654176e-07, 0.5554257458998e+01, 0.1676215758509e+03,
0.5197545738384e-07, 0.6251760961735e+01, 0.1807370494127e+02,
0.5031345378608e-07, 0.2497341091913e+01, 0.4705732307012e+01,
0.4527110205840e-07, 0.2335079920992e+01, 0.6309374173736e+01,
0.4753355798089e-07, 0.7094148987474e+00, 0.5884926831456e+01,
0.4296951977516e-07, 0.1101916352091e+01, 0.6681224869435e+01,
0.3855341568387e-07, 0.1825495405486e+01, 0.5486777812467e+01,
0.5253930970990e-07, 0.4424740687208e+01, 0.7860419393880e+01,
0.4024630496471e-07, 0.5120498157053e+01, 0.1336797263425e+02,
0.4061069791453e-07, 0.6029771435451e+01, 0.3930209696940e+01,
0.3797883804205e-07, 0.4435193600836e+00, 0.3154687086868e+01,
0.2933033225587e-07, 0.5124157356507e+01, 0.1059381944224e+01,
0.3503000930426e-07, 0.5421830162065e+01, 0.6069776770667e+01,
0.3670096214050e-07, 0.4582101667297e+01, 0.1219403291462e+02,
0.2905609437008e-07, 0.1926566420072e+01, 0.1097707878456e+02,
0.2466827821713e-07, 0.6090174539834e+00, 0.6496374930224e+01,
0.2691647295332e-07, 0.1393432595077e+01, 0.2200391463820e+02,
0.2150554667946e-07, 0.4308671715951e+01, 0.5643178611111e+01,
0.2237481922680e-07, 0.8133968269414e+00, 0.8635942003952e+01,
0.1817741038157e-07, 0.3755205127454e+01, 0.3340612434717e+01,
0.2227820762132e-07, 0.2759558596664e+01, 0.1203646072878e+02,
0.1944713772307e-07, 0.5699645869121e+01, 0.1179062909082e+02,
0.1527340520662e-07, 0.1986749091746e+01, 0.3981490189893e+00,
0.1577282574914e-07, 0.3205017217983e+01, 0.5088628793478e+01,
0.1424738825424e-07, 0.6256747903666e+01, 0.2544314396739e+01,
0.1616563121701e-07, 0.2601671259394e+00, 0.1729818233119e+02,
0.1401210391692e-07, 0.4686939173506e+01, 0.7058598460518e+01,
0.1488726974214e-07, 0.2815862451372e+01, 0.2593412433514e+02,
0.1692626442388e-07, 0.4956894109797e+01, 0.1564752902480e+03,
0.1123571582910e-07, 0.2381192697696e+01, 0.3738761453707e+01,
0.9903308606317e-08, 0.4294851657684e+01, 0.9225539266174e+01,
0.9174533187191e-08, 0.3075171510642e+01, 0.4164311961999e+01,
0.8645985631457e-08, 0.5477534821633e+00, 0.8429241228195e+01,
-0.1085876492688e-07, 0.0000000000000e+00, 0.0000000000000e+00,
0.9264309077815e-08, 0.5968571670097e+01, 0.7079373888424e+01,
0.8243116984954e-08, 0.1489098777643e+01, 0.1044738781244e+02,
0.8268102113708e-08, 0.3512977691983e+01, 0.1150676975667e+02,
0.9043613988227e-08, 0.1290704408221e+00, 0.1101510648075e+02,
0.7432912038789e-08, 0.1991086893337e+01, 0.2608790314060e+02,
0.8586233727285e-08, 0.4238357924414e+01, 0.2986433403208e+02,
0.7612230060131e-08, 0.2911090150166e+01, 0.4732030630302e+01,
0.7097787751408e-08, 0.1908938392390e+01, 0.8031092209206e+01,
0.7640237040175e-08, 0.6129219000168e+00, 0.7962980379786e+00,
0.7070445688081e-08, 0.1380417036651e+01, 0.2146165377750e+01,
0.7690770957702e-08, 0.1680504249084e+01, 0.2122839202813e+02,
0.8051292542594e-08, 0.5127423484511e+01, 0.2942463415728e+01,
0.5902709104515e-08, 0.2020274190917e+01, 0.7755226100720e+00,
0.5134567496462e-08, 0.2606778676418e+01, 0.1256615170089e+02,
0.5525802046102e-08, 0.1613011769663e+01, 0.8018209333619e+00,
0.5880724784221e-08, 0.4604483417236e+01, 0.4690479774488e+01,
0.5211699081370e-08, 0.5718964114193e+01, 0.8827390247185e+01,
0.4891849573562e-08, 0.3689658932196e+01, 0.2132990797783e+00,
0.5150246069997e-08, 0.4099769855122e+01, 0.6480980550449e+02,
0.5102434319633e-08, 0.5660834602509e+01, 0.3379454372902e+02,
0.5083405254252e-08, 0.9842221218974e+00, 0.4136910472696e+01,
0.4206562585682e-08, 0.1341363634163e+00, 0.3128388763578e+01,
0.4663249683579e-08, 0.8130132735866e+00, 0.5216580451554e+01,
0.4099474416530e-08, 0.5791497770644e+01, 0.4265981595566e+00,
0.4628251220767e-08, 0.1249802769331e+01, 0.1572083878776e+02,
0.5024068728142e-08, 0.4795684802743e+01, 0.6290189305114e+01,
0.5120234327758e-08, 0.3810420387208e+01, 0.5230807360890e+01,
0.5524029815280e-08, 0.1029264714351e+01, 0.2397622045175e+03,
0.4757415718860e-08, 0.3528044781779e+01, 0.1649636139783e+02,
0.3915786131127e-08, 0.5593889282646e+01, 0.1589072916335e+01,
0.4869053149991e-08, 0.3299636454433e+01, 0.7632943190217e+01,
0.3649365703729e-08, 0.1286049002584e+01, 0.6206810014183e+01,
0.3992493949002e-08, 0.3100307589464e+01, 0.2515860172507e+02,
0.3320247477418e-08, 0.6212683940807e+01, 0.1216800268190e+02,
0.3287123739696e-08, 0.4699118445928e+01, 0.7234794171227e+01,
0.3472776811103e-08, 0.2630507142004e+01, 0.7342457794669e+01,
0.3423253294767e-08, 0.2946432844305e+01, 0.9623688285163e+01,
0.3896173898244e-08, 0.1224834179264e+01, 0.6438496133249e+01,
0.3388455337924e-08, 0.1543807616351e+01, 0.1494531617769e+02,
0.3062704716523e-08, 0.1191777572310e+01, 0.8662240327241e+01,
0.3270075600400e-08, 0.5483498767737e+01, 0.1194447056968e+01,
0.3101209215259e-08, 0.8000833804348e+00, 0.3772475342596e+02,
0.2780883347311e-08, 0.4077980721888e+00, 0.5863591145557e+01,
0.2903605931824e-08, 0.2617490302147e+01, 0.1965104848470e+02,
0.2682014743119e-08, 0.2634703158290e+01, 0.7238675589263e+01,
0.2534360108492e-08, 0.6102446114873e+01, 0.6836645152238e+01,
0.2392564882509e-08, 0.3681820208691e+01, 0.5849364236221e+01,
0.2656667254856e-08, 0.6216045388886e+01, 0.6133512519065e+01,
0.2331242096773e-08, 0.5864949777744e+01, 0.4535059491685e+01,
0.2287898363668e-08, 0.4566628532802e+01, 0.7477522907414e+01,
0.2336944521306e-08, 0.2442722126930e+01, 0.1137170464392e+02,
0.3156632236269e-08, 0.1626628050682e+01, 0.2509084901204e+03,
0.2982612402766e-08, 0.2803604512609e+01, 0.1748016358760e+01,
0.2774031674807e-08, 0.4654002897158e+01, 0.8223916695780e+02,
0.2295236548638e-08, 0.4326518333253e+01, 0.3378142627421e+00,
0.2190714699873e-08, 0.4519614578328e+01, 0.2908881142201e+02,
0.2191495845045e-08, 0.3012626912549e+01, 0.1673046366289e+02,
0.2492901628386e-08, 0.1290101424052e+00, 0.1543797956245e+03,
0.1993778064319e-08, 0.3864046799414e+01, 0.1778984560711e+02,
0.1898146479022e-08, 0.5053777235891e+01, 0.2042657109477e+02,
0.1918280127634e-08, 0.2222470192548e+01, 0.4165496312290e+02,
0.1916351061607e-08, 0.8719067257774e+00, 0.7737595720538e+02,
0.1834720181466e-08, 0.4031491098040e+01, 0.2358125818164e+02,
0.1249201523806e-08, 0.5938379466835e+01, 0.3301902111895e+02,
0.1477304050539e-08, 0.6544722606797e+00, 0.9548094718417e+02,
0.1264316431249e-08, 0.2059072853236e+01, 0.8399684731857e+02,
0.1203526495039e-08, 0.3644813532605e+01, 0.4558517281984e+02,
0.9221681059831e-09, 0.3241815055602e+01, 0.7805158573086e+02,
0.7849278367646e-09, 0.5043812342457e+01, 0.5217580628120e+02,
0.7983392077387e-09, 0.5000024502753e+01, 0.1501922143975e+03,
0.7925395431654e-09, 0.1398734871821e-01, 0.9061773743175e+02,
0.7640473285886e-09, 0.5067111723130e+01, 0.4951538251678e+02,
0.5398937754482e-09, 0.5597382200075e+01, 0.1613385000004e+03,
0.5626247550193e-09, 0.2601338209422e+01, 0.7318837597844e+02,
0.5525197197855e-09, 0.5814832109256e+01, 0.1432335100216e+03,
0.5407629837898e-09, 0.3384820609076e+01, 0.3230491187871e+03,
0.3856739119801e-09, 0.1072391840473e+01, 0.2334791286671e+03,
0.3856425239987e-09, 0.2369540393327e+01, 0.1739046517013e+03,
0.4350867755983e-09, 0.5255575751082e+01, 0.1620484330494e+03,
0.3844113924996e-09, 0.5482356246182e+01, 0.9757644180768e+02,
0.2854869155431e-09, 0.9573634763143e+00, 0.1697170704744e+03,
0.1719227671416e-09, 0.1887203025202e+01, 0.2265204242912e+03,
0.1527846879755e-09, 0.3982183931157e+01, 0.3341954043900e+03,
0.1128229264847e-09, 0.2787457156298e+01, 0.3119028331842e+03}
/* Sun-to-Earth, T^1, X */
e1x := []float64{
0.1234046326004e-05, 0.0000000000000e+00, 0.0000000000000e+00,
0.5150068824701e-06, 0.6002664557501e+01, 0.1256615170089e+02,
0.1290743923245e-07, 0.5959437664199e+01, 0.1884922755134e+02,
0.1068615564952e-07, 0.2015529654209e+01, 0.6283075850446e+01,
0.2079619142538e-08, 0.1732960531432e+01, 0.6279552690824e+01,
0.2078009243969e-08, 0.4915604476996e+01, 0.6286599010068e+01,
0.6206330058856e-09, 0.3616457953824e+00, 0.4705732307012e+01,
0.5989335313746e-09, 0.3802607304474e+01, 0.6256777527156e+01,
0.5958495663840e-09, 0.2845866560031e+01, 0.6309374173736e+01,
0.4866923261539e-09, 0.5213203771824e+01, 0.7755226100720e+00,
0.4267785823142e-09, 0.4368189727818e+00, 0.1059381944224e+01,
0.4610675141648e-09, 0.1837249181372e-01, 0.7860419393880e+01,
0.3626989993973e-09, 0.2161590545326e+01, 0.5753384878334e+01,
0.3563071194389e-09, 0.1452631954746e+01, 0.5884926831456e+01,
0.3557015642807e-09, 0.4470593393054e+01, 0.6812766822558e+01,
0.3210412089122e-09, 0.5195926078314e+01, 0.6681224869435e+01,
0.2875473577986e-09, 0.5916256610193e+01, 0.2513230340178e+02,
0.2842913681629e-09, 0.1149902426047e+01, 0.6127655567643e+01,
0.2751248215916e-09, 0.5502088574662e+01, 0.6438496133249e+01,
0.2481432881127e-09, 0.2921989846637e+01, 0.5486777812467e+01,
0.2059885976560e-09, 0.3718070376585e+01, 0.7079373888424e+01,
0.2015522342591e-09, 0.5979395259740e+01, 0.6290189305114e+01,
0.1995364084253e-09, 0.6772087985494e+00, 0.6275962395778e+01,
0.1957436436943e-09, 0.2899210654665e+01, 0.5507553240374e+01,
0.1651609818948e-09, 0.6228206482192e+01, 0.1150676975667e+02,
0.1822980550699e-09, 0.1469348746179e+01, 0.1179062909082e+02,
0.1675223159760e-09, 0.3813910555688e+01, 0.7058598460518e+01,
0.1706491764745e-09, 0.3004380506684e+00, 0.7113454667900e-02,
0.1392952362615e-09, 0.1440393973406e+01, 0.7962980379786e+00,
0.1209868266342e-09, 0.4150425791727e+01, 0.4694002934110e+01,
0.1009827202611e-09, 0.3290040429843e+01, 0.3738761453707e+01,
0.1047261388602e-09, 0.4229590090227e+01, 0.6282095334605e+01,
0.1047006652004e-09, 0.2418967680575e+01, 0.6284056366286e+01,
0.9609993143095e-10, 0.4627943659201e+01, 0.6069776770667e+01,
0.9590900593873e-10, 0.1894393939924e+01, 0.4136910472696e+01,
0.9146249188071e-10, 0.2010647519562e+01, 0.6496374930224e+01,
0.8545274480290e-10, 0.5529846956226e-01, 0.1194447056968e+01,
0.8224377881194e-10, 0.1254304102174e+01, 0.1589072916335e+01,
0.6183529510410e-10, 0.3360862168815e+01, 0.8827390247185e+01,
0.6259255147141e-10, 0.4755628243179e+01, 0.8429241228195e+01,
0.5539291694151e-10, 0.5371746955142e+01, 0.4933208510675e+01,
0.7328259466314e-10, 0.4927699613906e+00, 0.4535059491685e+01,
0.6017835843560e-10, 0.5776682001734e-01, 0.1255903824622e+02,
0.7079827775243e-10, 0.4395059432251e+01, 0.5088628793478e+01,
0.5170358878213e-10, 0.5154062619954e+01, 0.1176985366291e+02,
0.4872301838682e-10, 0.6289611648973e+00, 0.6040347114260e+01,
0.5249869411058e-10, 0.5617272046949e+01, 0.3154687086868e+01,
0.4716172354411e-10, 0.3965901800877e+01, 0.5331357529664e+01,
0.4871214940964e-10, 0.4627507050093e+01, 0.1256967486051e+02,
0.4598076850751e-10, 0.6023631226459e+01, 0.6525804586632e+01,
0.4562196089485e-10, 0.4138562084068e+01, 0.3930209696940e+01,
0.4325493872224e-10, 0.1330845906564e+01, 0.7632943190217e+01,
0.5673781176748e-10, 0.2558752615657e+01, 0.5729506548653e+01,
0.3961436642503e-10, 0.2728071734630e+01, 0.7234794171227e+01,
0.5101868209058e-10, 0.4113444965144e+01, 0.6836645152238e+01,
0.5257043167676e-10, 0.6195089830590e+01, 0.8031092209206e+01,
0.5076613989393e-10, 0.2305124132918e+01, 0.7477522907414e+01,
0.3342169352778e-10, 0.5415998155071e+01, 0.1097707878456e+02,
0.3545881983591e-10, 0.3727160564574e+01, 0.4164311961999e+01,
0.3364063738599e-10, 0.2901121049204e+00, 0.1137170464392e+02,
0.3357039670776e-10, 0.1652229354331e+01, 0.5223693906222e+01,
0.4307412268687e-10, 0.4938909587445e+01, 0.1592596075957e+01,
0.3405769115435e-10, 0.2408890766511e+01, 0.3128388763578e+01,
0.3001926198480e-10, 0.4862239006386e+01, 0.1748016358760e+01,
0.2778264787325e-10, 0.5241168661353e+01, 0.7342457794669e+01,
0.2676159480666e-10, 0.3423593942199e+01, 0.2146165377750e+01,
0.2954273399939e-10, 0.1881721265406e+01, 0.5368044267797e+00,
0.3309362888795e-10, 0.1931525677349e+01, 0.8018209333619e+00,
0.2810283608438e-10, 0.2414659495050e+01, 0.5225775174439e+00,
0.3378045637764e-10, 0.4238019163430e+01, 0.1554202828031e+00,
0.2558134979840e-10, 0.1828225235805e+01, 0.5230807360890e+01,
0.2273755578447e-10, 0.5858184283998e+01, 0.7084896783808e+01,
0.2294176037690e-10, 0.4514589779057e+01, 0.1726015463500e+02,
0.2533506099435e-10, 0.2355717851551e+01, 0.5216580451554e+01,
0.2716685375812e-10, 0.2221003625100e+01, 0.8635942003952e+01,
0.2419043435198e-10, 0.5955704951635e+01, 0.4690479774488e+01,
0.2521232544812e-10, 0.1395676848521e+01, 0.5481254917084e+01,
0.2630195021491e-10, 0.5727468918743e+01, 0.2629832328990e-01,
0.2548395840944e-10, 0.2628351859400e-03, 0.1349867339771e+01}
/* Sun-to-Earth, T^1, Y */
e1y := []float64{
0.9304690546528e-06, 0.0000000000000e+00, 0.0000000000000e+00,
0.5150715570663e-06, 0.4431807116294e+01, 0.1256615170089e+02,
0.1290825411056e-07, 0.4388610039678e+01, 0.1884922755134e+02,
0.4645466665386e-08, 0.5827263376034e+01, 0.6283075850446e+01,
0.2079625310718e-08, 0.1621698662282e+00, 0.6279552690824e+01,
0.2078189850907e-08, 0.3344713435140e+01, 0.6286599010068e+01,
0.6207190138027e-09, 0.5074049319576e+01, 0.4705732307012e+01,
0.5989826532569e-09, 0.2231842216620e+01, 0.6256777527156e+01,
0.5961360812618e-09, 0.1274975769045e+01, 0.6309374173736e+01,
0.4874165471016e-09, 0.3642277426779e+01, 0.7755226100720e+00,
0.4283834034360e-09, 0.5148765510106e+01, 0.1059381944224e+01,
0.4652389287529e-09, 0.4715794792175e+01, 0.7860419393880e+01,
0.3751707476401e-09, 0.6617207370325e+00, 0.5753384878334e+01,
0.3559998806198e-09, 0.6155548875404e+01, 0.5884926831456e+01,
0.3558447558857e-09, 0.2898827297664e+01, 0.6812766822558e+01,
0.3211116927106e-09, 0.3625813502509e+01, 0.6681224869435e+01,
0.2875609914672e-09, 0.4345435813134e+01, 0.2513230340178e+02,
0.2843109704069e-09, 0.5862263940038e+01, 0.6127655567643e+01,
0.2744676468427e-09, 0.3926419475089e+01, 0.6438496133249e+01,
0.2481285237789e-09, 0.1351976572828e+01, 0.5486777812467e+01,
0.2060338481033e-09, 0.2147556998591e+01, 0.7079373888424e+01,
0.2015822358331e-09, 0.4408358972216e+01, 0.6290189305114e+01,
0.2001195944195e-09, 0.5385829822531e+01, 0.6275962395778e+01,
0.1953667642377e-09, 0.1304933746120e+01, 0.5507553240374e+01,
0.1839744078713e-09, 0.6173567228835e+01, 0.1179062909082e+02,
0.1643334294845e-09, 0.4635942997523e+01, 0.1150676975667e+02,
0.1768051018652e-09, 0.5086283558874e+01, 0.7113454667900e-02,
0.1674874205489e-09, 0.2243332137241e+01, 0.7058598460518e+01,
0.1421445397609e-09, 0.6186899771515e+01, 0.7962980379786e+00,
0.1255163958267e-09, 0.5730238465658e+01, 0.4694002934110e+01,
0.1013945281961e-09, 0.1726055228402e+01, 0.3738761453707e+01,
0.1047294335852e-09, 0.2658801228129e+01, 0.6282095334605e+01,
0.1047103879392e-09, 0.8481047835035e+00, 0.6284056366286e+01,
0.9530343962826e-10, 0.3079267149859e+01, 0.6069776770667e+01,
0.9604637611690e-10, 0.3258679792918e+00, 0.4136910472696e+01,
0.9153518537177e-10, 0.4398599886584e+00, 0.6496374930224e+01,
0.8562458214922e-10, 0.4772686794145e+01, 0.1194447056968e+01,
0.8232525360654e-10, 0.5966220721679e+01, 0.1589072916335e+01,
0.6150223411438e-10, 0.1780985591923e+01, 0.8827390247185e+01,
0.6272087858000e-10, 0.3184305429012e+01, 0.8429241228195e+01,
0.5540476311040e-10, 0.3801260595433e+01, 0.4933208510675e+01,
0.7331901699361e-10, 0.5205948591865e+01, 0.4535059491685e+01,
0.6018528702791e-10, 0.4770139083623e+01, 0.1255903824622e+02,
0.5150530724804e-10, 0.3574796899585e+01, 0.1176985366291e+02,
0.6471933741811e-10, 0.2679787266521e+01, 0.5088628793478e+01,
0.5317460644174e-10, 0.9528763345494e+00, 0.3154687086868e+01,
0.4832187748783e-10, 0.5329322498232e+01, 0.6040347114260e+01,
0.4716763555110e-10, 0.2395235316466e+01, 0.5331357529664e+01,
0.4871509139861e-10, 0.3056663648823e+01, 0.1256967486051e+02,
0.4598417696768e-10, 0.4452762609019e+01, 0.6525804586632e+01,
0.5674189533175e-10, 0.9879680872193e+00, 0.5729506548653e+01,
0.4073560328195e-10, 0.5939127696986e+01, 0.7632943190217e+01,
0.5040994945359e-10, 0.4549875824510e+01, 0.8031092209206e+01,
0.5078185134679e-10, 0.7346659893982e+00, 0.7477522907414e+01,
0.3769343537061e-10, 0.1071317188367e+01, 0.7234794171227e+01,
0.4980331365299e-10, 0.2500345341784e+01, 0.6836645152238e+01,
0.3458236594757e-10, 0.3825159450711e+01, 0.1097707878456e+02,
0.3578859493602e-10, 0.5299664791549e+01, 0.4164311961999e+01,
0.3370504646419e-10, 0.5002316301593e+01, 0.1137170464392e+02,
0.3299873338428e-10, 0.2526123275282e+01, 0.3930209696940e+01,
0.4304917318409e-10, 0.3368078557132e+01, 0.1592596075957e+01,
0.3402418753455e-10, 0.8385495425800e+00, 0.3128388763578e+01,
0.2778460572146e-10, 0.3669905203240e+01, 0.7342457794669e+01,
0.2782710128902e-10, 0.2691664812170e+00, 0.1748016358760e+01,
0.2711725179646e-10, 0.4707487217718e+01, 0.5296909721118e+00,
0.2981760946340e-10, 0.3190260867816e+00, 0.5368044267797e+00,
0.2811672977772e-10, 0.3196532315372e+01, 0.7084896783808e+01,
0.2863454474467e-10, 0.2263240324780e+00, 0.5223693906222e+01,
0.3333464634051e-10, 0.3498451685065e+01, 0.8018209333619e+00,
0.3312991747609e-10, 0.5839154477412e+01, 0.1554202828031e+00,
0.2813255564006e-10, 0.8268044346621e+00, 0.5225775174439e+00,
0.2665098083966e-10, 0.3934021725360e+01, 0.5216580451554e+01,
0.2349795705216e-10, 0.5197620913779e+01, 0.2146165377750e+01,
0.2330352293961e-10, 0.2984999231807e+01, 0.1726015463500e+02,
0.2728001683419e-10, 0.6521679638544e+00, 0.8635942003952e+01,
0.2484061007669e-10, 0.3468955561097e+01, 0.5230807360890e+01,
0.2646328768427e-10, 0.1013724533516e+01, 0.2629832328990e-01,
0.2518630264831e-10, 0.6108081057122e+01, 0.5481254917084e+01,
0.2421901455384e-10, 0.1651097776260e+01, 0.1349867339771e+01,
0.6348533267831e-11, 0.3220226560321e+01, 0.8433466158131e+02}
/* Sun-to-Earth, T^1, Z */
e1z := []float64{
0.2278290449966e-05, 0.3413716033863e+01, 0.6283075850446e+01,
0.5429458209830e-07, 0.0000000000000e+00, 0.0000000000000e+00,
0.1903240492525e-07, 0.3370592358297e+01, 0.1256615170089e+02,
0.2385409276743e-09, 0.3327914718416e+01, 0.1884922755134e+02,
0.8676928342573e-10, 0.1824006811264e+01, 0.5223693906222e+01,
0.7765442593544e-10, 0.3888564279247e+01, 0.5507553240374e+01,
0.7066158332715e-10, 0.5194267231944e+01, 0.2352866153506e+01,
0.7092175288657e-10, 0.2333246960021e+01, 0.8399684731857e+02,
0.5357582213535e-10, 0.2224031176619e+01, 0.5296909721118e+00,
0.3828035865021e-10, 0.2156710933584e+01, 0.6279552690824e+01,
0.3824857220427e-10, 0.1529755219915e+01, 0.6286599010068e+01,
0.3286995181628e-10, 0.4879512900483e+01, 0.1021328554739e+02}
/* Sun-to-Earth, T^2, X */
e2x := []float64{
-0.4143818297913e-10, 0.0000000000000e+00, 0.0000000000000e+00,
0.2171497694435e-10, 0.4398225628264e+01, 0.1256615170089e+02,
0.9845398442516e-11, 0.2079720838384e+00, 0.6283075850446e+01,
0.9256833552682e-12, 0.4191264694361e+01, 0.1884922755134e+02,
0.1022049384115e-12, 0.5381133195658e+01, 0.8399684731857e+02}
/* Sun-to-Earth, T^2, Y */
e2y := []float64{
0.5063375872532e-10, 0.0000000000000e+00, 0.0000000000000e+00,
0.2173815785980e-10, 0.2827805833053e+01, 0.1256615170089e+02,
0.1010231999920e-10, 0.4634612377133e+01, 0.6283075850446e+01,
0.9259745317636e-12, 0.2620612076189e+01, 0.1884922755134e+02,
0.1022202095812e-12, 0.3809562326066e+01, 0.8399684731857e+02}
/* Sun-to-Earth, T^2, Z */
e2z := []float64{
0.9722666114891e-10, 0.5152219582658e+01, 0.6283075850446e+01,
-0.3494819171909e-11, 0.0000000000000e+00, 0.0000000000000e+00,
0.6713034376076e-12, 0.6440188750495e+00, 0.1256615170089e+02}
/* SSB-to-Sun, T^0, X */
s0x := []float64{
0.4956757536410e-02, 0.3741073751789e+01, 0.5296909721118e+00,
0.2718490072522e-02, 0.4016011511425e+01, 0.2132990797783e+00,
0.1546493974344e-02, 0.2170528330642e+01, 0.3813291813120e-01,
0.8366855276341e-03, 0.2339614075294e+01, 0.7478166569050e-01,
0.2936777942117e-03, 0.0000000000000e+00, 0.0000000000000e+00,
0.1201317439469e-03, 0.4090736353305e+01, 0.1059381944224e+01,
0.7578550887230e-04, 0.3241518088140e+01, 0.4265981595566e+00,
0.1941787367773e-04, 0.1012202064330e+01, 0.2061856251104e+00,
0.1889227765991e-04, 0.3892520416440e+01, 0.2204125344462e+00,
0.1937896968613e-04, 0.4797779441161e+01, 0.1495633313810e+00,
0.1434506110873e-04, 0.3868960697933e+01, 0.5225775174439e+00,
0.1406659911580e-04, 0.4759766557397e+00, 0.5368044267797e+00,
0.1179022300202e-04, 0.7774961520598e+00, 0.7626583626240e-01,
0.8085864460959e-05, 0.3254654471465e+01, 0.3664874755930e-01,
0.7622752967615e-05, 0.4227633103489e+01, 0.3961708870310e-01,
0.6209171139066e-05, 0.2791828325711e+00, 0.7329749511860e-01,
0.4366435633970e-05, 0.4440454875925e+01, 0.1589072916335e+01,
0.3792124889348e-05, 0.5156393842356e+01, 0.7113454667900e-02,
0.3154548963402e-05, 0.6157005730093e+01, 0.4194847048887e+00,
0.3088359882942e-05, 0.2494567553163e+01, 0.6398972393349e+00,
0.2788440902136e-05, 0.4934318747989e+01, 0.1102062672231e+00,
0.3039928456376e-05, 0.4895077702640e+01, 0.6283075850446e+01,
0.2272258457679e-05, 0.5278394064764e+01, 0.1030928125552e+00,
0.2162007057957e-05, 0.5802978019099e+01, 0.3163918923335e+00,
0.1767632855737e-05, 0.3415346595193e-01, 0.1021328554739e+02,
0.1349413459362e-05, 0.2001643230755e+01, 0.1484170571900e-02,
0.1170141900476e-05, 0.2424750491620e+01, 0.6327837846670e+00,
0.1054355266820e-05, 0.3123311487576e+01, 0.4337116142245e+00,
0.9800822461610e-06, 0.3026258088130e+01, 0.1052268489556e+01,
0.1091203749931e-05, 0.3157811670347e+01, 0.1162474756779e+01,
0.6960236715913e-06, 0.8219570542313e+00, 0.1066495398892e+01,
0.5689257296909e-06, 0.1323052375236e+01, 0.9491756770005e+00,
0.6613172135802e-06, 0.2765348881598e+00, 0.8460828644453e+00,
0.6277702517571e-06, 0.5794064466382e+01, 0.1480791608091e+00,
0.6304884066699e-06, 0.7323555380787e+00, 0.2243449970715e+00,
0.4897850467382e-06, 0.3062464235399e+01, 0.3340612434717e+01,
0.3759148598786e-06, 0.4588290469664e+01, 0.3516457698740e-01,
0.3110520548195e-06, 0.1374299536572e+01, 0.6373574839730e-01,
0.3064708359780e-06, 0.4222267485047e+01, 0.1104591729320e-01,
0.2856347168241e-06, 0.3714202944973e+01, 0.1510475019529e+00,
0.2840945514288e-06, 0.2847972875882e+01, 0.4110125927500e-01,
0.2378951599405e-06, 0.3762072563388e+01, 0.2275259891141e+00,
0.2714229481417e-06, 0.1036049980031e+01, 0.2535050500000e-01,
0.2323551717307e-06, 0.4682388599076e+00, 0.8582758298370e-01,
0.1881790512219e-06, 0.4790565425418e+01, 0.2118763888447e+01,
0.2261353968371e-06, 0.1669144912212e+01, 0.7181332454670e-01,
0.2214546389848e-06, 0.3937717281614e+01, 0.2968341143800e-02,
0.2184915594933e-06, 0.1129169845099e+00, 0.7775000683430e-01,
0.2000164937936e-06, 0.4030009638488e+01, 0.2093666171530e+00,
0.1966105136719e-06, 0.8745955786834e+00, 0.2172315424036e+00,
0.1904742332624e-06, 0.5919743598964e+01, 0.2022531624851e+00,
0.1657399705031e-06, 0.2549141484884e+01, 0.7358765972222e+00,
0.1574070533987e-06, 0.5277533020230e+01, 0.7429900518901e+00,
0.1832261651039e-06, 0.3064688127777e+01, 0.3235053470014e+00,
0.1733615346569e-06, 0.3011432799094e+01, 0.1385174140878e+00,
0.1549124014496e-06, 0.4005569132359e+01, 0.5154640627760e+00,
0.1637044713838e-06, 0.1831375966632e+01, 0.8531963191132e+00,
0.1123420082383e-06, 0.1180270407578e+01, 0.1990721704425e+00,
0.1083754165740e-06, 0.3414101320863e+00, 0.5439178814476e+00,
0.1156638012655e-06, 0.6130479452594e+00, 0.5257585094865e+00,
0.1142548785134e-06, 0.3724761948846e+01, 0.5336234347371e+00,
0.7921463895965e-07, 0.2435425589361e+01, 0.1478866649112e+01,
0.7428600285231e-07, 0.3542144398753e+01, 0.2164800718209e+00,
0.8323211246747e-07, 0.3525058072354e+01, 0.1692165728891e+01,
0.7257595116312e-07, 0.1364299431982e+01, 0.2101180877357e+00,
0.7111185833236e-07, 0.2460478875808e+01, 0.4155522422634e+00,
0.6868090383716e-07, 0.4397327670704e+01, 0.1173197218910e+00,
0.7226419974175e-07, 0.4042647308905e+01, 0.1265567569334e+01,
0.6955642383177e-07, 0.2865047906085e+01, 0.9562891316684e+00,
0.7492139296331e-07, 0.5014278994215e+01, 0.1422690933580e-01,
0.6598363128857e-07, 0.2376730020492e+01, 0.6470106940028e+00,
0.7381147293385e-07, 0.3272990384244e+01, 0.1581959461667e+01,
0.6402909624032e-07, 0.5302290955138e+01, 0.9597935788730e-01,
0.6237454263857e-07, 0.5444144425332e+01, 0.7084920306520e-01,
0.5241198544016e-07, 0.4215359579205e+01, 0.5265099800692e+00,
0.5144463853918e-07, 0.1218916689916e+00, 0.5328719641544e+00,
0.5868164772299e-07, 0.2369402002213e+01, 0.7871412831580e-01,
0.6233195669151e-07, 0.1254922242403e+01, 0.2608790314060e+02,
0.6068463791422e-07, 0.5679713760431e+01, 0.1114304132498e+00,
0.4359361135065e-07, 0.6097219641646e+00, 0.1375773836557e+01,
0.4686510366826e-07, 0.4786231041431e+01, 0.1143987543936e+00,
0.3758977287225e-07, 0.1167368068139e+01, 0.1596186371003e+01,
0.4282051974778e-07, 0.1519471064319e+01, 0.2770348281756e+00,
0.5153765386113e-07, 0.1860532322984e+01, 0.2228608264996e+00,
0.4575129387188e-07, 0.7632857887158e+00, 0.1465949902372e+00,
0.3326844933286e-07, 0.1298219485285e+01, 0.5070101000000e-01,
0.3748617450984e-07, 0.1046510321062e+01, 0.4903339079539e+00,
0.2816756661499e-07, 0.3434522346190e+01, 0.2991266627620e+00,
0.3412750405039e-07, 0.2523766270318e+01, 0.3518164938661e+00,
0.2655796761776e-07, 0.2904422260194e+01, 0.6256703299991e+00,
0.2963597929458e-07, 0.5923900431149e+00, 0.1099462426779e+00,
0.2539523734781e-07, 0.4851947722567e+01, 0.1256615170089e+02,
0.2283087914139e-07, 0.3400498595496e+01, 0.6681224869435e+01,
0.2321309799331e-07, 0.5789099148673e+01, 0.3368040641550e-01,
0.2549657649750e-07, 0.3991856479792e-01, 0.1169588211447e+01,
0.2290462303977e-07, 0.2788567577052e+01, 0.1045155034888e+01,
0.1945398522914e-07, 0.3290896998176e+01, 0.1155361302111e+01,
0.1849171512638e-07, 0.2698060129367e+01, 0.4452511715700e-02,
0.1647199834254e-07, 0.3016735644085e+01, 0.4408250688924e+00,
0.1529530765273e-07, 0.5573043116178e+01, 0.6521991896920e-01,
0.1433199339978e-07, 0.1481192356147e+01, 0.9420622223326e+00,
0.1729134193602e-07, 0.1422817538933e+01, 0.2108507877249e+00,
0.1716463931346e-07, 0.3469468901855e+01, 0.2157473718317e+00,
0.1391206061378e-07, 0.6122436220547e+01, 0.4123712502208e+00,
0.1404746661924e-07, 0.1647765641936e+01, 0.4258542984690e-01,
0.1410452399455e-07, 0.5989729161964e+01, 0.2258291676434e+00,
0.1089828772168e-07, 0.2833705509371e+01, 0.4226656969313e+00,
0.1047374564948e-07, 0.5090690007331e+00, 0.3092784376656e+00,
0.1358279126532e-07, 0.5128990262836e+01, 0.7923417740620e-01,
0.1020456476148e-07, 0.9632772880808e+00, 0.1456308687557e+00,
0.1033428735328e-07, 0.3223779318418e+01, 0.1795258541446e+01,
0.1412435841540e-07, 0.2410271572721e+01, 0.1525316725248e+00,
0.9722759371574e-08, 0.2333531395690e+01, 0.8434341241180e-01,
0.9657334084704e-08, 0.6199270974168e+01, 0.1272681024002e+01,
0.1083641148690e-07, 0.2864222292929e+01, 0.7032915397480e-01,
0.1067318403838e-07, 0.5833458866568e+00, 0.2123349582968e+00,
0.1062366201976e-07, 0.4307753989494e+01, 0.2142632012598e+00,
0.1236364149266e-07, 0.2873917870593e+01, 0.1847279083684e+00,
0.1092759489593e-07, 0.2959887266733e+01, 0.1370332435159e+00,
0.8912069362899e-08, 0.5141213702562e+01, 0.2648454860559e+01,
0.9656467707970e-08, 0.4532182462323e+01, 0.4376440768498e+00,
0.8098386150135e-08, 0.2268906338379e+01, 0.2880807454688e+00,
0.7857714675000e-08, 0.4055544260745e+01, 0.2037373330570e+00,
0.7288455940646e-08, 0.5357901655142e+01, 0.1129145838217e+00,
0.9450595950552e-08, 0.4264926963939e+01, 0.5272426800584e+00,
0.9381718247537e-08, 0.7489366976576e-01, 0.5321392641652e+00,
0.7079052646038e-08, 0.1923311052874e+01, 0.6288513220417e+00,
0.9259004415344e-08, 0.2970256853438e+01, 0.1606092486742e+00,
0.8259801499742e-08, 0.3327056314697e+01, 0.8389694097774e+00,
0.6476334355779e-08, 0.2954925505727e+01, 0.2008557621224e+01,
0.5984021492007e-08, 0.9138753105829e+00, 0.2042657109477e+02,
0.5989546863181e-08, 0.3244464082031e+01, 0.2111650433779e+01,
0.6233108606023e-08, 0.4995232638403e+00, 0.4305306221819e+00,
0.6877299149965e-08, 0.2834987233449e+01, 0.9561746721300e-02,
0.8311234227190e-08, 0.2202951835758e+01, 0.3801276407308e+00,
0.6599472832414e-08, 0.4478581462618e+01, 0.1063314406849e+01,
0.6160491096549e-08, 0.5145858696411e+01, 0.1368660381889e+01,
0.6164772043891e-08, 0.3762976697911e+00, 0.4234171675140e+00,
0.6363248684450e-08, 0.3162246718685e+01, 0.1253008786510e-01,
0.6448587520999e-08, 0.3442693302119e+01, 0.5287268506303e+00,
0.6431662283977e-08, 0.8977549136606e+00, 0.5306550935933e+00,
0.6351223158474e-08, 0.4306447410369e+01, 0.5217580628120e+02,
0.5476721393451e-08, 0.3888529177855e+01, 0.2221856701002e+01,
0.5341772572619e-08, 0.2655560662512e+01, 0.7466759693650e-01,
0.5337055758302e-08, 0.5164990735946e+01, 0.7489573444450e-01,
0.5373120816787e-08, 0.6041214553456e+01, 0.1274714967946e+00,
0.5392351705426e-08, 0.9177763485932e+00, 0.1055449481598e+01,
0.6688495850205e-08, 0.3089608126937e+01, 0.2213766559277e+00,
0.5072003660362e-08, 0.4311316541553e+01, 0.2132517061319e+00,
0.5070726650455e-08, 0.5790675464444e+00, 0.2133464534247e+00,
0.5658012950032e-08, 0.2703945510675e+01, 0.7287631425543e+00,
0.4835509924854e-08, 0.2975422976065e+01, 0.7160067364790e-01,
0.6479821978012e-08, 0.1324168733114e+01, 0.2209183458640e-01,
0.6230636494980e-08, 0.2860103632836e+01, 0.3306188016693e+00,
0.4649239516213e-08, 0.4832259763403e+01, 0.7796265773310e-01,
0.6487325792700e-08, 0.2726165825042e+01, 0.3884652414254e+00,
0.4682823682770e-08, 0.6966602455408e+00, 0.1073608853559e+01,
0.5704230804976e-08, 0.5669634104606e+01, 0.8731175355560e-01,
0.6125413585489e-08, 0.1513386538915e+01, 0.7605151500000e-01,
0.6035825038187e-08, 0.1983509168227e+01, 0.9846002785331e+00,
0.4331123462303e-08, 0.2782892992807e+01, 0.4297791515992e+00,
0.4681107685143e-08, 0.5337232886836e+01, 0.2127790306879e+00,
0.4669105829655e-08, 0.5837133792160e+01, 0.2138191288687e+00,
0.5138823602365e-08, 0.3080560200507e+01, 0.7233337363710e-01,
0.4615856664534e-08, 0.1661747897471e+01, 0.8603097737811e+00,
0.4496916702197e-08, 0.2112508027068e+01, 0.7381754420900e-01,
0.4278479042945e-08, 0.5716528462627e+01, 0.7574578717200e-01,
0.3840525503932e-08, 0.6424172726492e+00, 0.3407705765729e+00,
0.4866636509685e-08, 0.4919244697715e+01, 0.7722995774390e-01,
0.3526100639296e-08, 0.2550821052734e+01, 0.6225157782540e-01,
0.3939558488075e-08, 0.3939331491710e+01, 0.5268983110410e-01,
0.4041268772576e-08, 0.2275337571218e+01, 0.3503323232942e+00,
0.3948761842853e-08, 0.1999324200790e+01, 0.1451108196653e+00,
0.3258394550029e-08, 0.9121001378200e+00, 0.5296435984654e+00,
0.3257897048761e-08, 0.3428428660869e+01, 0.5297383457582e+00,
0.3842559031298e-08, 0.6132927720035e+01, 0.9098186128426e+00,
0.3109920095448e-08, 0.7693650193003e+00, 0.3932462625300e-02,
0.3132237775119e-08, 0.3621293854908e+01, 0.2346394437820e+00,
0.3942189421510e-08, 0.4841863659733e+01, 0.3180992042600e-02,
0.3796972285340e-08, 0.1814174994268e+01, 0.1862120789403e+00,
0.3995640233688e-08, 0.1386990406091e+01, 0.4549093064213e+00,
0.2875013727414e-08, 0.9178318587177e+00, 0.1905464808669e+01,
0.3073719932844e-08, 0.2688923811835e+01, 0.3628624111593e+00,
0.2731016580075e-08, 0.1188259127584e+01, 0.2131850110243e+00,
0.2729549896546e-08, 0.3702160634273e+01, 0.2134131485323e+00,
0.3339372892449e-08, 0.7199163960331e+00, 0.2007689919132e+00,
0.2898833764204e-08, 0.1916709364999e+01, 0.5291709230214e+00,
0.2894536549362e-08, 0.2424043195547e+01, 0.5302110212022e+00,
0.3096872473843e-08, 0.4445894977497e+01, 0.2976424921901e+00,
0.2635672326810e-08, 0.3814366984117e+01, 0.1485980103780e+01,
0.3649302697001e-08, 0.2924200596084e+01, 0.6044726378023e+00,
0.3127954585895e-08, 0.1842251648327e+01, 0.1084620721060e+00,
0.2616040173947e-08, 0.4155841921984e+01, 0.1258454114666e+01,
0.2597395859860e-08, 0.1158045978874e+00, 0.2103781122809e+00,
0.2593286172210e-08, 0.4771850408691e+01, 0.2162200472757e+00,
0.2481823585747e-08, 0.4608842558889e+00, 0.1062562936266e+01,
0.2742219550725e-08, 0.1538781127028e+01, 0.5651155736444e+00,
0.3199558469610e-08, 0.3226647822878e+00, 0.7036329877322e+00,
0.2666088542957e-08, 0.1967991731219e+00, 0.1400015846597e+00,
0.2397067430580e-08, 0.3707036669873e+01, 0.2125476091956e+00,
0.2376570772738e-08, 0.1182086628042e+01, 0.2140505503610e+00,
0.2547228007887e-08, 0.4906256820629e+01, 0.1534957940063e+00,
0.2265575594114e-08, 0.3414949866857e+01, 0.2235935264888e+00,
0.2464381430585e-08, 0.4599122275378e+01, 0.2091065926078e+00,
0.2433408527044e-08, 0.2830751145445e+00, 0.2174915669488e+00,
0.2443605509076e-08, 0.4212046432538e+01, 0.1739420156204e+00,
0.2319779262465e-08, 0.9881978408630e+00, 0.7530171478090e-01,
0.2284622835465e-08, 0.5565347331588e+00, 0.7426161660010e-01,
0.2467268750783e-08, 0.5655708150766e+00, 0.2526561439362e+00,
0.2808513492782e-08, 0.1418405053408e+01, 0.5636314030725e+00,
0.2329528932532e-08, 0.4069557545675e+01, 0.1056200952181e+01,
0.9698639532817e-09, 0.1074134313634e+01, 0.7826370942180e+02}
/* SSB-to-Sun, T^0, Y */
s0y := []float64{
0.4955392320126e-02, 0.2170467313679e+01, 0.5296909721118e+00,
0.2722325167392e-02, 0.2444433682196e+01, 0.2132990797783e+00,
0.1546579925346e-02, 0.5992779281546e+00, 0.3813291813120e-01,
0.8363140252966e-03, 0.7687356310801e+00, 0.7478166569050e-01,
0.3385792683603e-03, 0.0000000000000e+00, 0.0000000000000e+00,
0.1201192221613e-03, 0.2520035601514e+01, 0.1059381944224e+01,
0.7587125720554e-04, 0.1669954006449e+01, 0.4265981595566e+00,
0.1964155361250e-04, 0.5707743963343e+01, 0.2061856251104e+00,
0.1891900364909e-04, 0.2320960679937e+01, 0.2204125344462e+00,
0.1937373433356e-04, 0.3226940689555e+01, 0.1495633313810e+00,
0.1437139941351e-04, 0.2301626908096e+01, 0.5225775174439e+00,
0.1406267683099e-04, 0.5188579265542e+01, 0.5368044267797e+00,
0.1178703080346e-04, 0.5489483248476e+01, 0.7626583626240e-01,
0.8079835186041e-05, 0.1683751835264e+01, 0.3664874755930e-01,
0.7623253594652e-05, 0.2656400462961e+01, 0.3961708870310e-01,
0.6248667483971e-05, 0.4992775362055e+01, 0.7329749511860e-01,
0.4366353695038e-05, 0.2869706279678e+01, 0.1589072916335e+01,
0.3829101568895e-05, 0.3572131359950e+01, 0.7113454667900e-02,
0.3175733773908e-05, 0.4535372530045e+01, 0.4194847048887e+00,
0.3092437902159e-05, 0.9230153317909e+00, 0.6398972393349e+00,
0.2874168812154e-05, 0.3363143761101e+01, 0.1102062672231e+00,
0.3040119321826e-05, 0.3324250895675e+01, 0.6283075850446e+01,
0.2699723308006e-05, 0.2917882441928e+00, 0.1030928125552e+00,
0.2134832683534e-05, 0.4220997202487e+01, 0.3163918923335e+00,
0.1770412139433e-05, 0.4747318496462e+01, 0.1021328554739e+02,
0.1377264209373e-05, 0.4305058462401e+00, 0.1484170571900e-02,
0.1127814538960e-05, 0.8538177240740e+00, 0.6327837846670e+00,
0.1055608090130e-05, 0.1551800742580e+01, 0.4337116142245e+00,
0.9802673861420e-06, 0.1459646735377e+01, 0.1052268489556e+01,
0.1090329461951e-05, 0.1587351228711e+01, 0.1162474756779e+01,
0.6959590025090e-06, 0.5534442628766e+01, 0.1066495398892e+01,
0.5664914529542e-06, 0.6030673003297e+01, 0.9491756770005e+00,
0.6607787763599e-06, 0.4989507233927e+01, 0.8460828644453e+00,
0.6269725742838e-06, 0.4222951804572e+01, 0.1480791608091e+00,
0.6301889697863e-06, 0.5444316669126e+01, 0.2243449970715e+00,
0.4891042662861e-06, 0.1490552839784e+01, 0.3340612434717e+01,
0.3457083123290e-06, 0.3030475486049e+01, 0.3516457698740e-01,
0.3032559967314e-06, 0.2652038793632e+01, 0.1104591729320e-01,
0.2841133988903e-06, 0.1276744786829e+01, 0.4110125927500e-01,
0.2855564444432e-06, 0.2143368674733e+01, 0.1510475019529e+00,
0.2765157135038e-06, 0.5444186109077e+01, 0.6373574839730e-01,
0.2382312465034e-06, 0.2190521137593e+01, 0.2275259891141e+00,
0.2808060365077e-06, 0.5735195064841e+01, 0.2535050500000e-01,
0.2332175234405e-06, 0.9481985524859e-01, 0.7181332454670e-01,
0.2322488199659e-06, 0.5180499361533e+01, 0.8582758298370e-01,
0.1881850258423e-06, 0.3219788273885e+01, 0.2118763888447e+01,
0.2196111392808e-06, 0.2366941159761e+01, 0.2968341143800e-02,
0.2183810335519e-06, 0.4825445110915e+01, 0.7775000683430e-01,
0.2002733093326e-06, 0.2457148995307e+01, 0.2093666171530e+00,
0.1967111767229e-06, 0.5586291545459e+01, 0.2172315424036e+00,
0.1568473250543e-06, 0.3708003123320e+01, 0.7429900518901e+00,
0.1852528314300e-06, 0.4310638151560e+01, 0.2022531624851e+00,
0.1832111226447e-06, 0.1494665322656e+01, 0.3235053470014e+00,
0.1746805502310e-06, 0.1451378500784e+01, 0.1385174140878e+00,
0.1555730966650e-06, 0.1068040418198e+01, 0.7358765972222e+00,
0.1554883462559e-06, 0.2442579035461e+01, 0.5154640627760e+00,
0.1638380568746e-06, 0.2597913420625e+00, 0.8531963191132e+00,
0.1159938593640e-06, 0.5834512021280e+01, 0.1990721704425e+00,
0.1083427965695e-06, 0.5054033177950e+01, 0.5439178814476e+00,
0.1156480369431e-06, 0.5325677432457e+01, 0.5257585094865e+00,
0.1141308860095e-06, 0.2153403923857e+01, 0.5336234347371e+00,
0.7913146470946e-07, 0.8642846847027e+00, 0.1478866649112e+01,
0.7439752463733e-07, 0.1970628496213e+01, 0.2164800718209e+00,
0.7280277104079e-07, 0.6073307250609e+01, 0.2101180877357e+00,
0.8319567719136e-07, 0.1954371928334e+01, 0.1692165728891e+01,
0.7137705549290e-07, 0.8904989440909e+00, 0.4155522422634e+00,
0.6900825396225e-07, 0.2825717714977e+01, 0.1173197218910e+00,
0.7245757216635e-07, 0.2481677513331e+01, 0.1265567569334e+01,
0.6961165696255e-07, 0.1292955312978e+01, 0.9562891316684e+00,
0.7571804456890e-07, 0.3427517575069e+01, 0.1422690933580e-01,
0.6605425721904e-07, 0.8052192701492e+00, 0.6470106940028e+00,
0.7375477357248e-07, 0.1705076390088e+01, 0.1581959461667e+01,
0.7041664951470e-07, 0.4848356967891e+00, 0.9597935788730e-01,
0.6322199535763e-07, 0.3878069473909e+01, 0.7084920306520e-01,
0.5244380279191e-07, 0.2645560544125e+01, 0.5265099800692e+00,
0.5143125704988e-07, 0.4834486101370e+01, 0.5328719641544e+00,
0.5871866319373e-07, 0.7981472548900e+00, 0.7871412831580e-01,
0.6300822573871e-07, 0.5979398788281e+01, 0.2608790314060e+02,
0.6062154271548e-07, 0.4108655402756e+01, 0.1114304132498e+00,
0.4361912339976e-07, 0.5322624319280e+01, 0.1375773836557e+01,
0.4417005920067e-07, 0.6240817359284e+01, 0.2770348281756e+00,
0.4686806749936e-07, 0.3214977301156e+01, 0.1143987543936e+00,
0.3758892132305e-07, 0.5879809634765e+01, 0.1596186371003e+01,
0.5151351332319e-07, 0.2893377688007e+00, 0.2228608264996e+00,
0.4554683578572e-07, 0.5475427144122e+01, 0.1465949902372e+00,
0.3442381385338e-07, 0.5992034796640e+01, 0.5070101000000e-01,
0.2831093954933e-07, 0.5367350273914e+01, 0.3092784376656e+00,
0.3756267090084e-07, 0.5758171285420e+01, 0.4903339079539e+00,
0.2816374679892e-07, 0.1863718700923e+01, 0.2991266627620e+00,
0.3419307025569e-07, 0.9524347534130e+00, 0.3518164938661e+00,
0.2904250494239e-07, 0.5304471615602e+01, 0.1099462426779e+00,
0.2471734511206e-07, 0.1297069793530e+01, 0.6256703299991e+00,
0.2539620831872e-07, 0.3281126083375e+01, 0.1256615170089e+02,
0.2281017868007e-07, 0.1829122133165e+01, 0.6681224869435e+01,
0.2275319473335e-07, 0.5797198160181e+01, 0.3932462625300e-02,
0.2547755368442e-07, 0.4752697708330e+01, 0.1169588211447e+01,
0.2285979669317e-07, 0.1223205292886e+01, 0.1045155034888e+01,
0.1913386560994e-07, 0.1757532993389e+01, 0.1155361302111e+01,
0.1809020525147e-07, 0.4246116108791e+01, 0.3368040641550e-01,
0.1649213300201e-07, 0.1445162890627e+01, 0.4408250688924e+00,
0.1834972793932e-07, 0.1126917567225e+01, 0.4452511715700e-02,
0.1439550648138e-07, 0.6160756834764e+01, 0.9420622223326e+00,
0.1487645457041e-07, 0.4358761931792e+01, 0.4123712502208e+00,
0.1731729516660e-07, 0.6134456753344e+01, 0.2108507877249e+00,
0.1717747163567e-07, 0.1898186084455e+01, 0.2157473718317e+00,
0.1418190430374e-07, 0.4180286741266e+01, 0.6521991896920e-01,
0.1404844134873e-07, 0.7654053565412e-01, 0.4258542984690e-01,
0.1409842846538e-07, 0.4418612420312e+01, 0.2258291676434e+00,
0.1090948346291e-07, 0.1260615686131e+01, 0.4226656969313e+00,
0.1357577323612e-07, 0.3558248818690e+01, 0.7923417740620e-01,
0.1018154061960e-07, 0.5676087241256e+01, 0.1456308687557e+00,
0.1412073972109e-07, 0.8394392632422e+00, 0.1525316725248e+00,
0.1030938326496e-07, 0.1653593274064e+01, 0.1795258541446e+01,
0.1180081567104e-07, 0.1285802592036e+01, 0.7032915397480e-01,
0.9708510575650e-08, 0.7631889488106e+00, 0.8434341241180e-01,
0.9637689663447e-08, 0.4630642649176e+01, 0.1272681024002e+01,
0.1068910429389e-07, 0.5294934032165e+01, 0.2123349582968e+00,
0.1063716179336e-07, 0.2736266800832e+01, 0.2142632012598e+00,
0.1234858713814e-07, 0.1302891146570e+01, 0.1847279083684e+00,
0.8912631189738e-08, 0.3570415993621e+01, 0.2648454860559e+01,
0.1036378285534e-07, 0.4236693440949e+01, 0.1370332435159e+00,
0.9667798501561e-08, 0.2960768892398e+01, 0.4376440768498e+00,
0.8108314201902e-08, 0.6987781646841e+00, 0.2880807454688e+00,
0.7648364324628e-08, 0.2499017863863e+01, 0.2037373330570e+00,
0.7286136828406e-08, 0.3787426951665e+01, 0.1129145838217e+00,
0.9448237743913e-08, 0.2694354332983e+01, 0.5272426800584e+00,
0.9374276106428e-08, 0.4787121277064e+01, 0.5321392641652e+00,
0.7100226287462e-08, 0.3530238792101e+00, 0.6288513220417e+00,
0.9253056659571e-08, 0.1399478925664e+01, 0.1606092486742e+00,
0.6636432145504e-08, 0.3479575438447e+01, 0.1368660381889e+01,
0.6469975312932e-08, 0.1383669964800e+01, 0.2008557621224e+01,
0.7335849729765e-08, 0.1243698166898e+01, 0.9561746721300e-02,
0.8743421205855e-08, 0.3776164289301e+01, 0.3801276407308e+00,
0.5993635744494e-08, 0.5627122113596e+01, 0.2042657109477e+02,
0.5981008479693e-08, 0.1674336636752e+01, 0.2111650433779e+01,
0.6188535145838e-08, 0.5214925208672e+01, 0.4305306221819e+00,
0.6596074017566e-08, 0.2907653268124e+01, 0.1063314406849e+01,
0.6630815126226e-08, 0.2127643669658e+01, 0.8389694097774e+00,
0.6156772830040e-08, 0.5082160803295e+01, 0.4234171675140e+00,
0.6446960563014e-08, 0.1872100916905e+01, 0.5287268506303e+00,
0.6429324424668e-08, 0.5610276103577e+01, 0.5306550935933e+00,
0.6302232396465e-08, 0.1592152049607e+01, 0.1253008786510e-01,
0.6399244436159e-08, 0.2746214421532e+01, 0.5217580628120e+02,
0.5474965172558e-08, 0.2317666374383e+01, 0.2221856701002e+01,
0.5339293190692e-08, 0.1084724961156e+01, 0.7466759693650e-01,
0.5334733683389e-08, 0.3594106067745e+01, 0.7489573444450e-01,
0.5392665782110e-08, 0.5630254365606e+01, 0.1055449481598e+01,
0.6682075673789e-08, 0.1518480041732e+01, 0.2213766559277e+00,
0.5079130495960e-08, 0.2739765115711e+01, 0.2132517061319e+00,
0.5077759793261e-08, 0.5290711290094e+01, 0.2133464534247e+00,
0.4832037368310e-08, 0.1404473217200e+01, 0.7160067364790e-01,
0.6463279674802e-08, 0.6038381695210e+01, 0.2209183458640e-01,
0.6240592771560e-08, 0.1290170653666e+01, 0.3306188016693e+00,
0.4672013521493e-08, 0.3261895939677e+01, 0.7796265773310e-01,
0.6500650750348e-08, 0.1154522312095e+01, 0.3884652414254e+00,
0.6344161389053e-08, 0.6206111545062e+01, 0.7605151500000e-01,
0.4682518370646e-08, 0.5409118796685e+01, 0.1073608853559e+01,
0.5329460015591e-08, 0.1202985784864e+01, 0.7287631425543e+00,
0.5701588675898e-08, 0.4098715257064e+01, 0.8731175355560e-01,
0.6030690867211e-08, 0.4132033218460e+00, 0.9846002785331e+00,
0.4336256312655e-08, 0.1211415991827e+01, 0.4297791515992e+00,
0.4688498808975e-08, 0.3765479072409e+01, 0.2127790306879e+00,
0.4675578609335e-08, 0.4265540037226e+01, 0.2138191288687e+00,
0.4225578112158e-08, 0.5237566010676e+01, 0.3407705765729e+00,
0.5139422230028e-08, 0.1507173079513e+01, 0.7233337363710e-01,
0.4619995093571e-08, 0.9023957449848e-01, 0.8603097737811e+00,
0.4494776255461e-08, 0.5414930552139e+00, 0.7381754420900e-01,
0.4274026276788e-08, 0.4145735303659e+01, 0.7574578717200e-01,
0.5018141789353e-08, 0.3344408829055e+01, 0.3180992042600e-02,
0.4866163952181e-08, 0.3348534657607e+01, 0.7722995774390e-01,
0.4111986020501e-08, 0.4198823597220e+00, 0.1451108196653e+00,
0.3356142784950e-08, 0.5609144747180e+01, 0.1274714967946e+00,
0.4070575554551e-08, 0.7028411059224e+00, 0.3503323232942e+00,
0.3257451857278e-08, 0.5624697983086e+01, 0.5296435984654e+00,
0.3256973703026e-08, 0.1857842076707e+01, 0.5297383457582e+00,
0.3830771508640e-08, 0.4562887279931e+01, 0.9098186128426e+00,
0.3725024005962e-08, 0.2358058692652e+00, 0.1084620721060e+00,
0.3136763921756e-08, 0.2049731526845e+01, 0.2346394437820e+00,
0.3795147256194e-08, 0.2432356296933e+00, 0.1862120789403e+00,
0.2877342229911e-08, 0.5631101279387e+01, 0.1905464808669e+01,
0.3076931798805e-08, 0.1117615737392e+01, 0.3628624111593e+00,
0.2734765945273e-08, 0.5899826516955e+01, 0.2131850110243e+00,
0.2733405296885e-08, 0.2130562964070e+01, 0.2134131485323e+00,
0.2898552353410e-08, 0.3462387048225e+00, 0.5291709230214e+00,
0.2893736103681e-08, 0.8534352781543e+00, 0.5302110212022e+00,
0.3095717734137e-08, 0.2875061429041e+01, 0.2976424921901e+00,
0.2636190425832e-08, 0.2242512846659e+01, 0.1485980103780e+01,
0.3645512095537e-08, 0.1354016903958e+01, 0.6044726378023e+00,
0.2808173547723e-08, 0.6705114365631e-01, 0.6225157782540e-01,
0.2625012866888e-08, 0.4775705748482e+01, 0.5268983110410e-01,
0.2572233995651e-08, 0.2638924216139e+01, 0.1258454114666e+01,
0.2604238824792e-08, 0.4826358927373e+01, 0.2103781122809e+00,
0.2596886385239e-08, 0.3200388483118e+01, 0.2162200472757e+00,
0.3228057304264e-08, 0.5384848409563e+01, 0.2007689919132e+00,
0.2481601798252e-08, 0.5173373487744e+01, 0.1062562936266e+01,
0.2745977498864e-08, 0.6250966149853e+01, 0.5651155736444e+00,
0.2669878833811e-08, 0.4906001352499e+01, 0.1400015846597e+00,
0.3203986611711e-08, 0.5034333010005e+01, 0.7036329877322e+00,
0.3354961227212e-08, 0.6108262423137e+01, 0.4549093064213e+00,
0.2400407324558e-08, 0.2135399294955e+01, 0.2125476091956e+00,
0.2379905859802e-08, 0.5893721933961e+01, 0.2140505503610e+00,
0.2550844302187e-08, 0.3331940762063e+01, 0.1534957940063e+00,
0.2268824211001e-08, 0.1843418461035e+01, 0.2235935264888e+00,
0.2464700891204e-08, 0.3029548547230e+01, 0.2091065926078e+00,
0.2436814726024e-08, 0.4994717970364e+01, 0.2174915669488e+00,
0.2443623894745e-08, 0.2645102591375e+01, 0.1739420156204e+00,
0.2318701783838e-08, 0.5700547397897e+01, 0.7530171478090e-01,
0.2284448700256e-08, 0.5268898905872e+01, 0.7426161660010e-01,
0.2468848123510e-08, 0.5276280575078e+01, 0.2526561439362e+00,
0.2814052350303e-08, 0.6130168623475e+01, 0.5636314030725e+00,
0.2243662755220e-08, 0.6631692457995e+00, 0.8886590321940e-01,
0.2330795855941e-08, 0.2499435487702e+01, 0.1056200952181e+01,
0.9757679038404e-09, 0.5796846023126e+01, 0.7826370942180e+02}
/* SSB-to-Sun, T^0, Z */
s0z := []float64{
0.1181255122986e-03, 0.4607918989164e+00, 0.2132990797783e+00,
0.1127777651095e-03, 0.4169146331296e+00, 0.5296909721118e+00,
0.4777754401806e-04, 0.4582657007130e+01, 0.3813291813120e-01,
0.1129354285772e-04, 0.5758735142480e+01, 0.7478166569050e-01,
-0.1149543637123e-04, 0.0000000000000e+00, 0.0000000000000e+00,
0.3298730512306e-05, 0.5978801994625e+01, 0.4265981595566e+00,
0.2733376706079e-05, 0.7665413691040e+00, 0.1059381944224e+01,
0.9426389657270e-06, 0.3710201265838e+01, 0.2061856251104e+00,
0.8187517749552e-06, 0.3390675605802e+00, 0.2204125344462e+00,
0.4080447871819e-06, 0.4552296640088e+00, 0.5225775174439e+00,
0.3169973017028e-06, 0.3445455899321e+01, 0.5368044267797e+00,
0.2438098615549e-06, 0.5664675150648e+01, 0.3664874755930e-01,
0.2601897517235e-06, 0.1931894095697e+01, 0.1495633313810e+00,
0.2314558080079e-06, 0.3666319115574e+00, 0.3961708870310e-01,
0.1962549548002e-06, 0.3167411699020e+01, 0.7626583626240e-01,
0.2180518287925e-06, 0.1544420746580e+01, 0.7113454667900e-02,
0.1451382442868e-06, 0.1583756740070e+01, 0.1102062672231e+00,
0.1358439007389e-06, 0.5239941758280e+01, 0.6398972393349e+00,
0.1050585898028e-06, 0.2266958352859e+01, 0.3163918923335e+00,
0.1050029870186e-06, 0.2711495250354e+01, 0.4194847048887e+00,
0.9934920679800e-07, 0.1116208151396e+01, 0.1589072916335e+01,
0.1048395331560e-06, 0.3408619600206e+01, 0.1021328554739e+02,
0.8370147196668e-07, 0.3810459401087e+01, 0.2535050500000e-01,
0.7989856510998e-07, 0.3769910473647e+01, 0.7329749511860e-01,
0.5441221655233e-07, 0.2416994903374e+01, 0.1030928125552e+00,
0.4610812906784e-07, 0.5858503336994e+01, 0.4337116142245e+00,
0.3923022803444e-07, 0.3354170010125e+00, 0.1484170571900e-02,
0.2610725582128e-07, 0.5410600646324e+01, 0.6327837846670e+00,
0.2455279767721e-07, 0.6120216681403e+01, 0.1162474756779e+01,
0.2375530706525e-07, 0.6055443426143e+01, 0.1052268489556e+01,
0.1782967577553e-07, 0.3146108708004e+01, 0.8460828644453e+00,
0.1581687095238e-07, 0.6255496089819e+00, 0.3340612434717e+01,
0.1594657672461e-07, 0.3782604300261e+01, 0.1066495398892e+01,
0.1563448615040e-07, 0.1997775733196e+01, 0.2022531624851e+00,
0.1463624258525e-07, 0.1736316792088e+00, 0.3516457698740e-01,
0.1331585056673e-07, 0.4331941830747e+01, 0.9491756770005e+00,
0.1130634557637e-07, 0.6152017751825e+01, 0.2968341143800e-02,
0.1028949607145e-07, 0.2101792614637e+00, 0.2275259891141e+00,
0.1024074971618e-07, 0.4071833211074e+01, 0.5070101000000e-01,
0.8826956060303e-08, 0.4861633688145e+00, 0.2093666171530e+00,
0.8572230171541e-08, 0.5268190724302e+01, 0.4110125927500e-01,
0.7649332643544e-08, 0.5134543417106e+01, 0.2608790314060e+02,
0.8581673291033e-08, 0.2920218146681e+01, 0.1480791608091e+00,
0.8430589300938e-08, 0.3604576619108e+01, 0.2172315424036e+00,
0.7776165501012e-08, 0.3772942249792e+01, 0.6373574839730e-01,
0.8311070234408e-08, 0.6200412329888e+01, 0.3235053470014e+00,
0.6927365212582e-08, 0.4543353113437e+01, 0.8531963191132e+00,
0.6791574208598e-08, 0.2882188406238e+01, 0.7181332454670e-01,
0.5593100811839e-08, 0.1776646892780e+01, 0.7429900518901e+00,
0.4553381853021e-08, 0.3949617611240e+01, 0.7775000683430e-01,
0.5758000450068e-08, 0.3859251775075e+01, 0.1990721704425e+00,
0.4281283457133e-08, 0.1466294631206e+01, 0.2118763888447e+01,
0.4206935661097e-08, 0.5421776011706e+01, 0.1104591729320e-01,
0.4213751641837e-08, 0.3412048993322e+01, 0.2243449970715e+00,
0.5310506239878e-08, 0.5421641370995e+00, 0.5154640627760e+00,
0.3827450341320e-08, 0.8887314524995e+00, 0.1510475019529e+00,
0.4292435241187e-08, 0.1405043757194e+01, 0.1422690933580e-01,
0.3189780702289e-08, 0.1060049293445e+01, 0.1173197218910e+00,
0.3226611928069e-08, 0.6270858897442e+01, 0.2164800718209e+00,
0.2893897608830e-08, 0.5117563223301e+01, 0.6470106940028e+00,
0.3239852024578e-08, 0.4079092237983e+01, 0.2101180877357e+00,
0.2956892222200e-08, 0.1594917021704e+01, 0.3092784376656e+00,
0.2980177912437e-08, 0.5258787667564e+01, 0.4155522422634e+00,
0.3163725690776e-08, 0.3854589225479e+01, 0.8582758298370e-01,
0.2662262399118e-08, 0.3561326430187e+01, 0.5257585094865e+00,
0.2766689135729e-08, 0.3180732086830e+00, 0.1385174140878e+00,
0.2411600278464e-08, 0.3324798335058e+01, 0.5439178814476e+00,
0.2483527695131e-08, 0.4169069291947e+00, 0.5336234347371e+00,
0.7788777276590e-09, 0.1900569908215e+01, 0.5217580628120e+02}
/* SSB-to-Sun, T^1, X */
s1x := []float64{
-0.1296310361520e-07, 0.0000000000000e+00, 0.0000000000000e+00,
0.8975769009438e-08, 0.1128891609250e+01, 0.4265981595566e+00,
0.7771113441307e-08, 0.2706039877077e+01, 0.2061856251104e+00,
0.7538303866642e-08, 0.2191281289498e+01, 0.2204125344462e+00,
0.6061384579336e-08, 0.3248167319958e+01, 0.1059381944224e+01,
0.5726994235594e-08, 0.5569981398610e+01, 0.5225775174439e+00,
0.5616492836424e-08, 0.5057386614909e+01, 0.5368044267797e+00,
0.1010881584769e-08, 0.3473577116095e+01, 0.7113454667900e-02,
0.7259606157626e-09, 0.3651858593665e+00, 0.6398972393349e+00,
0.8755095026935e-09, 0.1662835408338e+01, 0.4194847048887e+00,
0.5370491182812e-09, 0.1327673878077e+01, 0.4337116142245e+00,
0.5743773887665e-09, 0.4250200846687e+01, 0.2132990797783e+00,
0.4408103140300e-09, 0.3598752574277e+01, 0.1589072916335e+01,
0.3101892374445e-09, 0.4887822983319e+01, 0.1052268489556e+01,
0.3209453713578e-09, 0.9702272295114e+00, 0.5296909721118e+00,
0.3017228286064e-09, 0.5484462275949e+01, 0.1066495398892e+01,
0.3200700038601e-09, 0.2846613338643e+01, 0.1495633313810e+00,
0.2137637279911e-09, 0.5692163292729e+00, 0.3163918923335e+00,
0.1899686386727e-09, 0.2061077157189e+01, 0.2275259891141e+00,
0.1401994545308e-09, 0.4177771136967e+01, 0.1102062672231e+00,
0.1578057810499e-09, 0.5782460597335e+01, 0.7626583626240e-01,
0.1237713253351e-09, 0.5705900866881e+01, 0.5154640627760e+00,
0.1313076837395e-09, 0.5163438179576e+01, 0.3664874755930e-01,
0.1184963304860e-09, 0.3054804427242e+01, 0.6327837846670e+00,
0.1238130878565e-09, 0.2317292575962e+01, 0.3961708870310e-01,
0.1015959527736e-09, 0.2194643645526e+01, 0.7329749511860e-01,
0.9017954423714e-10, 0.2868603545435e+01, 0.1990721704425e+00,
0.8668024955603e-10, 0.4923849675082e+01, 0.5439178814476e+00,
0.7756083930103e-10, 0.3014334135200e+01, 0.9491756770005e+00,
0.7536503401741e-10, 0.2704886279769e+01, 0.1030928125552e+00,
0.5483308679332e-10, 0.6010983673799e+01, 0.8531963191132e+00,
0.5184339620428e-10, 0.1952704573291e+01, 0.2093666171530e+00,
0.5108658712030e-10, 0.2958575786649e+01, 0.2172315424036e+00,
0.5019424524650e-10, 0.1736317621318e+01, 0.2164800718209e+00,
0.4909312625978e-10, 0.3167216416257e+01, 0.2101180877357e+00,
0.4456638901107e-10, 0.7697579923471e+00, 0.3235053470014e+00,
0.4227030350925e-10, 0.3490910137928e+01, 0.6373574839730e-01,
0.4095456040093e-10, 0.5178888984491e+00, 0.6470106940028e+00,
0.4990537041422e-10, 0.3323887668974e+01, 0.1422690933580e-01,
0.4321170010845e-10, 0.4288484987118e+01, 0.7358765972222e+00,
0.3544072091802e-10, 0.6021051579251e+01, 0.5265099800692e+00,
0.3480198638687e-10, 0.4600027054714e+01, 0.5328719641544e+00,
0.3440287244435e-10, 0.4349525970742e+01, 0.8582758298370e-01,
0.3330628322713e-10, 0.2347391505082e+01, 0.1104591729320e-01,
0.2973060707184e-10, 0.4789409286400e+01, 0.5257585094865e+00,
0.2932606766089e-10, 0.5831693799927e+01, 0.5336234347371e+00,
0.2876972310953e-10, 0.2692638514771e+01, 0.1173197218910e+00,
0.2827488278556e-10, 0.2056052487960e+01, 0.2022531624851e+00,
0.2515028239756e-10, 0.7411863262449e+00, 0.9597935788730e-01,
0.2853033744415e-10, 0.3948481024894e+01, 0.2118763888447e+01}
/* SSB-to-Sun, T^1, Y */
s1y := []float64{
0.8989047573576e-08, 0.5840593672122e+01, 0.4265981595566e+00,
0.7815938401048e-08, 0.1129664707133e+01, 0.2061856251104e+00,
0.7550926713280e-08, 0.6196589104845e+00, 0.2204125344462e+00,
0.6056556925895e-08, 0.1677494667846e+01, 0.1059381944224e+01,
0.5734142698204e-08, 0.4000920852962e+01, 0.5225775174439e+00,
0.5614341822459e-08, 0.3486722577328e+01, 0.5368044267797e+00,
0.1028678147656e-08, 0.1877141024787e+01, 0.7113454667900e-02,
0.7270792075266e-09, 0.5077167301739e+01, 0.6398972393349e+00,
0.8734141726040e-09, 0.9069550282609e-01, 0.4194847048887e+00,
0.5377371402113e-09, 0.6039381844671e+01, 0.4337116142245e+00,
0.4729719431571e-09, 0.2153086311760e+01, 0.2132990797783e+00,
0.4458052820973e-09, 0.5059830025565e+01, 0.5296909721118e+00,
0.4406855467908e-09, 0.2027971692630e+01, 0.1589072916335e+01,
0.3101659310977e-09, 0.3317677981860e+01, 0.1052268489556e+01,
0.3016749232545e-09, 0.3913703482532e+01, 0.1066495398892e+01,
0.3198541352656e-09, 0.1275513098525e+01, 0.1495633313810e+00,
0.2142065389871e-09, 0.5301351614597e+01, 0.3163918923335e+00,
0.1902615247592e-09, 0.4894943352736e+00, 0.2275259891141e+00,
0.1613410990871e-09, 0.2449891130437e+01, 0.1102062672231e+00,
0.1576992165097e-09, 0.4211421447633e+01, 0.7626583626240e-01,
0.1241637259894e-09, 0.4140803368133e+01, 0.5154640627760e+00,
0.1313974830355e-09, 0.3591920305503e+01, 0.3664874755930e-01,
0.1181697118258e-09, 0.1506314382788e+01, 0.6327837846670e+00,
0.1238239742779e-09, 0.7461405378404e+00, 0.3961708870310e-01,
0.1010107068241e-09, 0.6271010795475e+00, 0.7329749511860e-01,
0.9226316616509e-10, 0.1259158839583e+01, 0.1990721704425e+00,
0.8664946419555e-10, 0.3353244696934e+01, 0.5439178814476e+00,
0.7757230468978e-10, 0.1447677295196e+01, 0.9491756770005e+00,
0.7693168628139e-10, 0.1120509896721e+01, 0.1030928125552e+00,
0.5487897454612e-10, 0.4439380426795e+01, 0.8531963191132e+00,
0.5196118677218e-10, 0.3788856619137e+00, 0.2093666171530e+00,
0.5110853339935e-10, 0.1386879372016e+01, 0.2172315424036e+00,
0.5027804534813e-10, 0.1647881805466e+00, 0.2164800718209e+00,
0.4922485922674e-10, 0.1594315079862e+01, 0.2101180877357e+00,
0.6155599524400e-10, 0.0000000000000e+00, 0.0000000000000e+00,
0.4447147832161e-10, 0.5480720918976e+01, 0.3235053470014e+00,
0.4144691276422e-10, 0.1931371033660e+01, 0.6373574839730e-01,
0.4099950625452e-10, 0.5229611294335e+01, 0.6470106940028e+00,
0.5060541682953e-10, 0.1731112486298e+01, 0.1422690933580e-01,
0.4293615946300e-10, 0.2714571038925e+01, 0.7358765972222e+00,
0.3545659845763e-10, 0.4451041444634e+01, 0.5265099800692e+00,
0.3479112041196e-10, 0.3029385448081e+01, 0.5328719641544e+00,
0.3438516493570e-10, 0.2778507143731e+01, 0.8582758298370e-01,
0.3297341285033e-10, 0.7898709807584e+00, 0.1104591729320e-01,
0.2972585818015e-10, 0.3218785316973e+01, 0.5257585094865e+00,
0.2931707295017e-10, 0.4260731012098e+01, 0.5336234347371e+00,
0.2897198149403e-10, 0.1120753978101e+01, 0.1173197218910e+00,
0.2832293240878e-10, 0.4597682717827e+00, 0.2022531624851e+00,
0.2864348326612e-10, 0.2169939928448e+01, 0.9597935788730e-01,
0.2852714675471e-10, 0.2377659870578e+01, 0.2118763888447e+01}
/* SSB-to-Sun, T^1, Z */
s1z := []float64{
0.5444220475678e-08, 0.1803825509310e+01, 0.2132990797783e+00,
0.3883412695596e-08, 0.4668616389392e+01, 0.5296909721118e+00,
0.1334341434551e-08, 0.0000000000000e+00, 0.0000000000000e+00,
0.3730001266883e-09, 0.5401405918943e+01, 0.2061856251104e+00,
0.2894929197956e-09, 0.4932415609852e+01, 0.2204125344462e+00,
0.2857950357701e-09, 0.3154625362131e+01, 0.7478166569050e-01,
0.2499226432292e-09, 0.3657486128988e+01, 0.4265981595566e+00,
0.1937705443593e-09, 0.5740434679002e+01, 0.1059381944224e+01,
0.1374894396320e-09, 0.1712857366891e+01, 0.5368044267797e+00,
0.1217248678408e-09, 0.2312090870932e+01, 0.5225775174439e+00,
0.7961052740870e-10, 0.5283368554163e+01, 0.3813291813120e-01,
0.4979225949689e-10, 0.4298290471860e+01, 0.4194847048887e+00,
0.4388552286597e-10, 0.6145515047406e+01, 0.7113454667900e-02,
0.2586835212560e-10, 0.3019448001809e+01, 0.6398972393349e+00}
/* SSB-to-Sun, T^2, X */
s2x := []float64{
0.1603551636587e-11, 0.4404109410481e+01, 0.2061856251104e+00,
0.1556935889384e-11, 0.4818040873603e+00, 0.2204125344462e+00,
0.1182594414915e-11, 0.9935762734472e+00, 0.5225775174439e+00,
0.1158794583180e-11, 0.3353180966450e+01, 0.5368044267797e+00,
0.9597358943932e-12, 0.5567045358298e+01, 0.2132990797783e+00,
0.6511516579605e-12, 0.5630872420788e+01, 0.4265981595566e+00,
0.7419792747688e-12, 0.2156188581957e+01, 0.5296909721118e+00,
0.3951972655848e-12, 0.1981022541805e+01, 0.1059381944224e+01,
0.4478223877045e-12, 0.0000000000000e+00, 0.0000000000000e+00}
/* SSB-to-Sun, T^2, Y */
s2y := []float64{
0.1609114495091e-11, 0.2831096993481e+01, 0.2061856251104e+00,
0.1560330784946e-11, 0.5193058213906e+01, 0.2204125344462e+00,
0.1183535479202e-11, 0.5707003443890e+01, 0.5225775174439e+00,
0.1158183066182e-11, 0.1782400404928e+01, 0.5368044267797e+00,
0.1032868027407e-11, 0.4036925452011e+01, 0.2132990797783e+00,
0.6540142847741e-12, 0.4058241056717e+01, 0.4265981595566e+00,
0.7305236491596e-12, 0.6175401942957e+00, 0.5296909721118e+00,
-0.5580725052968e-12, 0.0000000000000e+00, 0.0000000000000e+00,
0.3946122651015e-12, 0.4108265279171e+00, 0.1059381944224e+01}
/* SSB-to-Sun, T^2, Z */
s2z := []float64{
0.3749920358054e-12, 0.3230285558668e+01, 0.2132990797783e+00,
0.2735037220939e-12, 0.6154322683046e+01, 0.5296909721118e+00}
/* Pointers to coefficient arrays, in x,y,z sets */
ce0 := [3][]float64{e0x, e0y, e0z}
ce1 := [3][]float64{e1x, e1y, e1z}
ce2 := [3][]float64{e2x, e2y, e2z}
cs0 := [3][]float64{s0x, s0y, s0z}
cs1 := [3][]float64{s1x, s1y, s1z}
cs2 := [3][]float64{s2x, s2y, s2z}
// const double *coeffs;
var coeffs *[]float64
/* Numbers of terms for each component of the model, in x,y,z sets */
ne0 := [3]int{len(e0x) / 3, len(e0y) / 3, len(e0z) / 3}
ne1 := [3]int{len(e1x) / 3, len(e1y) / 3, len(e1z) / 3}
ne2 := [3]int{len(e2x) / 3, len(e2y) / 3, len(e2z) / 3}
ns0 := [3]int{len(s0x) / 3, len(s0y) / 3, len(s0z) / 3}
ns1 := [3]int{len(s1x) / 3, len(s1y) / 3, len(s1z) / 3}
ns2 := [3]int{len(s2x) / 3, len(s2y) / 3, len(s2z) / 3}
var nterms int
/* Miscellaneous */
var jstat, i, j int
var t, t2, xyz, xyzd, a, b, c, ct, p, cp float64
var ph, vh, pb, vb [3]float64
var x, y, z float64
/* ------------------------------------------------------------------ */
/* Time since reference epoch, Julian years. */
t = ((date1 - DJ00) + date2) / DJY
t2 = t * t
/* Set status. */
// jstat = fabs(t) <= 100.0 ? 0 : 1;
if fabs(t) <= 100.0 {
jstat = 0
} else {
jstat = 1
}
/* X then Y then Z. */
for i = 0; i < 3; i++ {
/* Initialize position and velocity component. */
xyz = 0.0
xyzd = 0.0
/* ------------------------------------------------ */
/* Obtain component of Sun to Earth ecliptic vector */
/* ------------------------------------------------ */
/* Sun to Earth, T^0 terms. */
coeffs = &ce0[i]
nterms = ne0[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
p = b + c*t
xyz += a * cos(p)
xyzd -= a * c * sin(p)
}
/* Sun to Earth, T^1 terms. */
coeffs = &ce1[i]
nterms = ne1[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
ct = c * t
p = b + ct
cp = cos(p)
xyz += a * t * cp
xyzd += a * (cp - ct*sin(p))
}
/* Sun to Earth, T^2 terms. */
coeffs = &ce2[i]
nterms = ne2[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
ct = c * t
p = b + ct
cp = cos(p)
xyz += a * t2 * cp
xyzd += a * t * (2.0*cp - ct*sin(p))
}
/* Heliocentric Earth position and velocity component. */
ph[i] = xyz
vh[i] = xyzd / DJY
/* ------------------------------------------------ */
/* Obtain component of SSB to Earth ecliptic vector */
/* ------------------------------------------------ */
/* SSB to Sun, T^0 terms. */
coeffs = &cs0[i]
nterms = ns0[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
p = b + c*t
xyz += a * cos(p)
xyzd -= a * c * sin(p)
}
/* SSB to Sun, T^1 terms. */
coeffs = &cs1[i]
nterms = ns1[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
ct = c * t
p = b + ct
cp = cos(p)
xyz += a * t * cp
xyzd += a * (cp - ct*sin(p))
}
/* SSB to Sun, T^2 terms. */
coeffs = &cs2[i]
nterms = ns2[i]
for j = 0; j < nterms; j++ {
a = (*coeffs)[j*3]
b = (*coeffs)[j*3+1]
c = (*coeffs)[j*3+2]
ct = c * t
p = b + ct
cp = cos(p)
xyz += a * t2 * cp
xyzd += a * t * (2.0*cp - ct*sin(p))
}
/* Barycentric Earth position and velocity component. */
pb[i] = xyz
vb[i] = xyzd / DJY
/* Next Cartesian component. */
}
/* Rotate from ecliptic to BCRS coordinates. */
x = ph[0]
y = ph[1]
z = ph[2]
pvh[0][0] = x + am12*y + am13*z
pvh[0][1] = am21*x + am22*y + am23*z
pvh[0][2] = am32*y + am33*z
x = vh[0]
y = vh[1]
z = vh[2]
pvh[1][0] = x + am12*y + am13*z
pvh[1][1] = am21*x + am22*y + am23*z
pvh[1][2] = am32*y + am33*z
x = pb[0]
y = pb[1]
z = pb[2]
pvb[0][0] = x + am12*y + am13*z
pvb[0][1] = am21*x + am22*y + am23*z
pvb[0][2] = am32*y + am33*z
x = vb[0]
y = vb[1]
z = vb[2]
pvb[1][0] = x + am12*y + am13*z
pvb[1][1] = am21*x + am22*y + am23*z
pvb[1][2] = am32*y + am33*z
/* Return the status. */
return jstat
}
/*
Moon98 Moon geocentric position and velocity
Approximate geocentric position and velocity of the Moon.
Given:
date1 float64 TT date part A (Notes 1,4)
date2 float64 TT date part B (Notes 1,4)
Returned:
pv [2][3]float64 Moon p,v, GCRS (AU, AU/d, Note 5)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. The limited
accuracy of the present algorithm is such that any of the methods
is satisfactory.
2) This function is a full implementation of the algorithm
published by Meeus (see reference) except that the light-time
correction to the Moon's mean longitude has been omitted.
3) Comparisons with ELP/MPP02 over the interval 1950-2100 gave RMS
errors of 2.9 arcsec in geocentric direction, 6.1 km in position
and 36 mm/s in velocity. The worst case errors were 18.3 arcsec
in geocentric direction, 31.7 km in position and 172 mm/s in
velocity.
4) The original algorithm is expressed in terms of "dynamical time",
which can either be TDB or TT without any significant change in
accuracy. UT cannot be used without incurring significant errors
(30 arcsec in the present era) due to the Moon's 0.5 arcsec/sec
movement.
5) The result is with respect to the GCRS (the same as J2000.0 mean
equator and equinox to within 23 mas).
6) Velocity is obtained by a complete analytical differentiation
of the Meeus model.
7) The Meeus algorithm generates position and velocity in mean
ecliptic coordinates of date, which the present function then
rotates into GCRS. Because the ecliptic system is precessing,
there is a coupling between this spin (about 1.4 degrees per
century) and the Moon position that produces a small velocity
contribution. In the present function this effect is neglected
as it corresponds to a maximum difference of less than 3 mm/s and
increases the RMS error by only 0.4%.
References:
Meeus, J., Astronomical Algorithms, 2nd edition, Willmann-Bell,
1998, p337.
Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663
Defined in sofam.go:
DAU astronomical unit (m)
DJC days per Julian century
DJ00 reference epoch (J2000.0), Julian Date
DD2R degrees to radians
Called:
S2pv spherical coordinates to pv-vector
Pfw06 bias-precession F-W angles, IAU 2006
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Rx rotate around X-axis
Rxpv product of r-matrix and pv-vector
*/
func Moon98(date1, date2 float64, pv *[2][3]float64) {
/*
Coefficients for fundamental arguments:
. Powers of time in Julian centuries
. Units are degrees.
*/
/* Moon's mean longitude (wrt mean equinox and ecliptic of date) */
const elp0 = 218.31665436 /* Simon et al. (1994). */
const elp1 = 481267.88123421
const elp2 = -0.0015786
const elp3 = 1.0 / 538841.0
const elp4 = -1.0 / 65194000.0
var elp, delp float64
/* Moon's mean elongation */
const d0 = 297.8501921
const d1 = 445267.1114034
const d2 = -0.0018819
const d3 = 1.0 / 545868.0
const d4 = 1.0 / 113065000.0
var d, dd float64
/* Sun's mean anomaly */
const em0 = 357.5291092
const em1 = 35999.0502909
const em2 = -0.0001536
const em3 = 1.0 / 24490000.0
const em4 = 0.0
var em, dem float64
/* Moon's mean anomaly */
const emp0 = 134.9633964
const emp1 = 477198.8675055
const emp2 = 0.0087414
const emp3 = 1.0 / 69699.0
const emp4 = -1.0 / 14712000.0
var emp, demp float64
/* Mean distance of the Moon from its ascending node */
const f0 = 93.2720950
const f1 = 483202.0175233
const f2 = -0.0036539
const f3 = 1.0 / 3526000.0
const f4 = 1.0 / 863310000.0
var f, df float64
/*
Other arguments
*/
/* Meeus A_1, due to Venus (deg) */
const a10 = 119.75
const a11 = 131.849
var a1, da1 float64
/* Meeus A_2, due to Jupiter (deg) */
const a20 = 53.09
const a21 = 479264.290
var a2, da2 float64
/* Meeus A_3, due to sidereal motion of the Moon in longitude (deg) */
const a30 = 313.45
const a31 = 481266.484
var a3, da3 float64
/* Coefficients for Meeus "additive terms" (deg) */
const al1 = 0.003958
const al2 = 0.001962
const al3 = 0.000318
const ab1 = -0.002235
const ab2 = 0.000382
const ab3 = 0.000175
const ab4 = 0.000175
const ab5 = 0.000127
const ab6 = -0.000115
/* Fixed term in distance (m) */
const r0 = 385000560.0
/* Coefficients for (dimensionless) E factor */
const (
e1 = -0.002516
e2 = -0.0000074
)
var e, de, esq, desq float64
/*
Coefficients for Moon longitude and distance series
*/
type termlr struct {
nd int /* multiple of D in argument */
nem int /* " " M " " */
nemp int /* " " M' " " */
nf int /* " " F " " */
coefl float64 /* coefficient of L sine argument (deg) */
coefr float64 /* coefficient of R cosine argument (m) */
}
tlr := []termlr{{0, 0, 1, 0, 6.288774, -20905355.0},
{2, 0, -1, 0, 1.274027, -3699111.0},
{2, 0, 0, 0, 0.658314, -2955968.0},
{0, 0, 2, 0, 0.213618, -569925.0},
{0, 1, 0, 0, -0.185116, 48888.0},
{0, 0, 0, 2, -0.114332, -3149.0},
{2, 0, -2, 0, 0.058793, 246158.0},
{2, -1, -1, 0, 0.057066, -152138.0},
{2, 0, 1, 0, 0.053322, -170733.0},
{2, -1, 0, 0, 0.045758, -204586.0},
{0, 1, -1, 0, -0.040923, -129620.0},
{1, 0, 0, 0, -0.034720, 108743.0},
{0, 1, 1, 0, -0.030383, 104755.0},
{2, 0, 0, -2, 0.015327, 10321.0},
{0, 0, 1, 2, -0.012528, 0.0},
{0, 0, 1, -2, 0.010980, 79661.0},
{4, 0, -1, 0, 0.010675, -34782.0},
{0, 0, 3, 0, 0.010034, -23210.0},
{4, 0, -2, 0, 0.008548, -21636.0},
{2, 1, -1, 0, -0.007888, 24208.0},
{2, 1, 0, 0, -0.006766, 30824.0},
{1, 0, -1, 0, -0.005163, -8379.0},
{1, 1, 0, 0, 0.004987, -16675.0},
{2, -1, 1, 0, 0.004036, -12831.0},
{2, 0, 2, 0, 0.003994, -10445.0},
{4, 0, 0, 0, 0.003861, -11650.0},
{2, 0, -3, 0, 0.003665, 14403.0},
{0, 1, -2, 0, -0.002689, -7003.0},
{2, 0, -1, 2, -0.002602, 0.0},
{2, -1, -2, 0, 0.002390, 10056.0},
{1, 0, 1, 0, -0.002348, 6322.0},
{2, -2, 0, 0, 0.002236, -9884.0},
{0, 1, 2, 0, -0.002120, 5751.0},
{0, 2, 0, 0, -0.002069, 0.0},
{2, -2, -1, 0, 0.002048, -4950.0},
{2, 0, 1, -2, -0.001773, 4130.0},
{2, 0, 0, 2, -0.001595, 0.0},
{4, -1, -1, 0, 0.001215, -3958.0},
{0, 0, 2, 2, -0.001110, 0.0},
{3, 0, -1, 0, -0.000892, 3258.0},
{2, 1, 1, 0, -0.000810, 2616.0},
{4, -1, -2, 0, 0.000759, -1897.0},
{0, 2, -1, 0, -0.000713, -2117.0},
{2, 2, -1, 0, -0.000700, 2354.0},
{2, 1, -2, 0, 0.000691, 0.0},
{2, -1, 0, -2, 0.000596, 0.0},
{4, 0, 1, 0, 0.000549, -1423.0},
{0, 0, 4, 0, 0.000537, -1117.0},
{4, -1, 0, 0, 0.000520, -1571.0},
{1, 0, -2, 0, -0.000487, -1739.0},
{2, 1, 0, -2, -0.000399, 0.0},
{0, 0, 2, -2, -0.000381, -4421.0},
{1, 1, 1, 0, 0.000351, 0.0},
{3, 0, -2, 0, -0.000340, 0.0},
{4, 0, -3, 0, 0.000330, 0.0},
{2, -1, 2, 0, 0.000327, 0.0},
{0, 2, 1, 0, -0.000323, 1165.0},
{1, 1, -1, 0, 0.000299, 0.0},
{2, 0, 3, 0, 0.000294, 0.0},
{2, 0, -1, -2, 0.000000, 8752.0}}
NLR := len(tlr)
/*
Coefficients for Moon latitude series
*/
type termb struct {
nd int /* multiple of D in argument */
nem int /* " " M " " */
nemp int /* " " M' " " */
nf int /* " " F " " */
coefb float64 /* coefficient of B sine argument (deg) */
}
tb := []termb{{0, 0, 0, 1, 5.128122},
{0, 0, 1, 1, 0.280602},
{0, 0, 1, -1, 0.277693},
{2, 0, 0, -1, 0.173237},
{2, 0, -1, 1, 0.055413},
{2, 0, -1, -1, 0.046271},
{2, 0, 0, 1, 0.032573},
{0, 0, 2, 1, 0.017198},
{2, 0, 1, -1, 0.009266},
{0, 0, 2, -1, 0.008822},
{2, -1, 0, -1, 0.008216},
{2, 0, -2, -1, 0.004324},
{2, 0, 1, 1, 0.004200},
{2, 1, 0, -1, -0.003359},
{2, -1, -1, 1, 0.002463},
{2, -1, 0, 1, 0.002211},
{2, -1, -1, -1, 0.002065},
{0, 1, -1, -1, -0.001870},
{4, 0, -1, -1, 0.001828},
{0, 1, 0, 1, -0.001794},
{0, 0, 0, 3, -0.001749},
{0, 1, -1, 1, -0.001565},
{1, 0, 0, 1, -0.001491},
{0, 1, 1, 1, -0.001475},
{0, 1, 1, -1, -0.001410},
{0, 1, 0, -1, -0.001344},
{1, 0, 0, -1, -0.001335},
{0, 0, 3, 1, 0.001107},
{4, 0, 0, -1, 0.001021},
{4, 0, -1, 1, 0.000833},
{0, 0, 1, -3, 0.000777},
{4, 0, -2, 1, 0.000671},
{2, 0, 0, -3, 0.000607},
{2, 0, 2, -1, 0.000596},
{2, -1, 1, -1, 0.000491},
{2, 0, -2, 1, -0.000451},
{0, 0, 3, -1, 0.000439},
{2, 0, 2, 1, 0.000422},
{2, 0, -3, -1, 0.000421},
{2, 1, -1, 1, -0.000366},
{2, 1, 0, 1, -0.000351},
{4, 0, 0, 1, 0.000331},
{2, -1, 1, 1, 0.000315},
{2, -2, 0, -1, 0.000302},
{0, 0, 1, 3, -0.000283},
{2, 1, 1, -1, -0.000229},
{1, 1, 0, -1, 0.000223},
{1, 1, 0, 1, 0.000223},
{0, 1, -2, -1, -0.000220},
{2, 1, -1, -1, -0.000220},
{1, 0, 1, 1, -0.000185},
{2, -1, -2, -1, 0.000181},
{0, 1, 2, 1, -0.000177},
{4, 0, -2, -1, 0.000176},
{4, -1, -1, -1, 0.000166},
{1, 0, 1, -1, -0.000164},
{4, 0, 1, -1, 0.000132},
{1, 0, -1, -1, -0.000119},
{4, -1, 0, -1, 0.000115},
{2, -2, 0, 1, 0.000107}}
NB := len(tb)
/* Miscellaneous */
var n, i int
var t, elpmf, delpmf, vel, vdel, vr, vdr, a1mf, da1mf, a1pf,
da1pf, dlpmp, slpmp, vb, vdb, v, dv, emn, empn, dn, fn, en,
den, arg, darg, farg, coeff, el, del, r, dr, b, db, gamb,
phib, psib, epsa float64
var rm [3][3]float64
/* ------------------------------------------------------------------ */
/* Centuries since J2000.0 */
t = ((date1 - DJ00) + date2) / DJC
/* --------------------- */
/* Fundamental arguments */
/* --------------------- */
/* Arguments (radians) and derivatives (radians per Julian century)
for the current date. */
/* Moon's mean longitude. */
elp = DD2R * fmod(elp0+
(elp1+
(elp2+
(elp3+
elp4*t)*t)*t)*t, 360.0)
delp = DD2R * (elp1 +
(elp2*2.0+
(elp3*3.0+
elp4*4.0*t)*t)*t)
/* Moon's mean elongation. */
d = DD2R * fmod(d0+
(d1+
(d2+
(d3+
d4*t)*t)*t)*t, 360.0)
dd = DD2R * (d1 +
(d2*2.0+
(d3*3.0+
d4*4.0*t)*t)*t)
/* Sun's mean anomaly. */
em = DD2R * fmod(em0+
(em1+
(em2+
(em3+
em4*t)*t)*t)*t, 360.0)
dem = DD2R * (em1 +
(em2*2.0+
(em3*3.0+
em4*4.0*t)*t)*t)
/* Moon's mean anomaly. */
emp = DD2R * fmod(emp0+
(emp1+
(emp2+
(emp3+
emp4*t)*t)*t)*t, 360.0)
demp = DD2R * (emp1 +
(emp2*2.0+
(emp3*3.0+
emp4*4.0*t)*t)*t)
/* Mean distance of the Moon from its ascending node. */
f = DD2R * fmod(f0+
(f1+
(f2+
(f3+
f4*t)*t)*t)*t, 360.0)
df = DD2R * (f1 +
(f2*2.0+
(f3*3.0+
f4*4.0*t)*t)*t)
/* Meeus further arguments. */
a1 = DD2R * (a10 + a11*t)
da1 = DD2R * al1
a2 = DD2R * (a20 + a21*t)
da2 = DD2R * a21
a3 = DD2R * (a30 + a31*t)
da3 = DD2R * a31
/* E-factor, and square. */
e = 1.0 + (e1+e2*t)*t
de = e1 + 2.0*e2*t
esq = e * e
desq = 2.0 * e * de
/* Use the Meeus additive terms (deg) to start off the summations. */
elpmf = elp - f
delpmf = delp - df
vel = al1*sin(a1) + al2*sin(elpmf) + al3*sin(a2)
vdel = al1*cos(a1)*da1 + al2*cos(elpmf)*delpmf + al3*cos(a2)*da2
vr = 0.0
vdr = 0.0
a1mf = a1 - f
da1mf = da1 - df
a1pf = a1 + f
da1pf = da1 + df
dlpmp = elp - emp
slpmp = elp + emp
vb = ab1*sin(elp) + ab2*sin(a3) + ab3*sin(a1mf) + ab4*sin(a1pf) + ab5*sin(dlpmp) + ab6*sin(slpmp)
vdb = ab1*cos(elp)*delp + ab2*cos(a3)*da3 + ab3*cos(a1mf)*da1mf + ab4*cos(a1pf)*da1pf + ab5*cos(dlpmp)*(delp-demp) + ab6*cos(slpmp)*(delp+demp)
/* ----------------- */
/* Series expansions */
/* ----------------- */
/* Longitude and distance plus derivatives. */
for n = NLR - 1; n >= 0; n-- {
dn = float64(tlr[n].nd)
//emn = float64 ( i = tlr[n].nem );
i = tlr[n].nem
emn = float64(tlr[n].nem)
empn = float64(tlr[n].nemp)
fn = float64(tlr[n].nf)
switch abs(i) {
case 1:
en = e
den = de
break
case 2:
en = esq
den = desq
break
default:
en = 1.0
den = 0.0
}
arg = dn*d + emn*em + empn*emp + fn*f
darg = dn*dd + emn*dem + empn*demp + fn*df
farg = sin(arg)
v = farg * en
dv = cos(arg)*darg*en + farg*den
coeff = tlr[n].coefl
vel += coeff * v
vdel += coeff * dv
farg = cos(arg)
v = farg * en
dv = -sin(arg)*darg*en + farg*den
coeff = tlr[n].coefr
vr += coeff * v
vdr += coeff * dv
}
el = elp + DD2R*vel
del = (delp + DD2R*vdel) / DJC
r = (vr + r0) / DAU
dr = vdr / DAU / DJC
/* Latitude plus derivative. */
for n = NB - 1; n >= 0; n-- {
dn = float64(tb[n].nd)
//emn = float64( i = tb[n].nem );
i = tb[n].nem
emn = float64(tb[n].nem)
empn = float64(tb[n].nemp)
fn = float64(tb[n].nf)
switch abs(i) {
case 1:
en = e
den = de
break
case 2:
en = esq
den = desq
break
default:
en = 1.0
den = 0.0
}
arg = dn*d + emn*em + empn*emp + fn*f
darg = dn*dd + emn*dem + empn*demp + fn*df
farg = sin(arg)
v = farg * en
dv = cos(arg)*darg*en + farg*den
coeff = tb[n].coefb
vb += coeff * v
vdb += coeff * dv
}
b = vb * DD2R
db = vdb * DD2R / DJC
/* ------------------------------ */
/* Transformation into final form */
/* ------------------------------ */
/* Longitude, latitude to x, y, z (AU). */
S2pv(el, b, r, del, db, dr, pv)
/* IAU 2006 Fukushima-Williams bias+precession angles. */
Pfw06(date1, date2, &gamb, &phib, &psib, &epsa)
/* Mean ecliptic coordinates to GCRS rotation matrix. */
Ir(&rm)
Rz(psib, &rm)
Rx(-phib, &rm)
Rz(-gamb, &rm)
/* Rotate the Moon position and velocity into GCRS (Note 6). */
Rxpv(rm, *pv, pv)
/* Finished. */
}
/*
Plan94 Major-planet position and velocity
Approximate heliocentric position and velocity of a nominated major
planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or
Neptune (but not the Earth itself).
Given:
date1 float64 TDB date part A (Note 1)
date2 float64 TDB date part B (Note 1)
np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
Returned (argument):
pv [2][3]float64 planet p,v (heliocentric, J2000.0, au,au/d)
Returned (function value):
int status: -1 = illegal NP (outside 1-8)
0 = OK
+1 = warning: year outside 1000-3000
+2 = warning: failed to converge
Notes:
1) The date date1+date2 is in the TDB time scale (in practice TT can
be used) and is a Julian Date, apportioned in any convenient way
between the two arguments. For example, JD(TDB)=2450123.7 could
be expressed in any of these ways, among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
resolution. The MJD method and the date & time methods are both
good compromises between resolution and convenience. The limited
accuracy of the present algorithm is such that any of the methods
is satisfactory.
2) If an np value outside the range 1-8 is supplied, an error status
(function value -1) is returned and the pv vector set to zeroes.
3) For np=3 the result is for the Earth-Moon Barycenter. To obtain
the heliocentric position and velocity of the Earth, use instead
the SOFA function iauEpv00.
4) On successful return, the array pv contains the following:
pv[0][0] x }
pv[0][1] y } heliocentric position, au
pv[0][2] z }
pv[1][0] xdot }
pv[1][1] ydot } heliocentric velocity, au/d
pv[1][2] zdot }
The reference frame is equatorial and is with respect to the
mean equator and equinox of epoch J2000.0.
5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront,
M. Chapront-Touze, G. Francou and J. Laskar (Bureau des
Longitudes, Paris, France). From comparisons with JPL
ephemeris DE102, they quote the following maximum errors
over the interval 1800-2050:
L (arcsec) B (arcsec) R (km)
Mercury 4 1 300
Venus 5 1 800
EMB 6 1 1000
Mars 17 1 7700
Jupiter 71 5 76000
Saturn 81 13 267000
Uranus 86 7 712000
Neptune 11 1 253000
Over the interval 1000-3000, they report that the accuracy is no
worse than 1.5 times that over 1800-2050. Outside 1000-3000 the
accuracy declines.
Comparisons of the present function with the JPL DE200 ephemeris
give the following RMS errors over the interval 1960-2025:
position (km) velocity (m/s)
Mercury 334 0.437
Venus 1060 0.855
EMB 2010 0.815
Mars 7690 1.98
Jupiter 71700 7.70
Saturn 199000 19.4
Uranus 564000 16.4
Neptune 158000 14.4
Comparisons against DE200 over the interval 1800-2100 gave the
following maximum absolute differences. (The results using
DE406 were essentially the same.)
L (arcsec) B (arcsec) R (km) Rdot (m/s)
Mercury 7 1 500 0.7
Venus 7 1 1100 0.9
EMB 9 1 1300 1.0
Mars 26 1 9000 2.5
Jupiter 78 6 82000 8.2
Saturn 87 14 263000 24.6
Uranus 86 7 661000 27.4
Neptune 11 2 248000 21.4
6) The present SOFA re-implementation of the original Simon et al.
Fortran code differs from the original in the following respects:
* C instead of Fortran.
* The date is supplied in two parts.
* The result is returned only in equatorial Cartesian form;
the ecliptic longitude, latitude and radius vector are not
returned.
* The result is in the J2000.0 equatorial frame, not ecliptic.
* More is done in-line: there are fewer calls to subroutines.
* Different error/warning status values are used.
* A different Kepler's-equation-solver is used (avoiding
use of double precision complex).
* Polynomials in t are nested to minimize rounding errors.
* Explicit double constants are used to avoid mixed-mode
expressions.
None of the above changes affects the result significantly.
7) The returned status indicates the most serious condition
encountered during execution of the function. Illegal np is
considered the most serious, overriding failure to converge,
which in turn takes precedence over the remote date warning.
Called:
Anpm normalize angle into range +/- pi
Reference: Simon, J.L, Bretagnon, P., Chapront, J.,
Chapront-Touze, M., Francou, G., and Laskar, J.,
Astron.Astrophys., 282, 663 (1994).
*/
func Plan94(date1, date2 float64, np int, pv *[2][3]float64) int {
/* Gaussian constant */
const GK = 0.017202098950
/* Sin and cos of J2000.0 mean obliquity (IAU 1976) */
const SINEPS = 0.3977771559319137
const COSEPS = 0.9174820620691818
/* Maximum number of iterations allowed to solve Kepler's equation */
const KMAX = 10
var jstat, i, k int
var t, da, dl, de, dp, di, dom, dmu, arga, argl, am,
ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw,
xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z float64
/* Planetary inverse masses */
amas := []float64{6023600.0, /* Mercury */
408523.5, /* Venus */
328900.5, /* EMB */
3098710.0, /* Mars */
1047.355, /* Jupiter */
3498.5, /* Saturn */
22869.0, /* Uranus */
19314.0} /* Neptune */
/*
Tables giving the mean Keplerian elements, limited to t^2 terms:
a semi-major axis (au)
dlm mean longitude (degree and arcsecond)
e eccentricity
pi longitude of the perihelion (degree and arcsecond)
dinc inclination (degree and arcsecond)
omega longitude of the ascending node (degree and arcsecond)
*/
a := [][3]float64{
{0.3870983098, 0.0, 0.0}, /* Mercury */
{0.7233298200, 0.0, 0.0}, /* Venus */
{1.0000010178, 0.0, 0.0}, /* EMB */
{1.5236793419, 3e-10, 0.0}, /* Mars */
{5.2026032092, 19132e-10, -39e-10}, /* Jupiter */
{9.5549091915, -0.0000213896, 444e-10}, /* Saturn */
{19.2184460618, -3716e-10, 979e-10}, /* Uranus */
{30.1103868694, -16635e-10, 686e-10}, /* Neptune */
}
dlm := [][3]float64{
{252.25090552, 5381016286.88982, -1.92789},
{181.97980085, 2106641364.33548, 0.59381},
{100.46645683, 1295977422.83429, -2.04411},
{355.43299958, 689050774.93988, 0.94264},
{34.35151874, 109256603.77991, -30.60378},
{50.07744430, 43996098.55732, 75.61614},
{314.05500511, 15424811.93933, -1.75083},
{304.34866548, 7865503.20744, 0.21103},
}
e := [][3]float64{
{0.2056317526, 0.0002040653, -28349e-10},
{0.0067719164, -0.0004776521, 98127e-10},
{0.0167086342, -0.0004203654, -0.0000126734},
{0.0934006477, 0.0009048438, -80641e-10},
{0.0484979255, 0.0016322542, -0.0000471366},
{0.0555481426, -0.0034664062, -0.0000643639},
{0.0463812221, -0.0002729293, 0.0000078913},
{0.0094557470, 0.0000603263, 0.0},
}
pi := [][3]float64{
{77.45611904, 5719.11590, -4.83016},
{131.56370300, 175.48640, -498.48184},
{102.93734808, 11612.35290, 53.27577},
{336.06023395, 15980.45908, -62.32800},
{14.33120687, 7758.75163, 259.95938},
{93.05723748, 20395.49439, 190.25952},
{173.00529106, 3215.56238, -34.09288},
{48.12027554, 1050.71912, 27.39717},
}
dinc := [][3]float64{
{7.00498625, -214.25629, 0.28977},
{3.39466189, -30.84437, -11.67836},
{0.0, 469.97289, -3.35053},
{1.84972648, -293.31722, -8.11830},
{1.30326698, -71.55890, 11.95297},
{2.48887878, 91.85195, -17.66225},
{0.77319689, -60.72723, 1.25759},
{1.76995259, 8.12333, 0.08135},
}
omega := [][3]float64{
{48.33089304, -4515.21727, -31.79892},
{76.67992019, -10008.48154, -51.32614},
{174.87317577, -8679.27034, 15.34191},
{49.55809321, -10620.90088, -230.57416},
{100.46440702, 6362.03561, 326.52178},
{113.66550252, -9240.19942, -66.23743},
{74.00595701, 2669.15033, 145.93964},
{131.78405702, -221.94322, -0.78728},
}
/* Tables for trigonometric terms to be added to the mean elements of */
/* the semi-major axes */
kp := [][9]float64{
{69613, 75645, 88306, 59899, 15746, 71087, 142173, 3086, 0},
{21863, 32794, 26934, 10931, 26250, 43725, 53867, 28939, 0},
{16002, 21863, 32004, 10931, 14529, 16368, 15318, 32794, 0},
{6345, 7818, 15636, 7077, 8184, 14163, 1107, 4872, 0},
{1760, 1454, 1167, 880, 287, 2640, 19, 2047, 1454},
{574, 0, 880, 287, 19, 1760, 1167, 306, 574},
{204, 0, 177, 1265, 4, 385, 200, 208, 204},
{0, 102, 106, 4, 98, 1367, 487, 204, 0},
}
ca := [][9]float64{
{4, -13, 11, -9, -9, -3, -1, 4, 0},
{-156, 59, -42, 6, 19, -20, -10, -12, 0},
{64, -152, 62, -8, 32, -41, 19, -11, 0},
{124, 621, -145, 208, 54, -57, 30, 15, 0},
{-23437, -2634, 6601, 6259, -1507, -1821, 2620, -2115, -1489},
{62911, -119919, 79336, 17814, -24241, 12068, 8306, -4893, 8902},
{389061, -262125, -44088, 8387, -22976, -2093, -615, -9720, 6633},
{-412235, -157046, -31430, 37817, -9740, -13, -7449, 9644, 0},
}
sa := [][9]float64{
{-29, -1, 9, 6, -6, 5, 4, 0, 0},
{-48, -125, -26, -37, 18, -13, -20, -2, 0},
{-150, -46, 68, 54, 14, 24, -28, 22, 0},
{-621, 532, -694, -20, 192, -94, 71, -73, 0},
{-14614, -19828, -5869, 1881, -4372, -2255, 782, 930, 913},
{139737, 0, 24667, 51123, -5102, 7429, -4095, -1976, -9566},
{-138081, 0, 37205, -49039, -41901, -33872, -27037, -12474, 18797},
{0, 28492, 133236, 69654, 52322, -49577, -26430, -3593, 0},
}
/* Tables giving the trigonometric terms to be added to the mean */
/* elements of the mean longitudes */
kq := [][10]float64{
{3086, 15746, 69613, 59899, 75645, 88306, 12661, 2658, 0, 0},
{21863, 32794, 10931, 73, 4387, 26934, 1473, 2157, 0, 0},
{10, 16002, 21863, 10931, 1473, 32004, 4387, 73, 0, 0},
{10, 6345, 7818, 1107, 15636, 7077, 8184, 532, 10, 0},
{19, 1760, 1454, 287, 1167, 880, 574, 2640, 19, 1454},
{19, 574, 287, 306, 1760, 12, 31, 38, 19, 574},
{4, 204, 177, 8, 31, 200, 1265, 102, 4, 204},
{4, 102, 106, 8, 98, 1367, 487, 204, 4, 102},
}
cl := [][10]float64{
{21, -95, -157, 41, -5, 42, 23, 30, 0, 0},
{-160, -313, -235, 60, -74, -76, -27, 34, 0, 0},
{-325, -322, -79, 232, -52, 97, 55, -41, 0, 0},
{2268, -979, 802, 602, -668, -33, 345, 201, -55, 0},
{7610, -4997, -7689, -5841, -2617, 1115, -748, -607, 6074, 354},
{-18549, 30125, 20012, -730, 824, 23, 1289, -352, -14767, -2062},
{-135245, -14594, 4197, -4030, -5630, -2898, 2540, -306, 2939, 1986},
{89948, 2103, 8963, 2695, 3682, 1648, 866, -154, -1963, -283},
}
sl := [][10]float64{
{-342, 136, -23, 62, 66, -52, -33, 17, 0, 0},
{524, -149, -35, 117, 151, 122, -71, -62, 0, 0},
{-105, -137, 258, 35, -116, -88, -112, -80, 0, 0},
{854, -205, -936, -240, 140, -341, -97, -232, 536, 0},
{-56980, 8016, 1012, 1448, -3024, -3710, 318, 503, 3767, 577},
{138606, -13478, -4964, 1441, -1319, -1482, 427, 1236, -9167, -1918},
{71234, -41116, 5334, -4935, -1848, 66, 434, -1748, 3780, -701},
{-47645, 11647, 2166, 3194, 679, 0, -244, -419, -2531, 48},
}
/* ------------------------------------------------------------------ */
/* Validate the planet number. */
if (np < 1) || (np > 8) {
jstat = -1
/* Reset the result in case of failure. */
for k = 0; k < 2; k++ {
for i = 0; i < 3; i++ {
pv[k][i] = 0.0
}
}
} else {
/* Decrement the planet number to start at zero. */
np--
/* Time: Julian millennia since J2000.0. */
t = ((date1 - DJ00) + date2) / DJM
/* OK status unless remote date. */
// jstat = fabs(t) <= 1.0 ? 0 : 1;
if fabs(t) <= 1.0 {
jstat = 0
} else {
jstat = 1
}
/* Compute the mean elements. */
da = a[np][0] +
(a[np][1]+
a[np][2]*t)*t
dl = (3600.0*dlm[np][0] +
(dlm[np][1]+
dlm[np][2]*t)*t) * DAS2R
de = e[np][0] +
(e[np][1]+
e[np][2]*t)*t
dp = Anpm((3600.0*pi[np][0] +
(pi[np][1]+
pi[np][2]*t)*t) * DAS2R)
di = (3600.0*dinc[np][0] +
(dinc[np][1]+
dinc[np][2]*t)*t) * DAS2R
dom = Anpm((3600.0*omega[np][0] +
(omega[np][1]+
omega[np][2]*t)*t) * DAS2R)
/* Apply the trigonometric terms. */
dmu = 0.35953620 * t
for k = 0; k < 8; k++ {
arga = kp[np][k] * dmu
argl = kq[np][k] * dmu
da += (ca[np][k]*cos(arga) +
sa[np][k]*sin(arga)) * 1e-7
dl += (cl[np][k]*cos(argl) +
sl[np][k]*sin(argl)) * 1e-7
}
arga = kp[np][8] * dmu
da += t * (ca[np][8]*cos(arga) +
sa[np][8]*sin(arga)) * 1e-7
for k = 8; k < 10; k++ {
argl = kq[np][k] * dmu
dl += t * (cl[np][k]*cos(argl) +
sl[np][k]*sin(argl)) * 1e-7
}
dl = fmod(dl, D2PI)
/* Iterative soln. of Kepler's equation to get eccentric anomaly. */
am = dl - dp
ae = am + de*sin(am)
k = 0
dae = 1.0
for k < KMAX && fabs(dae) > 1e-12 {
dae = (am - ae + de*sin(ae)) / (1.0 - de*cos(ae))
ae += dae
k++
if k == KMAX-1 {
jstat = 2
}
}
/* True anomaly. */
ae2 = ae / 2.0
at = 2.0 * atan2(sqrt((1.0+de)/(1.0-de))*sin(ae2),
cos(ae2))
/* Distance (au) and speed (radians per day). */
r = da * (1.0 - de*cos(ae))
v = GK * sqrt((1.0+1.0/amas[np])/(da*da*da))
si2 = sin(di / 2.0)
xq = si2 * cos(dom)
xp = si2 * sin(dom)
tl = at + dp
xsw = sin(tl)
xcw = cos(tl)
xm2 = 2.0 * (xp*xcw - xq*xsw)
xf = da / sqrt(1-de*de)
ci2 = cos(di / 2.0)
xms = (de*sin(dp) + xsw) * xf
xmc = (de*cos(dp) + xcw) * xf
xpxq2 = 2 * xp * xq
/* Position (J2000.0 ecliptic x,y,z in au). */
x = r * (xcw - xm2*xp)
y = r * (xsw + xm2*xq)
z = r * (-xm2 * ci2)
/* Rotate to equatorial. */
pv[0][0] = x
pv[0][1] = y*COSEPS - z*SINEPS
pv[0][2] = y*SINEPS + z*COSEPS
/* Velocity (J2000.0 ecliptic xdot,ydot,zdot in au/d). */
x = v * ((-1.0+2.0*xp*xp)*xms + xpxq2*xmc)
y = v * ((1.0-2.0*xq*xq)*xmc - xpxq2*xms)
z = v * (2.0 * ci2 * (xp*xms + xq*xmc))
/* Rotate to equatorial. */
pv[1][0] = x
pv[1][1] = y*COSEPS - z*SINEPS
pv[1][2] = y*SINEPS + z*COSEPS
}
/* Return the status. */
return jstat
}
gofa-1.19.1/erast.go 0000664 0000000 0000000 00000120164 14535740236 0014201 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Earth Rotation and Sidereal Time
/*
Ee00 Equation of the equinoxes, IAU 2000
The equation of the equinoxes, compatible with IAU 2000 resolutions,
given the nutation in longitude and the mean obliquity.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
epsa float64 mean obliquity (Note 2)
dpsi float64 nutation in longitude (Note 3)
Returned (function value):
float64 equation of the equinoxes (Note 4)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The obliquity, in radians, is mean of date.
3) The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
4) The result is compatible with the IAU 2000 resolutions. For
further details, see IERS Conventions 2003 and Capitaine et al.
(2002).
Called:
Eect00 equation of the equinoxes complementary terms
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Ee00(date1, date2 float64, epsa, dpsi float64) float64 {
var ee float64
/* Equation of the equinoxes. */
ee = dpsi*cos(epsa) + Eect00(date1, date2)
return ee
}
/*
Ee00a Equation of the equinoxes, IAU 2000A
Equation of the equinoxes, compatible with IAU 2000 resolutions.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 equation of the equinoxes (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
3) The result is compatible with the IAU 2000 resolutions. For
further details, see IERS Conventions 2003 and Capitaine et al.
(2002).
Called:
Pr00 IAU 2000 precession adjustments
Obl80 mean obliquity, IAU 1980
Nut00a nutation, IAU 2000A
Ee00 equation of the equinoxes, IAU 2000
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003).
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004).
*/
func Ee00a(date1, date2 float64) float64 {
var dpsipr, depspr, epsa, dpsi, deps, ee float64
/* IAU 2000 precession-rate adjustments. */
Pr00(date1, date2, &dpsipr, &depspr)
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
epsa = Obl80(date1, date2) + depspr
/* Nutation in longitude. */
Nut00a(date1, date2, &dpsi, &deps)
/* Equation of the equinoxes. */
ee = Ee00(date1, date2, epsa, dpsi)
return ee
}
/*
Ee00b Equation of the equinoxes, IAU 2000B
Equation of the equinoxes, compatible with IAU 2000 resolutions but
using the truncated nutation model IAU 2000B.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 equation of the equinoxes (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
3) The result is compatible with the IAU 2000 resolutions except
that accuracy has been compromised (1 mas) for the sake of speed.
For further details, see McCarthy & Luzum (2003), IERS
Conventions 2003 and Capitaine et al. (2003).
Called:
Pr00 IAU 2000 precession adjustments
Obl80 mean obliquity, IAU 1980
Nut00b nutation, IAU 2000B
Ee00 equation of the equinoxes, IAU 2000
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003)
McCarthy, D.D. & Luzum, B.J., "An abridged model of the
precession-nutation of the celestial pole", Celestial Mechanics &
Dynamical Astronomy, 85, 37-49 (2003)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Ee00b(date1, date2 float64) float64 {
var dpsipr, depspr, epsa, dpsi, deps, ee float64
/* IAU 2000 precession-rate adjustments. */
Pr00(date1, date2, &dpsipr, &depspr)
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
epsa = Obl80(date1, date2) + depspr
/* Nutation in longitude. */
Nut00b(date1, date2, &dpsi, &deps)
/* Equation of the equinoxes. */
ee = Ee00(date1, date2, epsa, dpsi)
return ee
}
/*
Ee06a Equation of the equinoxes, IAU 2006/2000A
Equation of the equinoxes, compatible with IAU 2000 resolutions and
IAU 2006/2000A precession-nutation.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 equation of the equinoxes (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
Called:
Anpm normalize angle into range +/- pi
Gst06a Greenwich apparent sidereal time, IAU 2006/2000A
Gmst06 Greenwich mean sidereal time, IAU 2006
Reference:
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
*/
func Ee06a(date1, date2 float64) float64 {
var gst06a, gmst06, ee float64
/* Apparent and mean sidereal times. */
gst06a = Gst06a(0.0, 0.0, date1, date2)
gmst06 = Gmst06(0.0, 0.0, date1, date2)
/* Equation of the equinoxes. */
ee = Anpm(gst06a - gmst06)
return ee
}
/*
Eect00 Equation of the equinoxes complementary terms, consistent with
IAU 2000 resolutions.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 complementary terms (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The "complementary terms" are part of the equation of the
equinoxes (EE), classically the difference between apparent and
mean Sidereal Time:
GAST = GMST + EE
with:
EE = dpsi * cos(eps)
where dpsi is the nutation in longitude and eps is the obliquity
of date. However, if the rotation of the Earth were constant in
an inertial frame the classical formulation would lead to
apparent irregularities in the UT1 timescale traceable to side-
effects of precession-nutation. In order to eliminate these
effects from UT1, "complementary terms" were introduced in 1994
(IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
1993):
GAST = GMST + CT + EE
By convention, the complementary terms are included as part of
the equation of the equinoxes rather than as part of the mean
Sidereal Time. This slightly compromises the "geometrical"
interpretation of mean sidereal time but is otherwise
inconsequential.
The present function computes CT in the above expression,
compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
IERS Conventions 2003).
Called:
Fal03 mean anomaly of the Moon
Falp03 mean anomaly of the Sun
Faf03 mean argument of the latitude of the Moon
Fad03 mean elongation of the Moon from the Sun
Faom03 mean longitude of the Moon's ascending node
Fave03 mean longitude of Venus
Fae03 mean longitude of Earth
Fapa03 general accumulated precession in longitude
References:
Capitaine, N. & Gontier, A.-M., Astron.Astrophys., 275,
645-650 (1993)
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astron.Astrophys., 406,
1135-1149 (2003)
IAU Resolution C7, Recommendation 3 (1994)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Eect00(date1, date2 float64) float64 {
/* Time since J2000.0, in Julian centuries */
var t float64
/* Miscellaneous */
var i, j int
var a, s0, s1 float64
/* Fundamental arguments */
var fa [14]float64
/* Returned value. */
var eect float64
/* ----------------------------------------- */
/* The series for the EE complementary terms */
/* ----------------------------------------- */
type TERM struct {
nfa [8]int /* coefficients of l,l',F,D,Om,LVe,LE,pA */
s, c float64 /* sine and cosine coefficients */
}
/* Terms of order t^0 */
e0 := []TERM{
/* 1-10 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6},
{[8]int{0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6},
{[8]int{0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6},
{[8]int{0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6},
{[8]int{0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6},
/* 11-20 */
{[8]int{1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6},
{[8]int{0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6},
{[8]int{0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6},
{[8]int{0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6},
/* 21-30 */
{[8]int{0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 0, 8, -13, -1}, -0.10e-6, 0.05e-6},
{[8]int{0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6},
{[8]int{2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6},
/* 31-33 */
{[8]int{0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6},
}
/* Terms of order t^1 */
e1 := []TERM{
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6},
}
/* Number of terms in the series */
NE0 := len(e0)
NE1 := len(e1)
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = Fal03(t)
/* Mean anomaly of the Sun. */
fa[1] = Falp03(t)
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = Faf03(t)
/* Mean elongation of the Moon from the Sun. */
fa[3] = Fad03(t)
/* Mean longitude of the ascending node of the Moon. */
fa[4] = Faom03(t)
/* Mean longitude of Venus. */
fa[5] = Fave03(t)
/* Mean longitude of Earth. */
fa[6] = Fae03(t)
/* General precession in longitude. */
fa[7] = Fapa03(t)
/* Evaluate the EE complementary terms. */
s0 = 0.0
s1 = 0.0
for i = NE0 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(e0[i].nfa[j]) * fa[j]
}
s0 += e0[i].s*sin(a) + e0[i].c*cos(a)
}
for i = NE1 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(e1[i].nfa[j]) * fa[j]
}
s1 += e1[i].s*sin(a) + e1[i].c*cos(a)
}
eect = (s0 + s1*t) * DAS2R
return eect
}
/*
Eqeq94 Equation of the equinoxes, IAU 1994
Equation of the equinoxes, IAU 1994 model.
Given:
date1,date2 float64 TDB date (Note 1)
Returned (function value):
float64 equation of the equinoxes (Note 2)
Notes:
1) The date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
Called:
Anpm normalize angle into range +/- pi
Nut80 nutation, IAU 1980
Obl80 mean obliquity, IAU 1980
References:
IAU Resolution C7, Recommendation 3 (1994).
Capitaine, N. & Gontier, A.-M., 1993, Astron.Astrophys., 275,
645-650.
*/
func Eqeq94(date1, date2 float64) float64 {
var t, om, dpsi, deps, eps0, ee float64
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Longitude of the mean ascending node of the lunar orbit on the */
/* ecliptic, measured from the mean equinox of date. */
om = Anpm((450160.280+(-482890.539+
(7.455+0.008*t)*t)*t)*DAS2R +
fmod(-5.0*t, 1.0)*D2PI)
/* Nutation components and mean obliquity. */
Nut80(date1, date2, &dpsi, &deps)
eps0 = Obl80(date1, date2)
/* Equation of the equinoxes. */
ee = dpsi*cos(eps0) + DAS2R*(0.00264*sin(om)+0.000063*sin(om+om))
return ee
}
/*
Era00 Earth Rotation Angle, IAU 2000
Given:
dj1,dj2 float64 UT1 as a 2-part Julian Date (see note)
Returned (function value):
float64 Earth rotation angle (radians), range 0-2pi
Notes:
1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any
convenient way between the arguments dj1 and dj2. For example,
JD(UT1)=2450123.7 could be expressed in any of these ways,
among others:
dj1 dj2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. The date & time method is
best matched to the algorithm used: maximum precision is
delivered when the dj1 argument is for 0hrs UT1 on the day in
question and the dj2 argument lies in the range 0 to 1, or vice
versa.
2) The algorithm is adapted from Expression 22 of Capitaine et al.
2000. The time argument has been expressed in days directly,
and, to retain precision, integer contributions have been
eliminated. The same formulation is given in IERS Conventions
(2003), Chap. 5, Eq. 14.
Called:
Anp normalize angle into range 0 to 2pi
References:
Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron.
Astrophys., 355, 398-405.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Era00(dj1, dj2 float64) float64 {
var d1, d2, t, f, theta float64
/* Days since fundamental epoch. */
if dj1 < dj2 {
d1 = dj1
d2 = dj2
} else {
d1 = dj2
d2 = dj1
}
t = d1 + (d2 - DJ00)
/* Fractional part of T (days). */
f = fmod(d1, 1.0) + fmod(d2, 1.0)
/* Earth rotation angle at this UT1. */
theta = Anp(D2PI * (f + 0.7790572732640 + 0.00273781191135448*t))
return theta
}
/*
Gmst00 Greenwich Mean Sidereal Time, IAU 2000
Greenwich mean sidereal time (model consistent with IAU 2000
resolutions).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
tta,ttb float64 TT as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich mean sidereal time (radians)
Notes:
1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
Julian Dates, apportioned in any convenient way between the
argument pairs. For example, JD(UT1)=2450123.7 could be
expressed in any of these ways, among others:
Part A Part B
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable (in the case of UT; the TT is not at all critical
in this respect). The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
Rotation Angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) Both UT1 and TT are required, UT1 to predict the Earth rotation
and TT to predict the effects of precession. If UT1 is used for
both purposes, errors of order 100 microarcseconds result.
3) This GMST is compatible with the IAU 2000 resolutions and must be
used only in conjunction with other IAU 2000 compatible
components such as precession-nutation and equation of the
equinoxes.
4) The result is returned in the range 0 to 2pi.
5) The algorithm is from Capitaine et al. (2003) and IERS
Conventions 2003.
Called:
Era00 Earth rotation angle, IAU 2000
Anp normalize angle into range 0 to 2pi
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Gmst00(uta, utb float64, tta, ttb float64) float64 {
var t, gmst float64
/* TT Julian centuries since J2000.0. */
t = ((tta - DJ00) + ttb) / DJC
/* Greenwich Mean Sidereal Time, IAU 2000. */
gmst = Anp(Era00(uta, utb) +
(0.014506+
(4612.15739966+
(1.39667721+
(-0.00009344+
(0.00001882)*t)*t)*t)*t)*DAS2R)
return gmst
}
/*
Gmst06 Greenwich Mean Sidereal Time, IAU 2006
Greenwich mean sidereal time (consistent with IAU 2006 precession).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
tta,ttb float64 TT as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich mean sidereal time (radians)
Notes:
1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
Julian Dates, apportioned in any convenient way between the
argument pairs. For example, JD=2450123.7 could be expressed in
any of these ways, among others:
Part A Part B
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable (in the case of UT; the TT is not at all critical
in this respect). The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
rotation angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) Both UT1 and TT are required, UT1 to predict the Earth rotation
and TT to predict the effects of precession. If UT1 is used for
both purposes, errors of order 100 microarcseconds result.
3) This GMST is compatible with the IAU 2006 precession and must not
be used with other precession models.
4) The result is returned in the range 0 to 2pi.
Called:
Era00 Earth rotation angle, IAU 2000
Anp normalize angle into range 0 to 2pi
Reference:
Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
Astron.Astrophys. 432, 355
*/
func Gmst06(uta, utb float64, tta, ttb float64) float64 {
var t, gmst float64
/* TT Julian centuries since J2000.0. */
t = ((tta - DJ00) + ttb) / DJC
/* Greenwich mean sidereal time, IAU 2006. */
gmst = Anp(Era00(uta, utb) +
(0.014506+
(4612.156534+
(1.3915817+
(-0.00000044+
(-0.000029956+
(-0.0000000368)*t)*t)*t)*t)*t)*DAS2R)
return gmst
}
/*
Gmst82 Greenwich Mean Sidereal Time, IAU 1982
Universal Time to Greenwich mean sidereal time (IAU 1982 model).
Given:
dj1,dj2 float64 UT1 Julian Date (see note)
Returned (function value):
float64 Greenwich mean sidereal time (radians)
Notes:
1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any
convenient way between the arguments dj1 and dj2. For example,
JD(UT1)=2450123.7 could be expressed in any of these ways,
among others:
dj1 dj2
2450123.7 0 (JD method)
2451545 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. The date & time method is
best matched to the algorithm used: maximum accuracy (or, at
least, minimum noise) is delivered when the dj1 argument is for
0hrs UT1 on the day in question and the dj2 argument lies in the
range 0 to 1, or vice versa.
2) The algorithm is based on the IAU 1982 expression. This is
always described as giving the GMST at 0 hours UT1. In fact, it
gives the difference between the GMST and the UT, the steady
4-minutes-per-day drawing-ahead of ST with respect to UT. When
whole days are ignored, the expression happens to equal the GMST
at 0 hours UT1 each day.
3) In this function, the entire UT1 (the sum of the two arguments
dj1 and dj2) is used directly as the argument for the standard
formula, the constant term of which is adjusted by 12 hours to
take account of the noon phasing of Julian Date. The UT1 is then
added, but omitting whole days to conserve accuracy.
Called:
Anp normalize angle into range 0 to 2pi
References:
Transactions of the International Astronomical Union,
XVIII B, 67 (1983).
Aoki et al., Astron.Astrophys., 105, 359-361 (1982).
*/
func Gmst82(dj1, dj2 float64) float64 {
/* Coefficients of IAU 1982 GMST-UT1 model */
A := 24110.54841 - DAYSEC/2.0
B := 8640184.812866
C := 0.093104
D := -6.2e-6
/* The first constant, A, has to be adjusted by 12 hours because the */
/* UT1 is supplied as a Julian date, which begins at noon. */
var d1, d2, t, f, gmst float64
/* Julian centuries since fundamental epoch. */
if dj1 < dj2 {
d1 = dj1
d2 = dj2
} else {
d1 = dj2
d2 = dj1
}
t = (d1 + (d2 - DJ00)) / DJC
/* Fractional part of JD(UT1), in seconds. */
f = DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0))
/* GMST at this UT1. */
gmst = Anp(DS2R * ((A + (B+(C+D*t)*t)*t) + f))
return gmst
}
/*
Gst00a Greenwich Apparent Sidereal Time, IAU 2000A
Greenwich apparent sidereal time (consistent with IAU 2000
resolutions).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
tta,ttb float64 TT as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich apparent sidereal time (radians)
Notes:
1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
Julian Dates, apportioned in any convenient way between the
argument pairs. For example, JD(UT1)=2450123.7 could be
expressed in any of these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable (in the case of UT; the TT is not at all critical
in this respect). The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
Rotation Angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) Both UT1 and TT are required, UT1 to predict the Earth rotation
and TT to predict the effects of precession-nutation. If UT1 is
used for both purposes, errors of order 100 microarcseconds
result.
3) This GAST is compatible with the IAU 2000 resolutions and must be
used only in conjunction with other IAU 2000 compatible
components such as precession-nutation.
4) The result is returned in the range 0 to 2pi.
5) The algorithm is from Capitaine et al. (2003) and IERS
Conventions 2003.
Called:
Gmst00 Greenwich mean sidereal time, IAU 2000
Ee00a equation of the equinoxes, IAU 2000A
Anp normalize angle into range 0 to 2pi
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Gst00a(uta, utb float64, tta, ttb float64) float64 {
var gmst00, ee00a, gst float64
gmst00 = Gmst00(uta, utb, tta, ttb)
ee00a = Ee00a(tta, ttb)
gst = Anp(gmst00 + ee00a)
return gst
}
/*
Gst00b Greenwich Apparent Sidereal Time, IAU 2000B
Greenwich apparent sidereal time (consistent with IAU 2000
resolutions but using the truncated nutation model IAU 2000B).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich apparent sidereal time (radians)
Notes:
1) The UT1 date uta+utb is a Julian Date, apportioned in any
convenient way between the argument pair. For example,
JD(UT1)=2450123.7 could be expressed in any of these ways,
among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
Rotation Angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) The result is compatible with the IAU 2000 resolutions, except
that accuracy has been compromised for the sake of speed and
convenience in two respects:
. UT is used instead of TDB (or TT) to compute the precession
component of GMST and the equation of the equinoxes. This
results in errors of order 0.1 mas at present.
. The IAU 2000B abridged nutation model (McCarthy & Luzum, 2003)
is used, introducing errors of up to 1 mas.
3) This GAST is compatible with the IAU 2000 resolutions and must be
used only in conjunction with other IAU 2000 compatible
components such as precession-nutation.
4) The result is returned in the range 0 to 2pi.
5) The algorithm is from Capitaine et al. (2003) and IERS
Conventions 2003.
Called:
Gmst00 Greenwich mean sidereal time, IAU 2000
Ee00b equation of the equinoxes, IAU 2000B
Anp normalize angle into range 0 to 2pi
References:
Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
implement the IAU 2000 definition of UT1", Astronomy &
Astrophysics, 406, 1135-1149 (2003)
McCarthy, D.D. & Luzum, B.J., "An abridged model of the
precession-nutation of the celestial pole", Celestial Mechanics &
Dynamical Astronomy, 85, 37-49 (2003)
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Gst00b(uta, utb float64) float64 {
var gmst00, ee00b, gst float64
gmst00 = Gmst00(uta, utb, uta, utb)
ee00b = Ee00b(uta, utb)
gst = Anp(gmst00 + ee00b)
return gst
}
/*
Gst06 Greenwich Apparent Sidereal Time, IAU 2006 given NPB matrix
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
tta,ttb float64 TT as a 2-part Julian Date (Notes 1,2)
rnpb [3][3]float64 nutation x precession x bias matrix
Returned (function value):
float64 Greenwich apparent sidereal time (radians)
Notes:
1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
Julian Dates, apportioned in any convenient way between the
argument pairs. For example, JD(UT1)=2450123.7 could be
expressed in any of these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable (in the case of UT; the TT is not at all critical
in this respect). The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
rotation angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) Both UT1 and TT are required, UT1 to predict the Earth rotation
and TT to predict the effects of precession-nutation. If UT1 is
used for both purposes, errors of order 100 microarcseconds
result.
3) Although the function uses the IAU 2006 series for s+XY/2, it is
otherwise independent of the precession-nutation model and can in
practice be used with any equinox-based NPB matrix.
4) The result is returned in the range 0 to 2pi.
Called:
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
Anp normalize angle into range 0 to 2pi
Era00 Earth rotation angle, IAU 2000
Eors equation of the origins, given NPB matrix and s
Reference:
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Gst06(uta, utb float64, tta, ttb float64, rnpb [3][3]float64) float64 {
var x, y, s, era, eors, gst float64
/* Extract CIP coordinates. */
Bpn2xy(rnpb, &x, &y)
/* The CIO locator, s. */
s = S06(tta, ttb, x, y)
/* Greenwich apparent sidereal time. */
era = Era00(uta, utb)
eors = Eors(rnpb, s)
gst = Anp(era - eors)
return gst
}
/*
Gst06a Greenwich Apparent Sidereal Time, IAU 2006/2000A
Greenwich apparent sidereal time (consistent with IAU 2000 and 2006
resolutions).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
tta,ttb float64 TT as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich apparent sidereal time (radians)
Notes:
1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
Julian Dates, apportioned in any convenient way between the
argument pairs. For example, JD(UT1)=2450123.7 could be
expressed in any of these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable (in the case of UT; the TT is not at all critical
in this respect). The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
rotation angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) Both UT1 and TT are required, UT1 to predict the Earth rotation
and TT to predict the effects of precession-nutation. If UT1 is
used for both purposes, errors of order 100 microarcseconds
result.
3) This GAST is compatible with the IAU 2000/2006 resolutions and
must be used only in conjunction with IAU 2006 precession and
IAU 2000A nutation.
4) The result is returned in the range 0 to 2pi.
Called:
Pnm06a classical NPB matrix, IAU 2006/2000A
Gst06 Greenwich apparent ST, IAU 2006, given NPB matrix
Reference:
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Gst06a(uta, utb float64, tta, ttb float64) float64 {
var rnpb [3][3]float64
var gst float64
/* Classical nutation x precession x bias matrix, IAU 2000A. */
Pnm06a(tta, ttb, &rnpb)
/* Greenwich apparent sidereal time. */
gst = Gst06(uta, utb, tta, ttb, rnpb)
return gst
}
/*
Gst94 Greenwich Apparent Sidereal Time, IAU 1994
Greenwich apparent sidereal time (consistent with IAU 1982/94
resolutions).
Given:
uta,utb float64 UT1 as a 2-part Julian Date (Notes 1,2)
Returned (function value):
float64 Greenwich apparent sidereal time (radians)
Notes:
1) The UT1 date uta+utb is a Julian Date, apportioned in any
convenient way between the argument pair. For example,
JD(UT1)=2450123.7 could be expressed in any of these ways, among
others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. For UT, the date & time
method is best matched to the algorithm that is used by the Earth
Rotation Angle function, called internally: maximum precision is
delivered when the uta argument is for 0hrs UT1 on the day in
question and the utb argument lies in the range 0 to 1, or vice
versa.
2) The result is compatible with the IAU 1982 and 1994 resolutions,
except that accuracy has been compromised for the sake of
convenience in that UT is used instead of TDB (or TT) to compute
the equation of the equinoxes.
3) This GAST must be used only in conjunction with contemporaneous
IAU standards such as 1976 precession, 1980 obliquity and 1982
nutation. It is not compatible with the IAU 2000 resolutions.
4) The result is returned in the range 0 to 2pi.
Called:
Gmst82 Greenwich mean sidereal time, IAU 1982
Eqeq94 equation of the equinoxes, IAU 1994
Anp normalize angle into range 0 to 2pi
References:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
IAU Resolution C7, Recommendation 3 (1994)
*/
func Gst94(uta, utb float64) float64 {
var gmst82, eqeq94, gst float64
gmst82 = Gmst82(uta, utb)
eqeq94 = Eqeq94(uta, utb)
gst = Anp(gmst82 + eqeq94)
return gst
}
gofa-1.19.1/examples/ 0000775 0000000 0000000 00000000000 14535740236 0014346 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/ast/ 0000775 0000000 0000000 00000000000 14535740236 0015135 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/ast/main.go 0000664 0000000 0000000 00000014555 14535740236 0016422 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package main
//astrometry example sofa_ast_c.pdf P17.
import (
"fmt"
"math"
"github.com/hebl/gofa"
)
/**
C out:
ICRS, epoch J2000.0: 14 34 16.8118300 -12 31 10.396500
catalog -> astrometric: 14 34 16.4960283 -12 31 02.523786
astrometric -> CIRS: 14 34 20.2370587 -12 34 36.381654
catalog -> CIRS: 14 34 20.2370587 -12 34 36.381654
geocentric apparent: 14 35 01.7725802 -12 34 36.381654
CIRS -> topocentric: 14 34 20.2570287 -12 34 36.141207
CIRS -> observed: 14 34 16.9649101 -12 34 44.643091
ICRS -> observed: 14 34 16.9649106 -12 34 44.643094
ICRS -> CIRS (JPL, IERS): 14 34 20.2370639 -12 34 36.381756
ICRS -> CIRS (+ planets): 14 34 20.2370658 -12 34 36.381784
CIRS -> astrometric: 14 34 16.4960283 -12 31 02.523786
This out:
ICRS, epoch J2000.0: 14 34 16.8118300 -12 31 10.396500
catalog -> astrometric: 14 34 16.4960283 -12 31 02.523786
astrometric -> CIRS: 14 34 20.2370587 -12 34 36.381654
catalog -> CIRS: 14 34 20.2370587 -12 34 36.381654
geocentric apparent: 14 35 01.7725802 -12 34 36.381654
CIRS -> topocentric: 14 34 20.2570287 -12 34 36.141207
CIRS -> observed: 14 34 16.9649101 -12 34 44.643091
ICRS -> observed: 14 34 16.9649106 -12 34 44.643094
ICRS -> CIRS (JPL, IERS): 14 34 20.2370639 -12 34 36.381756
ICRS -> CIRS (+ planets): 14 34 20.2370658 -12 34 36.381784
CIRS -> astrometric: 14 34 16.4960283 -12 31 02.523786
*/
const (
DAS2R = 4.848136811095359935899141e-6 /* arcsec to radians */
)
func main() {
var astrom gofa.ASTROM
b := make([]gofa.LDBODY, 3)
var phi, elong, hm, phpa, tc, rh, wl, utc1, utc2, tai1, tai2 float64
var tt1, tt2, xp, yp, dut1, dx, dy, rc, dc, pr, pd, px, rv, rca, dca float64
var ri, di, eo, ra, da, aot, zot, hot, dot, rot, aob, zob, hob, dob, rob float64
var pvh, pvb [2][3]float64
var r [3][3]float64
var x, y, s float64
/* Site longitude, latitude (radians) and height above the geoid (m). */
gofa.Af2a('-', 5, 41, 54.2, &elong)
gofa.Af2a('-', 15, 57, 42.8, &phi)
hm = 625.0
/* Ambient pressure (HPa), temperature (C) and rel. humidity (frac). */
phpa = 952.0
tc = 18.5
rh = 0.83
/* Effective color (microns). */
wl = 0.55
/* UTC date. */
if gofa.Dtf2d("UTC", 2013, 4, 2, 23, 15, 43.55, &utc1, &utc2) != 0 {
return
}
/* TT date. */
if gofa.Utctai(utc1, utc2, &tai1, &tai2) != 0 {
return
}
if gofa.Taitt(tai1, tai2, &tt1, &tt2) != 0 {
return
}
/* EOPs: polar motion in radians, UT1-UTC in seconds. */
xp = 50.995e-3 * DAS2R
yp = 376.723e-3 * DAS2R
dut1 = 155.0675e-3
/* Corrections to IAU 2000A CIP (radians). */
dx = 0.269e-3 * DAS2R
dy = -0.274e-3 * DAS2R
/* Star ICRS RA,Dec (radians). */
if gofa.Tf2a(' ', 14, 34, 16.81183, &rc) != 0 {
return
}
if gofa.Af2a('-', 12, 31, 10.3965, &dc) != 0 {
return
}
reprd("ICRS, epoch J2000.0:", rc, dc)
/* Annual proper motion: RA/Dec derivatives, epoch J2000.0. */
pr = math.Atan2(-354.45e-3*DAS2R, math.Cos(dc))
pd = 595.35e-3 * DAS2R
/* Parallax (arcsec) and recession speed (km/s). */
px = 164.99e-3
rv = 0.0
/* ICRS catalog to astrometric place... */
gofa.Atcc13(rc, dc, pr, pd, px, rv, tt1, tt2, &rca, &dca)
reprd("catalog -> astrometric:", rca, dca)
/* ...then to CIRS (geocentric observer). */
gofa.Atci13(rca, dca, 0.0, 0.0, 0.0, 0.0, tt1, tt2, &ri, &di, &eo)
reprd("astrometric -> CIRS:", ri, di)
/* ICRS catalog directly to CIRS (geocentric observer). */
gofa.Atci13(rc, dc, pr, pd, px, rv, tt1, tt2, &ri, &di, &eo)
reprd("catalog -> CIRS:", ri, di)
/* Apparent place. */
ra = gofa.Anp(ri - eo)
da = di
reprd("geocentric apparent:", ra, da)
/* CIRS to topocentric. */
if gofa.Atio13(ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp,
0.0, 0.0, 0.0, 0.0,
&aot, &zot, &hot, &dot, &rot) != 0 {
return
}
reprd("CIRS -> topocentric:", rot, dot)
/* CIRS to observed. */
if gofa.Atio13(ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp,
phpa, tc, rh, wl,
&aob, &zob, &hob, &dob, &rob) != 0 {
return
}
reprd("CIRS -> observed:", rob, dob)
/* ICRS to observed. */
if gofa.Atco13(rc, dc, pr, pd, px, rv, utc1, utc2, dut1,
elong, phi, hm, xp, yp, phpa, tc, rh, wl,
&aob, &zob, &hob, &dob, &rob, &eo) != 0 {
return
}
reprd("ICRS -> observed:", rob, dob)
/* ICRS to CIRS using some user-supplied parameters. */
/* SOFA heliocentric Earth ephemeris. */
if gofa.Epv00(tt1, tt2, &pvh, &pvb) != 0 {
return
}
/* JPL DE405 barycentric Earth ephemeris. */
pvb[0][0] = -0.9741704366519668
pvb[0][1] = -0.2115201000882231
pvb[0][2] = -0.0917583114068277
pvb[1][0] = 0.0036436589347388
pvb[1][1] = -0.0154287318503146
pvb[1][2] = -0.0066892203821059
/* IAU 2000A CIP. */
gofa.Pnm00a(tt1, tt2, &r)
gofa.Bpn2xy(r, &x, &y)
/* Apply IERS corrections. */
x += dx
y += dy
/* SOFA CIO locator. */
s = gofa.S06(tt1, tt2, x, y)
/* Populate the context. */
gofa.Apci(tt1, tt2, pvb, pvh[0], x, y, s, &astrom)
/* Carry out the transformation and report the results. */
gofa.Atciq(rc, dc, pr, pd, px, rv, &astrom, &ri, &di)
reprd("ICRS -> CIRS (JPL, IERS):", ri, di)
/* The same but with Saturn then Jupiter then Sun light deflection. */
b[0].Bm = 0.00028574
b[0].Dl = 3e-10
b[0].Pv[0][0] = -7.8101442680818964
b[0].Pv[0][1] = -5.6095668114887358
b[0].Pv[0][2] = -1.9807981923749924
b[0].Pv[1][0] = 0.0030723248971152
b[0].Pv[1][1] = -0.0040699547707598
b[0].Pv[1][2] = -0.0018133584165345
b[1].Bm = 0.00095435
b[1].Dl = 3e-9
b[1].Pv[0][0] = 0.7380987962351833
b[1].Pv[0][1] = 4.6365869247538951
b[1].Pv[0][2] = 1.9693136030111202
b[1].Pv[1][0] = -0.0075581692172088
b[1].Pv[1][1] = 0.0012691372216750
b[1].Pv[1][2] = 0.0007279990012801
b[2].Bm = 1.0
b[2].Dl = 6e-6
b[2].Pv[0][0] = -0.0007121743770509
b[2].Pv[0][1] = -0.0023047830339257
b[2].Pv[0][2] = -0.0010586596574639
b[2].Pv[1][0] = 0.0000062923521264
b[2].Pv[1][1] = -0.0000003308883872
b[2].Pv[1][2] = -0.0000002964866231
gofa.Atciqn(rc, dc, pr, pd, px, rv, &astrom, 3, b, &ri, &di)
reprd("ICRS -> CIRS (+ planets):", ri, di)
/* CIRS to ICRS (astrometric). */
gofa.Aticqn(ri, di, &astrom, 3, b, &rca, &dca)
reprd("CIRS -> astrometric:", rca, dca)
}
func reprd(s string, ra, dc float64) {
var pm byte
var i [4]int
fmt.Printf("%25s", s)
gofa.A2tf(7, ra, &pm, &i)
fmt.Printf(" %2.2d %2.2d %2.2d.%7.7d", i[0], i[1], i[2], i[3])
gofa.A2af(6, dc, &pm, &i)
fmt.Printf(" %c%2.2d %2.2d %2.2d.%6.6d\n", pm, i[0], i[1], i[2], i[3])
}
gofa-1.19.1/examples/pn/ 0000775 0000000 0000000 00000000000 14535740236 0014763 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/pn/main.go 0000664 0000000 0000000 00000016555 14535740236 0016252 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package main
import (
"fmt"
"math"
"github.com/hebl/gofa"
)
// gofa_pn_c.pdf examples
func printMatrix(m [3][3]float64) {
for i := 0; i < 3; i++ {
fmt.Printf("%19.15f %19.15f %19.15f\n", m[i][0], m[i][1], m[i][2])
}
fmt.Println(" ")
}
func fmtDeg(v float64) string {
return fmt.Sprintf("%.15f", v*gofa.DR2D)
}
func fmtHms(v float64) string {
var sign byte
var ihmsf [4]int
gofa.A2tf(9, v, &sign, &ihmsf)
return fmt.Sprintf("%s%02dh %02dm %02d.%09ds", string(sign), ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
}
func main() {
var iy, im, id, ih, min int
var sec, xp, yp, dut1,
ddp80, dde80, dx00, dy00, dx06, dy06,
utc1, utc2, tai1, tai2, tt1, tt2, ut11, ut12, dp80, de80,
dpsi, deps, epsa,
ee, gst, x, y, s,
era, sp, dp00, de00, ddp00, dde00 float64
var v1, v2 [3]float64
var rp, rn, rnpb, rc2ti, rpom, rc2it, rc2i, rb, rpb [3][3]float64
/* UTC. */
iy = 2007
im = 4
id = 5
ih = 12
min = 0
sec = 0.0
/* Polar motion (arcsec->radians). */
xp = 0.0349282 * gofa.DAS2R
yp = 0.4833163 * gofa.DAS2R
/* UT1-UTC (s). */
dut1 = -0.072073685
/* Nutation corrections wrt IAU 1976/1980 (mas->radians). */
ddp80 = -55.0655 * gofa.DMAS2R
dde80 = -6.3580 * gofa.DMAS2R
/* CIP offsets wrt IAU 2000A (mas->radians). */
dx00 = 0.1725 * gofa.DMAS2R
dy00 = -0.2650 * gofa.DMAS2R
/* CIP offsets wrt IAU 2006/2000A (mas->radians). */
dx06 = 0.1750 * gofa.DMAS2R
dy06 = -0.2259 * gofa.DMAS2R
/* From UTC get TT and UT1. */
gofa.Dtf2d("utc", iy, im, id, ih, min, sec, &utc1, &utc2)
gofa.Utctai(utc1, utc2, &tai1, &tai2)
gofa.Taitt(tai1, tai2, &tt1, &tt2)
gofa.Utcut1(utc1, utc2, dut1, &ut11, &ut12)
fmt.Printf("TT = %.1f + %.15f\n", tt1, tt2)
fmt.Printf("UT1 = %.1f + %.15f\n\n", ut11, ut12)
/* ============= */
/* IAU 1976/1980 */
/* ============= */
/* IAU 1976 precession matrix, J2000.0 to date. */
gofa.Pmat76(tt1, tt2, &rp)
/* IAU 1980 nutation. */
gofa.Nut80(tt1, tt2, &dp80, &de80)
/* Add adjustments: frame bias, precession-rates, geophysical. */
dpsi = dp80 + ddp80
deps = de80 + dde80
/* Mean obliquity. */
epsa = gofa.Obl80(tt1, tt2)
/* Build the rotation matrix. */
gofa.Numat(epsa, dpsi, deps, &rn)
/* Combine the matrices: PN = N x P. */
gofa.Rxr(rn, rp, &rnpb)
/* Equation of the equinoxes, including nutation correction. */
ee = gofa.Eqeq94(tt1, tt2) + ddp80*math.Cos(epsa)
/* Greenwich apparent sidereal time (IAU 1982/1994). */
gst = gofa.Anp(gofa.Gmst82(ut11, ut12) + ee)
/* Form celestial-terrestrial matrix (no polar motion yet). */
gofa.Cr(rnpb, &rc2ti)
gofa.Rz(gst, &rc2ti)
/* Polar motion matrix (TIRS->ITRS, IERS 1996). */
gofa.Ir(&rpom)
gofa.Rx(-yp, &rpom)
gofa.Ry(-xp, &rpom)
/* Form celestial-terrestrial matrix (including polar motion). */
gofa.Rxr(rpom, rc2ti, &rc2it)
//
fmt.Printf("IAU 1976/1980\n\n")
//
fmt.Printf("NPB matrix, equinox based:\n")
printMatrix(rnpb)
fmt.Printf("GST = %s°\n = %s\n\n", fmtDeg(gst), fmtHms(gst))
//
fmt.Printf("celestial to terrestrial matrix (no polar motion)\n")
printMatrix(rc2ti)
//
fmt.Printf("celestial to terrestrial matrix\n")
printMatrix(rc2it) //
//
/* ==================== */
/* IAU 2000A, CIO based */
/* ==================== */
/* CIP and CIO, IAU 2000A. */
gofa.Xys00a(tt1, tt2, &x, &y, &s)
/* Add CIP corrections. */
x = x + dx00
y = y + dy00
/* GCRS to CIRS matrix. */
gofa.C2ixys(x, y, s, &rc2i)
/* Earth rotation angle. */
era = gofa.Era00(ut11, ut12)
/* Form celestial-terrestrial matrix (no polar motion yet). */
gofa.Cr(rc2i, &rc2ti)
gofa.Rz(era, &rc2ti)
/* Polar motion matrix (TIRS->ITRS, IERS 2003). */
sp = gofa.Sp00(tt1, tt2)
gofa.Pom00(xp, yp, sp, &rpom)
/* Form celestial-terrestrial matrix (including polar motion). */
gofa.Rxr(rpom, rc2ti, &rc2it)
//
fmt.Printf("IAU 2000A, CIO based\n\n")
fmt.Printf("X = %.15f\nY = %.15f\ns = %.9f\"\n\n", x, y, s*gofa.DR2AS)
//
fmt.Printf("NPB matrix, CIO based\n")
printMatrix(rc2i)
//
fmt.Printf("ERA = %s°\n = %s\n\n", fmtDeg(era), fmtHms(era))
fmt.Printf("celestial to terrestrial matrix (no polar motion)\n")
printMatrix(rc2ti)
fmt.Printf("celestial to terrestrial matrix\n")
printMatrix(rc2it) //
//
/* ======================== */
/* IAU 2000A, equinox based */
/* ======================== */
/* Nutation, IAU 2000A. */
gofa.Nut00a(tt1, tt2, &dp00, &de00)
/* Precession-nutation quantities, IAU 2000. */
gofa.Pn00(tt1, tt2, dp00, de00, &epsa, &rb, &rp, &rpb, &rn, &rnpb)
/* Transform dX,dY corrections from GCRS to mean of date. */
v1[0] = dx00
v1[1] = dy00
v1[2] = 0.0
gofa.Rxp(rnpb, v1, &v2)
ddp00 = v2[0] / math.Sin(epsa)
dde00 = v2[1]
/* Corrected nutation. */
dpsi = dp00 + ddp00
deps = de00 + dde00
/* Build the rotation matrix. */
gofa.Numat(epsa, dpsi, deps, &rn)
/* Combine the matrices: PN = N x P. */
gofa.Rxr(rn, rpb, &rnpb)
/* Greenwich apparent sidereal time (IAU 2000). */
gst = gofa.Anp(gofa.Gmst00(ut11, ut12, tt1, tt2) + gofa.Ee00(tt1, tt2, epsa, dpsi))
/* Form celestial-terrestrial matrix (no polar motion yet). */
gofa.Cr(rnpb, &rc2ti)
gofa.Rz(gst, &rc2ti)
/* Polar motion matrix (TIRS->ITRS, IERS 2003). */
sp = gofa.Sp00(tt1, tt2)
gofa.Pom00(xp, yp, sp, &rpom)
/* Form celestial-terrestrial matrix (including polar motion). */
gofa.Rxr(rpom, rc2ti, &rc2it)
//
fmt.Printf("IAU 2000A, equinox based\n\n")
//
fmt.Printf("NPB matrix, CIO based\n")
printMatrix(rnpb)
//
fmt.Printf("GST = %s°\n = %s\n\n", fmtDeg(gst), fmtHms(gst))
fmt.Printf("celestial to terrestrial matrix (no polar motion)\n")
printMatrix(rc2ti)
fmt.Printf("celestial to terrestrial matrix\n")
printMatrix(rc2it) //
//
/* ========================= */
/* IAU 2006/2000A, CIO based */
/* ========================= */
/* CIP and CIO, IAU 2006/2000A. */
gofa.Xys06a(tt1, tt2, &x, &y, &s)
/* Add CIP corrections. */
x += dx06
y += dy06
/* GCRS to CIRS matrix. */
gofa.C2ixys(x, y, s, &rc2i)
/* Earth rotation angle. */
era = gofa.Era00(ut11, ut12)
/* Form celestial-terrestrial matrix (no polar motion yet). */
gofa.Cr(rc2i, &rc2ti)
gofa.Rz(era, &rc2ti)
/* Polar motion matrix (TIRS->ITRS, IERS 2003). */
sp = gofa.Sp00(tt1, tt2)
gofa.Pom00(xp, yp, sp, &rpom)
/* Form celestial-terrestrial matrix (including polar motion). */
gofa.Rxr(rpom, rc2ti, &rc2it)
/* =========================================== */
/* IAU 2006/2000A, CIO based, using X,Y series */
/* =========================================== */
/* CIP and CIO, IAU 2006/2000A. */
gofa.Xy06(tt1, tt2, &x, &y)
s = gofa.S06(tt1, tt2, x, y)
/* Add CIP corrections. */
x += dx06
y += dy06
/* GCRS to CIRS matrix. */
gofa.C2ixys(x, y, s, &rc2i)
/* Earth rotation angle. */
era = gofa.Era00(ut11, ut12)
/* Form celestial-terrestrial matrix (no polar motion yet). */
gofa.Cr(rc2i, &rc2ti)
gofa.Rz(era, &rc2ti)
/* Polar motion matrix (TIRS->ITRS, IERS 2003). */
sp = gofa.Sp00(tt1, tt2)
gofa.Pom00(xp, yp, sp, &rpom)
/* Form celestial-terrestrial matrix (including polar motion). */
gofa.Rxr(rpom, rc2ti, &rc2it)
//
fmt.Printf("IAU 2006/2000A, CIO based\n\n")
fmt.Printf("X = %.15f\nY = %.15f\ns = %.9f\"\n\n", x, y, s*gofa.DR2AS)
//
fmt.Printf("NPB matrix, CIO based\n")
printMatrix(rc2i)
//
fmt.Printf("ERA = %s°\n = %s\n\n", fmtDeg(era), fmtHms(era))
fmt.Printf("celestial to terrestrial matrix (no polar motion)\n")
printMatrix(rc2ti)
fmt.Printf("celestial to terrestrial matrix\n")
printMatrix(rc2it) //
}
gofa-1.19.1/examples/proj/ 0000775 0000000 0000000 00000000000 14535740236 0015320 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/proj/main.go 0000664 0000000 0000000 00000004050 14535740236 0016572 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package main
import (
"fmt"
"github.com/hebl/gofa"
)
// Gnomonic projection example sofa_ast_c.pdf P26.
func main() {
const fl = 3430.0 /* Focal length (mm) */
var sign byte
var j, n int
var i [4]int
var raz, decz, ra, dec, xi, eta, x, y, az1, bz1, az2, bz2 float64
/* Observed [RA,Dec] of tangent point (radians). */
raz = 9.0 * 15.0 * gofa.DD2R
decz = 89.5 * gofa.DD2R
//
/* Observed [RA,Dec] of a star (radians). */
ra = 5.0 * 15.0 * gofa.DD2R
dec = 89.75 * gofa.DD2R
/* Plate coordinates of star image. */
j = gofa.Tpxes(ra, dec, raz, decz, &xi, &eta)
if j != 0 {
return
}
fmt.Printf("image [x,y]/mm = %+8.3f, %+8.3f\n", xi*fl, eta*fl)
// C out: image [x,y]/mm = -12.961, +22.450
// This out: image [x,y]/mm = -12.961, +22.450
/* Plate coordinates of a different star image. */
x = -20.0
y = 60.0
/* Celestial coordinates of that star. */
xi = x / fl
eta = y / fl
gofa.Tpsts(xi, eta, raz, decz, &ra, &dec)
gofa.A2tf(2, ra, &sign, &i)
fmt.Printf("star [RA,Dec] = %2.2d %2.2d %2.2d.%2.2d",
i[0], i[1], i[2], i[3])
gofa.A2af(1, dec, &sign, &i)
fmt.Printf(" %c%2.2d %2.2d %2.2d.%1d\n", sign, i[0], i[1], i[2], i[3])
// C out: star [RA,Dec] = 23 14 31.74 +89 23 48.8
// This out: star [RA,Dec] = 23 14 31.74 +89 23 48.8
//
/* Given that star's [RA,Dec] and [x,y], solve for tangent point. */
n = gofa.Tpors(xi, eta, ra, dec, &az1, &bz1, &az2, &bz2)
if n != 0 {
gofa.A2tf(2, az1, &sign, &i)
fmt.Printf("TP1 = %2.2d %2.2d %2.2d.%2.2d",
i[0], i[1], i[2], i[3])
gofa.A2af(1, bz1, &sign, &i)
fmt.Printf(" %c%2.2d %2.2d %2.2d.%1d\n", sign, i[0], i[1], i[2], i[3])
if n == 2 {
gofa.A2tf(2, az2, &sign, &i)
fmt.Printf("TP2 = %2.2d %2.2d %2.2d.%2.2d",
i[0], i[1], i[2], i[3])
gofa.A2af(1, bz2, &sign, &i)
fmt.Printf(" %c%2.2d %2.2d %2.2d.%1d\n", sign, i[0], i[1], i[2], i[3])
}
}
// C out:
// TP1 = 01 29 03.48 +88 29 44.5
// TP2 = 09 00 00.00 +89 30 00.0
// This out:
// TP1 = 01 29 03.48 +88 29 44.5
// TP2 = 09 00 00.00 +89 30 00.0
}
gofa-1.19.1/examples/ts/ 0000775 0000000 0000000 00000000000 14535740236 0014774 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/ts/main.go 0000664 0000000 0000000 00000007255 14535740236 0016260 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package main
import (
"fmt"
"math"
"github.com/hebl/gofa"
)
func main() {
ts()
}
/**
C version out:
UTC 2006/01/15 21:24:37.500000
UT1 2006/01/15 21:24:37.834100
TAI 2006/01/15 21:25:10.500000
TT 2006/01/15 21:25:42.684000
TCG 2006/01/15 21:25:43.322690
TDB 2006/01/15 21:25:42.684373
TCB 2006/01/15 21:25:56.893952
This version out:
UTC 2006/01/15 21:24:37.500000
UT1 2006/01/15 21:24:37.834100
TAI 2006/01/15 21:25:10.500000
TT 2006/01/15 21:25:42.684000
TCG 2006/01/15 21:25:43.322690
TDB 2006/01/15 21:25:42.684373
TCB 2006/01/15 21:25:56.893952
It's same!!!
*/
func ts() int {
var latnd, latnm, lonwd, lonwm, j, iy, mo, id, ih, im int
var ihmsf [4]int
var slatn, slonw, hm, elon, phi, u, v, sec float64
var utc1, utc2, dut, ut11, ut12, ut, tai1, tai2, tt1, tt2, tcg1, tcg2, dtr, tdb1, tdb2, tcb1, tcb2 float64
var xyz [3]float64
/* Site terrestrial coordinates (WGS84). */
latnd = 19
latnm = 28
slatn = 52.5
lonwd = 155
lonwm = 55
slonw = 59.6
hm = 0.0
/* Transform to geocentric. */
j = gofa.Af2a('+', latnd, latnm, slatn, &phi)
if j != 0 {
return 1
}
j = gofa.Af2a('-', lonwd, lonwm, slonw, &elon)
if j != 0 {
return 1
}
j = gofa.Gd2gc(1, elon, phi, hm, &xyz)
if j != 0 {
return 1
}
u = math.Sqrt(xyz[0]*xyz[0] + xyz[1]*xyz[1])
v = xyz[2]
/* UTC date and time. */
iy = 2006
mo = 1
id = 15
ih = 21
im = 24
sec = 37.5
/* Transform into internal format. */
j = gofa.Dtf2d("UTC", iy, mo, id, ih, im, sec, &utc1, &utc2)
if j != 0 {
return 1
}
/* UT1-UTC (s, from IERS). */
dut = 0.3341
/* UTC -> UT1. */
j = gofa.Utcut1(utc1, utc2, dut, &ut11, &ut12)
if j != 0 {
return 1
}
/* Extract fraction for TDB-TT calculation, later. */
ut = math.Mod(math.Mod(ut11, 1.0)+math.Mod(ut12, 1.0), 1.0) + 0.5
/* UTC -> TAI -> TT -> TCG. */
j = gofa.Utctai(utc1, utc2, &tai1, &tai2)
if j != 0 {
return 1
}
j = gofa.Taitt(tai1, tai2, &tt1, &tt2)
if j != 0 {
return 1
}
j = gofa.Tttcg(tt1, tt2, &tcg1, &tcg2)
if j != 0 {
return 1
}
/*TDB-TT (using TT as a substitute for TDB). */
dtr = gofa.Dtdb(tt1, tt2, ut, elon, u/1e3, v/1e3)
/* TT -> TDB -> TCB. */
j = gofa.Tttdb(tt1, tt2, dtr, &tdb1, &tdb2)
if j != 0 {
return 1
}
j = gofa.Tdbtcb(tdb1, tdb2, &tcb1, &tcb2)
if j != 0 {
return 1
}
/* Report. */
j = gofa.D2dtf("UTC", 6, utc1, utc2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("UTC%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("ut1", 6, ut11, ut12, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("UT1%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("tai", 6, tai1, tai2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("TAI%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("tt", 6, tt1, tt2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("TT %5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("tcg", 6, tcg1, tcg2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("TCG%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("tdb", 6, tdb1, tdb2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("TDB%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
j = gofa.D2dtf("tcb", 6, tcb1, tcb2, &iy, &mo, &id, &ihmsf)
if j != 0 {
return 1
}
fmt.Printf("TCB%5d/%2.2d/%2.2d%3d:%2.2d:%2.2d.%6.6d\n",
iy, mo, id, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
return 0
}
gofa-1.19.1/examples/vml/ 0000775 0000000 0000000 00000000000 14535740236 0015144 5 ustar 00root root 0000000 0000000 gofa-1.19.1/examples/vml/main.go 0000664 0000000 0000000 00000006062 14535740236 0016423 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package main
import (
"fmt"
"math"
"github.com/hebl/gofa"
)
func main() {
p03()
fmt.Println()
p05()
fmt.Println()
p09()
fmt.Println()
p11()
}
func p03() {
// C out:
// 17011 km, 61 deg
// This out:
// 17011 km, 61 deg
const R2D = 57.2957795 /* radians to degrees */
const RKM = 6375.0 /* Earth radius in km */
/* Longitudes and latitudes (radians) for London and Sydney. */
al := -0.2 / R2D
bl := 51.5 / R2D
as := 151.2 / R2D
bs := -33.9 / R2D
/*Great-circle distance and initial heading. */
fmt.Printf("%5.0f km,%4.0f deg\n",
gofa.Seps(al, bl, as, bs)*RKM,
gofa.Pas(al, bl, as, bs)*R2D)
}
func p05() {
// C out:
// -00 59 59.999
// -01 00 00.00
// This out:
// -00 59 59.999
// -01 00 00.00
var ha float64
var sign byte
var ihmsf [4]int
ha = -0.261799315
gofa.A2tf(3, ha, &sign, &ihmsf)
fmt.Printf("%c%2.2d %2.2d %2.2d.%3.3d\n", sign, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
gofa.A2tf(2, ha, &sign, &ihmsf)
fmt.Printf("%c%2.2d %2.2d %2.2d.%2.2d\n", sign, ihmsf[0], ihmsf[1], ihmsf[2], ihmsf[3])
}
func p09() {
// C out:
// The two positions are 0.000000 arcsec apart.
// The two positions are 0.000612 arcsec apart.
// This out:
// The two positions are 0.000000 arcsec apart.
// The two positions are 0.000612 arcsec apart.
var ra, da, rb, db, theta, s, c float64
var a, b, axb [3]float64
/* RA,Dec of source ICRF J044238.6-001743 in the ICRF2 catalog. */
gofa.Tf2a('+', 04, 42, 38.66073910, &ra)
gofa.Af2a('-', 00, 17, 43.4203921, &da)
/* RA,Dec of the same source in the ICRF3 (S/X) catalog. */
gofa.Tf2a('+', 04, 42, 38.66072366, &rb)
gofa.Af2a('-', 00, 17, 43.4209582, &db)
/* Method 1: spherical trigonometry (cosine rule). */
theta = math.Acos(math.Sin(da)*math.Sin(db) + math.Cos(da)*math.Cos(db)*math.Cos(rb-ra))
fmt.Printf("The two positions are %9.6f arcsec apart.\n", theta*206264.80624709635515647335733)
/* Method 2: vectors (sine and cosine from cross and dot product). */
gofa.S2c(ra, da, &a)
gofa.S2c(rb, db, &b)
gofa.Pxp(a, b, &axb)
s = gofa.Pm(axb)
c = gofa.Pdp(a, b)
theta = math.Atan2(s, c)
fmt.Printf("The two positions are %9.6f arcsec apart.\n", theta*206264.80624709635515647335733)
}
func p11() {
// sofa_vm_c.pdf p11
// C out:
// Frame bias is 23.1 mas around 19 29 14.8 -39 06 19 GCRS.
// This out:
// Frame bias is 23.1 mas around 19 29 14.8 -39 06 19 GCRS.
var sign byte
var i4 [4]int
var rb [3][3]float64
var vb [3]float64
var angle, ra, dec float64
/* Generate frame bias matrix. */
gofa.Ir(&rb)
gofa.Rz(-0.0146*gofa.DAS2R, &rb)
gofa.Ry(-0.041775*gofa.DAS2R*math.Sin(84381.448*gofa.DAS2R), &rb)
gofa.Rx(0.0068192*gofa.DAS2R, &rb)
/* Convert into r-vector form. */
gofa.Rm2v(rb, &vb)
/* Report. */
gofa.P2s(vb, &ra, &dec, &angle)
fmt.Printf("Frame bias is %4.1f mas around", angle*1e3/gofa.DAS2R)
gofa.A2tf(1, gofa.Anp(ra), &sign, &i4)
fmt.Printf("%3.2d %2.2d %2.2d.%d", i4[0], i4[1], i4[2], i4[3])
gofa.A2af(0, dec, &sign, &i4)
fmt.Printf(" %c%2.2d %2.2d %2.2d GCRS. \n", sign, i4[0], i4[1], i4[2])
}
gofa-1.19.1/fundargs.go 0000664 0000000 0000000 00000033256 14535740236 0014701 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Fundamental Arguments (14)
/*
Fad03 mean elongation of the Moon from the Sun.
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 D, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Fad03(t float64) float64 {
var a float64
/* Mean elongation of the Moon from the Sun (IERS Conventions 2003). */
a = fmod(1072260.703692+
t*(1602961601.2090+
t*(-6.3706+
t*(0.006593+
t*(-0.00003169)))), TURNAS) * DAS2R
return a
}
/*
Fae03 mean longitude of Earth.
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Earth, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Fae03(t float64) float64 {
var a float64
/* Mean longitude of Earth (IERS Conventions 2003). */
a = fmod(1.753470314+628.3075849991*t, D2PI)
return a
}
/*
Faf03 mean longitude of the Moon minus mean longitude of the ascending node.
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 F, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Faf03(t float64) float64 {
var a float64
/* Mean longitude of the Moon minus that of the ascending node */
/* (IERS Conventions 2003). */
a = fmod(335779.526232+
t*(1739527262.8478+
t*(-12.7512+
t*(-0.001037+
t*(0.00000417)))), TURNAS) * DAS2R
return a
}
/*
Faju03 Mean longitude of Jupiter
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Jupiter, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Faju03(t float64) float64 {
var a float64
/* Mean longitude of Jupiter (IERS Conventions 2003). */
a = fmod(0.599546497+52.9690962641*t, D2PI)
return a
}
/*
Fal03 Mean anomaly of the Moon
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 l, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Fal03(t float64) float64 {
var a float64
/* Mean anomaly of the Moon (IERS Conventions 2003). */
a = fmod(485868.249036+
t*(1717915923.2178+
t*(31.8792+
t*(0.051635+
t*(-0.00024470)))), TURNAS) * DAS2R
return a
}
/*
Falp03 Mean anomaly of the Sun
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 l', radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Falp03(t float64) float64 {
var a float64
/* Mean anomaly of the Sun (IERS Conventions 2003). */
a = fmod(1287104.793048+
t*(129596581.0481+
t*(-0.5532+
t*(0.000136+
t*(-0.00001149)))), TURNAS) * DAS2R
return a
}
/*
Fama03 Mean longitude of Mars
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Mars, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Fama03(t float64) float64 {
var a float64
/* Mean longitude of Mars (IERS Conventions 2003). */
a = fmod(6.203480913+334.0612426700*t, D2PI)
return a
}
/*
Fame03 Mean longitude of Mercury
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Mercury, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Fame03(t float64) float64 {
var a float64
/* Mean longitude of Mercury (IERS Conventions 2003). */
a = fmod(4.402608842+2608.7903141574*t, D2PI)
return a
}
/*
Fane03 Mean longitude of Neptune
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Neptune, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is adapted from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Fane03(t float64) float64 {
var a float64
/* Mean longitude of Neptune (IERS Conventions 2003). */
a = fmod(5.311886287+3.8133035638*t, D2PI)
return a
}
/*
Faom03 Mean longitude of the Moon's ascending node
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 Omega, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J., 1994, Astron.Astrophys. 282, 663-683.
*/
func Faom03(t float64) float64 {
var a float64
/* Mean longitude of the Moon's ascending node */
/* (IERS Conventions 2003). */
a = fmod(450160.398036+
t*(-6962890.5431+
t*(7.4722+
t*(0.007702+
t*(-0.00005939)))), TURNAS) * DAS2R
return a
}
/*
Fapa03 General accumulated precession in longitude
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 general precession in longitude, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003). It
is taken from Kinoshita & Souchay (1990) and comes originally
from Lieske et al. (1977).
References:
Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron.
48, 187
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
Astron.Astrophys. 58, 1-16
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Fapa03(t float64) float64 {
var a float64
/* General accumulated precession in longitude. */
a = (0.024381750 + 0.00000538691*t) * t
return a
}
/*
Fasa03 Mean longitude of Saturn
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Saturn, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Fasa03(t float64) float64 {
var a float64
/* Mean longitude of Saturn (IERS Conventions 2003). */
a = fmod(0.874016757+21.3299104960*t, D2PI)
return a
}
/*
Faur03 Mean longitude of Uranus
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Uranus, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
is adapted from Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
*/
func Faur03(t float64) float64 {
var a float64
/* Mean longitude of Uranus (IERS Conventions 2003). */
a = fmod(5.481293872+7.4781598567*t, D2PI)
return a
}
/*
Fave03 Mean longitude of Venus
Fundamental argument, IERS Conventions (2003)
Given:
t float64 TDB, Julian centuries since J2000.0 (Note 1)
Returned (function value):
float64 mean longitude of Venus, radians (Note 2)
Notes:
1) Though t is strictly TDB, it is usually more convenient to use
TT, which makes no significant difference.
2) The expression used is as adopted in IERS Conventions (2003) and
comes from Souchay et al. (1999) after Simon et al. (1994).
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
*/
func Fave03(t float64) float64 {
var a float64
/* Mean longitude of Venus (IERS Conventions 2003). */
a = fmod(3.176146697+1021.3285546211*t, D2PI)
return a
}
gofa-1.19.1/go.mod 0000664 0000000 0000000 00000000045 14535740236 0013635 0 ustar 00root root 0000000 0000000 module github.com/hebl/gofa
go 1.18
gofa-1.19.1/gofa.go 0000664 0000000 0000000 00000003027 14535740236 0013775 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
const (
VERSION = 1.18
)
/*
ASTROM Star-independent astrometry parameters
(Vectors Eb, Eh, Em and V are all with respect to BCRS axes.)
*/
type ASTROM struct {
Pmt float64 /* PM time interval (SSB, Julian years) */
Eb [3]float64 /* SSB to observer (vector, au) */
Eh [3]float64 /* Sun to observer (unit vector) */
Em float64 /* distance from Sun to observer (au) */
V [3]float64 /* barycentric observer velocity (vector, c) */
Bm1 float64 /* sqrt(1-|v|^2): reciprocal of Lorenz factor */
Bpn [3][3]float64 /* bias-precession-nutation matrix */
Along float64 /* longitude + s' + dERA(DUT) (radians) */
Phi float64 /* geodetic latitude (radians) */
Xpl float64 /* polar motion xp wrt local meridian (radians) */
Ypl float64 /* polar motion yp wrt local meridian (radians) */
Sphi float64 /* sine of geodetic latitude */
Cphi float64 /* cosine of geodetic latitude */
Diurab float64 /* magnitude of diurnal aberration vector */
Eral float64 /* "local" Earth rotation angle (radians) */
Refa float64 /* refraction constant A (radians) */
Refb float64 /* refraction constant B (radians) */
}
/*
LDBODY Body parameters for light deflection
*/
type LDBODY struct {
Bm float64 /* mass of the body (solar masses) */
Dl float64 /* deflection limiter (radians^2/2) */
Pv [2][3]float64 /* barycentric PV of the body (au, au/day) */
}
gofa-1.19.1/gofam.go 0000664 0000000 0000000 00000006661 14535740236 0014161 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Constant value and math functions
import "math"
// Const
const (
/* Pi */
DPI = 3.141592653589793238462643
/* 2Pi */
D2PI = 6.283185307179586476925287
/* Pi/2 */
DPI2 = 1.570796326794896619231322
/* Radians to degrees */
DR2D = 57.29577951308232087679815
/* Degrees to radians */
DD2R = 1.745329251994329576923691e-2
/* Radians to arcseconds */
DR2AS = 206264.8062470963551564734
/* Arcseconds to radians */
DAS2R = 4.848136811095359935899141e-6
/* Seconds of time to radians */
DS2R = 7.272205216643039903848712e-5
/* Arcseconds in a full circle */
TURNAS = 1296000.0
/* Milliarcseconds to radians */
DMAS2R = (DAS2R / 1e3)
/* Length of tropical year B1900 (days) */
DTY = 365.242198781
/* Seconds per day. */
DAYSEC = 86400.0
/* Days per Julian year */
DJY = 365.25
/* Days per Julian century */
DJC = 36525.0
/* Days per Julian millennium */
DJM = 365250.0
/* Reference epoch (J2000.0), Julian Date */
DJ00 = 2451545.0
/* Julian Date of Modified Julian Date zero */
DJM0 = 2400000.5
/* Reference epoch (J2000.0), Modified Julian Date */
DJM00 = 51544.5
/* 1977 Jan 1.0 as MJD */
DJM77 = 43144.0
/* TT minus TAI (s) */
TTMTAI = 32.184
/* Astronomical unit (m, IAU 2012) */
DAU = 149597870.7e3
/* Speed of light (m/s) */
CMPS = 299792458.0
/* Light time for 1 au (s) */
AULT = (DAU / CMPS)
/* Speed of light (au per day) */
DC = (DAYSEC / AULT)
/* L_G = 1 - d(TT)/d(TCG) */
ELG = 6.969290134e-10
/* L_B = 1 - d(TDB)/d(TCB), and TDB (s) at TAI 1977/1/1.0 */
ELB = 1.550519768e-8
TDB0 = -6.55e-5
/* Schwarzschild radius of the Sun (au) */
/* = 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */
SRS = 1.97412574336e-8
/* Reference ellipsoids */
WGS84 = 1
GRS80 = 2
WGS72 = 3
//
DBL_EPSILON = 2.220446049250313080847263336181640625e-16
)
/* dint(A) - truncate to nearest whole number towards zero (double) */
func dint(A float64) float64 {
if A < 0.0 {
return math.Ceil(A)
} else {
return math.Floor(A)
}
}
/* dnint(A) - round to nearest whole number (double) */
func dnint(A float64) float64 {
if math.Abs(A) < 0.5 {
return 0.0
} else {
if A < 0.0 {
return math.Ceil(A - 0.5)
} else {
return math.Floor(A + 0.5)
}
}
}
/* dsign(A,B) - magnitude of A with sign of B (double) */
func dsign(A, B float64) float64 {
if B < 0.0 {
return -math.Abs(A)
} else {
return math.Abs(A)
}
}
/* max(A,B) - larger (most +ve) of two numbers (generic) */
func gmax(A, B float64) float64 {
if A > B {
return A
}
return B
}
/* min(A,B) - smaller (least +ve) of two numbers (generic) */
func gmin(A, B float64) float64 {
if A < B {
return A
}
return B
}
func abs(A int) int {
if A < 0 {
return -A
} else {
return A
}
}
//math function
func fabs(x float64) float64 { return math.Abs(x) }
func sin(x float64) float64 { return math.Sin(x) }
func cos(x float64) float64 { return math.Cos(x) }
func tan(x float64) float64 { return math.Tan(x) }
func asin(x float64) float64 { return math.Asin(x) }
func atan(x float64) float64 { return math.Atan(x) }
func atan2(x, y float64) float64 { return math.Atan2(x, y) }
func sqrt(x float64) float64 { return math.Sqrt(x) }
func fmod(x, y float64) float64 { return math.Mod(x, y) }
func pow10(n int) float64 { return math.Pow10(n) }
func pow(x, y float64) float64 { return math.Pow(x, y) }
const (
sqrt2 = math.Sqrt2
)
gofa-1.19.1/jd.go 0000664 0000000 0000000 00000023770 14535740236 0013465 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Calendar
/*
Cal2jd Gregorian Calendar to Julian Date.
Given:
iy,im,id int year, month, day in Gregorian calendar (Note 1)
Returned:
djm0 float64 MJD zero-point: always 2400000.5
djm float64 Modified Julian Date for 0 hrs
Returned (function value):
int status:
0 = OK
-1 = bad year (Note 3: JD not computed)
-2 = bad month (JD not computed)
-3 = bad day (JD computed)
Notes:
1. The algorithm used is valid from -4800 March 1, but this
implementation rejects dates before -4799 January 1.
2. The Julian Date is returned in two pieces, in the usual SOFA
manner, which is designed to preserve time resolution. The
Julian Date is available as a single number by adding djm0 and
djm.
3. In early eras the conversion is from the "Proleptic Gregorian
Calendar"; no account is taken of the date(s) of adoption of
the Gregorian Calendar, nor is the AD/BC numbering convention
observed.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 12.92 (p604).
*/
func Cal2jd(iy, im, id int, djm0, djm *float64) int {
var j, ly, my int
var iypmy int
/* Earliest year allowed (4800BC) */
const IYMIN = -4799
/* Month lengths in days */
mtab := []int{31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
/* Preset status. */
j = 0
/* Validate year and month. */
if iy < IYMIN {
return -1
}
if im < 1 || im > 12 {
return -2
}
/* If February in a leap year, 1, otherwise 0. */
// ly = ((im == 2) && !(iy%4) && (iy%100 || !(iy%400)));
if (im == 2) && (iy%4 == 0) && ((iy%100 != 0) || (iy%400 == 0)) {
ly = 1
} else {
ly = 0
}
/* Validate day, taking into account leap years. */
if (id < 1) || (id > (mtab[im-1] + ly)) {
j = -3
}
/* Return result. */
my = (im - 14) / 12
iypmy = (iy + my)
*djm0 = DJM0
*djm = float64((1461*(iypmy+4800))/4 + (367*(im-2-12*my))/12 - (3*((iypmy+4900)/100))/4 + id - 2432076)
/* Return status. */
return j
}
/*
Jd2cal Julian Date to Gregorian year, month, day, and fraction of a day.
Given:
dj1,dj2 float64 Julian Date (Notes 1, 2)
Returned (arguments):
iy int year
im int month
id int day
fd float64 fraction of day
Returned (function value):
int status:
0 = OK
-1 = unacceptable date (Note 1)
Notes:
1) The earliest valid date is -68569.5 (-4900 March 1). The
largest value accepted is 1e9.
2) The Julian Date is apportioned in any convenient way between
the arguments dj1 and dj2. For example, JD=2450123.7 could
be expressed in any of these ways, among others:
dj1 dj2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
Separating integer and fraction uses the "compensated summation"
algorithm of Kahan-Neumaier to preserve as much precision as
possible irrespective of the jd1+jd2 apportionment.
3) In early eras the conversion is from the "proleptic Gregorian
calendar"; no account is taken of the date(s) of adoption of
the Gregorian calendar, nor is the AD/BC numbering convention
observed.
References:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 12.92 (p604).
Klein, A., A Generalized Kahan-Babuska-Summation-Algorithm.
Computing, 76, 279-293 (2006), Section 3.
*/
func Jd2cal(dj1, dj2 float64, iy, im, id *int, fd *float64) int {
/* Minimum and maximum allowed JD */
const DJMIN = -68569.5
const DJMAX = 1e9
var jd, i, l, n, k int64
var dj, f1, f2, d, s, cs, x, t, f float64
var v [2]float64
/* Verify date is acceptable. */
dj = dj1 + dj2
if dj < DJMIN || dj > DJMAX {
return -1
}
/* Separate day and fraction (where -0.5 <= fraction < 0.5). */
d = dnint(dj1)
f1 = dj1 - d
jd = int64(d)
d = dnint(dj2)
f2 = dj2 - d
jd += int64(d)
/* Compute f1+f2+0.5 using compensated summation (Klein 2006). */
s = 0.5
cs = 0.0
v[0] = f1
v[1] = f2
for i := 0; i < 2; i++ {
x = v[i]
t = s + x
if fabs(s) >= fabs(x) {
cs += (s - t) + x
} else {
cs += (x - t) + s
}
s = t
if s >= 1.0 {
jd++
s -= 1.0
}
}
f = s + cs
cs = f - s
/* Deal with negative f. */
if f < 0.0 {
/* Compensated summation: assume that |s| <= 1.0. */
f = s + 1.0
cs += (1.0 - f) + s
s = f
f = s + cs
cs = f - s
jd--
}
/* Deal with f that is 1.0 or more (when rounded to double). */
if (f - 1.0) >= -DBL_EPSILON/4.0 {
/* Compensated summation: assume that |s| <= 1.0. */
t = s - 1.0
cs += (s - t) - 1.0
s = t
f = s + cs
if -DBL_EPSILON/2.0 < f {
jd++
f = gmax(f, 0.0)
}
}
/* Express day in Gregorian calendar. */
l = jd + 68569
n = (4 * l) / 146097
l -= (146097*n + 3) / 4
i = (4000 * (l + 1)) / 1461001
l -= (1461*i)/4 - 31
k = (80 * l) / 2447
*id = int(l - (2447*k)/80)
l = k / 11
*im = int(k + 2 - 12*l)
*iy = int(100*(n-49) + i + l)
*fd = f
/* Success. */
return 0
}
/*
Jdcalf Julian Date to Gregorian Calendar, expressed in a form convenient
for formatting messages: rounded to a specified precision.
Given:
ndp int number of decimal places of days in fraction
dj1,dj2 float64 dj1+dj2 = Julian Date (Note 1)
Returned:
iymdf [4]int year, month, day, fraction in Gregorian calendar
Returned (function value):
int status:
-1 = date out of range
0 = OK
+1 = NDP not 0-9 (interpreted as 0)
Notes:
1) The Julian Date is apportioned in any convenient way between
the arguments dj1 and dj2. For example, JD=2450123.7 could
be expressed in any of these ways, among others:
dj1 dj2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
2) In early eras the conversion is from the "Proleptic Gregorian
Calendar"; no account is taken of the date(s) of adoption of
the Gregorian Calendar, nor is the AD/BC numbering convention
observed.
3) See also the function Jd2cal.
4) The number of decimal places ndp should be 4 or less if internal
overflows are to be avoided on platforms which use 16-bit
integers.
Called:
Jd2cal JD to Gregorian calendar
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 12.92 (p604).
*/
func Jdcalf(ndp int, dj1, dj2 float64, iymdf *[4]int) int {
var j, js int
var denom, d1, d2, f1, f2, d, djd, f, rf float64
/* Denominator of fraction (e.g. 100 for 2 decimal places). */
if (ndp >= 0) && (ndp <= 9) {
j = 0
denom = pow10(ndp)
} else {
j = 1
denom = 1.0
}
/* Copy the date, big then small. */
if fabs(dj1) >= fabs(dj2) {
d1 = dj1
d2 = dj2
} else {
d1 = dj2
d2 = dj1
}
/* Realign to midnight (without rounding error). */
d1 -= 0.5
/* Separate day and fraction (as precisely as possible). */
d = dnint(d1)
f1 = d1 - d
djd = d
d = dnint(d2)
f2 = d2 - d
djd += d
d = dnint(f1 + f2)
f = (f1 - d) + f2
if f < 0.0 {
f += 1.0
d -= 1.0
}
djd += d
/* Round the total fraction to the specified number of places. */
rf = dnint(f*denom) / denom
/* Re-align to noon. */
djd += 0.5
/* Convert to Gregorian calendar. */
js = Jd2cal(djd, rf, &iymdf[0], &iymdf[1], &iymdf[2], &f)
if js == 0 {
iymdf[3] = int(dnint(f * denom))
} else {
j = js
}
/* Return the status. */
return j
}
/*
Epb Julian Date to Besselian Epoch.
Given:
dj1,dj2 float64 Julian Date (see note)
Returned (function value):
float64 Besselian Epoch.
Note:
The Julian Date is supplied in two pieces, in the usual SOFA
manner, which is designed to preserve time resolution. The
Julian Date is available as a single number by adding dj1 and
dj2. The maximum resolution is achieved if dj1 is 2451545.0
(J2000.0).
Reference:
Lieske, J.H., 1979. Astron.Astrophys., 73, 282.
*/
func Epb(dj1, dj2 float64) float64 {
/* J2000.0-B1900.0 (2415019.81352) in days */
const D1900 = 36524.68648
return 1900.0 + ((dj1-DJ00)+(dj2+D1900))/DTY
}
/*
Epb2jd Besselian Epoch to Julian Date.
Given:
epb float64 Besselian Epoch (e.g. 1957.3)
Returned:
djm0 float64 MJD zero-point: always 2400000.5
djm float64 Modified Julian Date
Note:
The Julian Date is returned in two pieces, in the usual SOFA
manner, which is designed to preserve time resolution. The
Julian Date is available as a single number by adding djm0 and
djm.
Reference:
Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
*/
func Epb2jd(epb float64, djm0, djm *float64) {
*djm0 = DJM0
*djm = 15019.81352 + (epb-1900.0)*DTY
}
/*
Epj Julian Date to Julian Epoch.
Given:
dj1,dj2 float64 Julian Date (see note)
Returned (function value):
float64 Julian Epoch
Note:
The Julian Date is supplied in two pieces, in the usual SOFA
manner, which is designed to preserve time resolution. The
Julian Date is available as a single number by adding dj1 and
dj2. The maximum resolution is achieved if dj1 is 2451545.0
(J2000.0).
Reference:
Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
*/
func Epj(dj1, dj2 float64) float64 {
epj := 2000.0 + ((dj1-DJ00)+dj2)/DJY
return epj
}
/*
Epj2jd Julian Epoch to Julian Date.
Given:
epj float64 Julian Epoch (e.g. 1996.8)
Returned:
djm0 float64 MJD zero-point: always 2400000.5
djm float64 Modified Julian Date
Note:
The Julian Date is returned in two pieces, in the usual SOFA
manner, which is designed to preserve time resolution. The
Julian Date is available as a single number by adding djm0 and
djm.
Reference:
Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
*/
func Epj2jd(epj float64, djm0, djm *float64) {
*djm0 = DJM0
*djm = DJM00 + (epj-2000.0)*365.25
}
gofa-1.19.1/pn.go 0000664 0000000 0000000 00001330703 14535740236 0013503 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// SOFA Precession / Nutation / Polar Motion
/*
Bi00 Frame bias components, IAU 2000 Frame bias components of IAU 2000
precession-nutation models; part of the Mathews-Herring-Buffett (MHB2000)
nutation series, with additions.
Returned:
dpsibi,depsbi float64 longitude and obliquity corrections
dra float64 the ICRS RA of the J2000.0 mean equinox
Notes:
1) The frame bias corrections in longitude and obliquity (radians)
are required in order to correct for the offset between the GCRS
pole and the mean J2000.0 pole. They define, with respect to the
GCRS frame, a J2000.0 mean pole that is consistent with the rest
of the IAU 2000A precession-nutation model.
2) In addition to the displacement of the pole, the complete
description of the frame bias requires also an offset in right
ascension. This is not part of the IAU 2000A model, and is from
Chapront et al. (2002). It is returned in radians.
3) This is a supplemented implementation of one aspect of the IAU
2000A nutation model, formally adopted by the IAU General
Assembly in 2000, namely MHB2000 (Mathews et al. 2002).
References:
Chapront, J., Chapront-Touze, M. & Francou, G., Astron.
Astrophys., 387, 700, 2002.
Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
and precession: New nutation series for nonrigid Earth and
insights into the Earth's interior", J.Geophys.Res., 107, B4,
2002. The MHB2000 code itself was obtained on 2002 September 9
from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
*/
func Bi00(dpsibi, depsbi, dra *float64) {
/* The frame bias corrections in longitude and obliquity */
const DPBIAS = -0.041775 * DAS2R
const DEBIAS = -0.0068192 * DAS2R
/* The ICRS RA of the J2000.0 equinox (Chapront et al., 2002) */
const DRA0 = -0.0146 * DAS2R
/* Return the results (which are fixed). */
*dpsibi = DPBIAS
*depsbi = DEBIAS
*dra = DRA0
}
/*
Bp00 Frame bias and precession matrices, IAU 2000 Frame bias and precession, IAU 2000.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rb [3][3]float64 frame bias matrix (Note 2)
rp [3][3]float64 precession matrix (Note 3)
rbp [3][3]float64 bias-precession matrix (Note 4)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
applying frame bias.
3) The matrix rp transforms vectors from J2000.0 mean equator and
equinox to mean equator and equinox of date by applying
precession.
4) The matrix rbp transforms vectors from GCRS to mean equator and
equinox of date by applying frame bias then precession. It is
the product rp x rb.
5) It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the order given.
Called:
Bi00 frame bias components, IAU 2000
Pr00 IAU 2000 precession adjustments
Ir initialize r-matrix to identity
Rx rotate around X-axis
Ry rotate around Y-axis
Rz rotate around Z-axis
Cr copy r-matrix
Rxr product of two r-matrices
Reference:
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
*/
func Bp00(date1, date2 float64, rb, rp, rbp *[3][3]float64) {
/* J2000.0 obliquity (Lieske et al. 1977) */
const EPS0 = 84381.448 * DAS2R
var t, dpsibi, depsbi, dra0, psia77, oma77, chia,
dpsipr, depspr, psia, oma float64
var rbw [3][3]float64
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Frame bias. */
Bi00(&dpsibi, &depsbi, &dra0)
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259+(-0.001147)*t)*t) * t * DAS2R
oma77 = EPS0 + ((0.05127+(-0.007726)*t)*t)*t*DAS2R
chia = (10.5526 + (-2.38064+(-0.001125)*t)*t) * t * DAS2R
/* Apply IAU 2000 precession corrections. */
Pr00(date1, date2, &dpsipr, &depspr)
psia = psia77 + dpsipr
oma = oma77 + depspr
/* Frame bias matrix: GCRS to J2000.0. */
Ir(&rbw)
Rz(dra0, &rbw)
Ry(dpsibi*sin(EPS0), &rbw)
Rx(-depsbi, &rbw)
Cr(rbw, rb)
/* Precession matrix: J2000.0 to mean of date. */
Ir(rp)
Rx(EPS0, rp)
Rz(-psia, rp)
Rx(-oma, rp)
Rz(chia, rp)
/* Bias-precession matrix: GCRS to mean of date. */
Rxr(*rp, rbw, rbp)
}
/*
Bp06 Frame bias and precession matrices, IAU 2006 Frame bias and precession, IAU 2006.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rb [3][3]float64 frame bias matrix (Note 2)
rp [3][3]float64 precession matrix (Note 3)
rbp [3][3]float64 bias-precession matrix (Note 4)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
applying frame bias.
3) The matrix rp transforms vectors from mean J2000.0 to mean of
date by applying precession.
4) The matrix rbp transforms vectors from GCRS to mean of date by
applying frame bias then precession. It is the product rp x rb.
5) It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the order given.
Called:
Pfw06 bias-precession F-W angles, IAU 2006
Fw2m F-W angles to r-matrix
Pmat06 PB matrix, IAU 2006
Tr transpose r-matrix
Rxr product of two r-matrices
Cr copy r-matrix
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Bp06(date1, date2 float64, rb, rp, rbp *[3][3]float64) {
var gamb, phib, psib, epsa float64
var rbpw, rbt [3][3]float64
/* B matrix. */
Pfw06(DJM0, DJM00, &gamb, &phib, &psib, &epsa)
Fw2m(gamb, phib, psib, epsa, rb)
/* PxB matrix (temporary). */
Pmat06(date1, date2, &rbpw)
/* P matrix. */
Tr(*rb, &rbt)
Rxr(rbpw, rbt, rp)
/* PxB matrix. */
Cr(rbpw, rbp)
}
/*
Bpn2xy CIP XY given Bias-precession-nutation matrix Extract from the
bias-precession-nutation matrix the X,Y coordinates of the Celestial Intermediate Pole.
Given:
rbpn [3][3]float64 celestial-to-true matrix (Note 1)
Returned:
x,y float64 Celestial Intermediate Pole (Note 2)
Notes:
1) The matrix rbpn transforms vectors from GCRS to true equator (and
CIO or equinox) of date, and therefore the Celestial Intermediate
Pole unit vector is the bottom row of the matrix.
2) The arguments x,y are components of the Celestial Intermediate
Pole unit vector in the Geocentric Celestial Reference System.
Reference:
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154
(2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
*/
func Bpn2xy(rbpn [3][3]float64, x, y *float64) {
/* Extract the X,Y coordinates. */
*x = rbpn[2][0]
*y = rbpn[2][1]
}
/*
C2i00a Celestial-to-intermediate matrix, IAU 2000A Form the
celestial-to-intermediate matrix for a given date using the
IAU 2000A precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
3) A faster, but slightly less accurate, result (about 1 mas) can be
obtained by using instead the iauC2i00b function.
Called:
Pnm00a classical NPB matrix, IAU 2000A
C2ibpn celestial-to-intermediate matrix, given NPB matrix
References:
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154
(2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2i00a(date1, date2 float64, rc2i *[3][3]float64) {
var rbpn [3][3]float64
/* Obtain the celestial-to-true matrix (IAU 2000A). */
Pnm00a(date1, date2, &rbpn)
/* Form the celestial-to-intermediate matrix. */
C2ibpn(date1, date2, rbpn, rc2i)
}
/*
C2i00b Celestial-to-intermediate matrix, IAU 2000B
Form the celestial-to-intermediate matrix for a given date using the
IAU 2000B precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
3) The present function is faster, but slightly less accurate (about
1 mas), than the iauC2i00a function.
Called:
Pnm00b classical NPB matrix, IAU 2000B
C2ibpn celestial-to-intermediate matrix, given NPB matrix
References:
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154
(2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2i00b(date1, date2 float64, rc2i *[3][3]float64) {
var rbpn [3][3]float64
/* Obtain the celestial-to-true matrix (IAU 2000B). */
Pnm00b(date1, date2, &rbpn)
/* Form the celestial-to-intermediate matrix. */
C2ibpn(date1, date2, rbpn, rc2i)
}
/*
C2i06a Celestial-to-intermediate matrix, IAU 2006/2000A
Form the celestial-to-intermediate matrix for a given date using the
IAU 2006 precession and IAU 2000A nutation models.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= RC2T * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
Called:
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
C2ixys celestial-to-intermediate matrix, given X,Y and s
References:
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
*/
func C2i06a(date1, date2 float64, rc2i *[3][3]float64) {
var rbpn [3][3]float64
var x, y, s float64
/* Obtain the celestial-to-true matrix (IAU 2006/2000A). */
Pnm06a(date1, date2, &rbpn)
/* Extract the X,Y coordinates. */
Bpn2xy(rbpn, &x, &y)
/* Obtain the CIO locator. */
s = S06(date1, date2, x, y)
/* Form the celestial-to-intermediate matrix. */
C2ixys(x, y, s, rc2i)
}
/*
C2ibpn Celestial-to-intermediate matrix given B-P-N
Form the celestial-to-intermediate matrix for a given date given
the bias-precession-nutation matrix. IAU 2000.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
rbpn [3][3]float64 celestial-to-true matrix (Note 2)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix rbpn transforms vectors from GCRS to true equator (and
CIO or equinox) of date. Only the CIP (bottom row) is used.
3) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= RC2T * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
4) Although its name does not include "00", This function is in fact
specific to the IAU 2000 models.
Called:
Bpn2xy extract CIP X,Y coordinates from NPB matrix
C2ixy celestial-to-intermediate matrix, given X,Y
References:
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2ibpn(date1, date2 float64, rbpn [3][3]float64, rc2i *[3][3]float64) {
var x, y float64
/* Extract the X,Y coordinates. */
Bpn2xy(rbpn, &x, &y)
/* Form the celestial-to-intermediate matrix (n.b. IAU 2000 specific). */
C2ixy(date1, date2, x, y, rc2i)
}
/*
C2ixy Celestial-to-intermediate matrix given CIP
Form the celestial to intermediate-frame-of-date matrix for a given
date when the CIP X,Y coordinates are known. IAU 2000.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
x,y float64 Celestial Intermediate Pole (Note 2)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The Celestial Intermediate Pole coordinates are the x,y components
of the unit vector in the Geocentric Celestial Reference System.
3) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= RC2T * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
4) Although its name does not include "00", This function is in fact
specific to the IAU 2000 models.
Called:
C2ixys celestial-to-intermediate matrix, given X,Y and s
S00 the CIO locator s, given X,Y, IAU 2000A
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2ixy(date1, date2 float64, x, y float64, rc2i *[3][3]float64) {
/* Compute s and then the matrix. */
C2ixys(x, y, S00(date1, date2, x, y), rc2i)
}
/*
C2ixys Celestial-to-intermediate matrix given CIP and s
Form the celestial to intermediate-frame-of-date matrix given the CIP
X,Y and the CIO locator s.
Given:
x,y float64 Celestial Intermediate Pole (Note 1)
s float64 the CIO locator s (Note 2)
Returned:
rc2i [3][3]float64 celestial-to-intermediate matrix (Note 3)
Notes:
1) The Celestial Intermediate Pole coordinates are the x,y
components of the unit vector in the Geocentric Celestial
Reference System.
2) The CIO locator s (in radians) positions the Celestial
Intermediate Origin on the equator of the CIP.
3) The matrix rc2i is the first stage in the transformation from
celestial to terrestrial coordinates:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= RC2T * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
Called:
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Ry rotate around Y-axis
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2ixys(x, y, s float64, rc2i *[3][3]float64) {
var r2, e, d float64
/* Obtain the spherical angles E and d. */
r2 = x*x + y*y
// e = (r2 > 0.0) ? atan2(y, x) : 0.0;
if r2 > 0.0 {
e = atan2(y, x)
} else {
e = 0.0
}
d = atan(sqrt(r2 / (1.0 - r2)))
/* Form the matrix. */
Ir(rc2i)
Rz(e, rc2i)
Ry(d, rc2i)
Rz(-(e + s), rc2i)
}
/*
C2t00a Celestial-to-terrestrial matrix, IAU 2000A
Form the celestial to terrestrial matrix given the date, the UT1 and
the polar motion, using the IAU 2000A precession-nutation model.
Given:
tta,ttb float64 TT as a 2-part Julian Date (Note 1)
uta,utb float64 UT1 as a 2-part Julian Date (Note 1)
xp,yp float64 CIP coordinates (radians, Note 2)
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 3)
Notes:
1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
apportioned in any convenient way between the arguments uta and
utb. For example, JD(UT1)=2450123.7 could be expressed in any of
these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. In the case of uta,utb, the
date & time method is best matched to the Earth rotation angle
algorithm used: maximum precision is delivered when the uta
argument is for 0hrs UT1 on the day in question and the utb
argument lies in the range 0 to 1, or vice versa.
2) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
3) The matrix rc2t transforms from celestial to terrestrial
coordinates:
[TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), RC2I is the
celestial-to-intermediate matrix, ERA is the Earth rotation
angle and RPOM is the polar motion matrix.
4) A faster, but slightly less accurate, result (about 1 mas) can
be obtained by using instead the iauC2t00b function.
Called:
C2i00a celestial-to-intermediate matrix, IAU 2000A
Era00 Earth rotation angle, IAU 2000
Sp00 the TIO locator s', IERS 2000
Pom00 polar motion matrix
C2tcio form CIO-based celestial-to-terrestrial matrix
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2t00a(tta, ttb float64, uta, utb float64, xp, yp float64, rc2t *[3][3]float64) {
var rc2i, rpom [3][3]float64
var era, sp float64
/* Form the celestial-to-intermediate matrix for this TT (IAU 2000A). */
C2i00a(tta, ttb, &rc2i)
/* Predict the Earth rotation angle for this UT1. */
era = Era00(uta, utb)
/* Estimate s'. */
sp = Sp00(tta, ttb)
/* Form the polar motion matrix. */
Pom00(xp, yp, sp, &rpom)
/* Combine to form the celestial-to-terrestrial matrix. */
C2tcio(rc2i, era, rpom, rc2t)
}
/*
C2t00b Celestial-to-terrestrial matrix, IAU 2000B
Form the celestial to terrestrial matrix given the date, the UT1 and
the polar motion, using the IAU 2000B precession-nutation model.
Given:
tta,ttb float64 TT as a 2-part Julian Date (Note 1)
uta,utb float64 UT1 as a 2-part Julian Date (Note 1)
xp,yp float64 coordinates of the pole (radians, Note 2)
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 3)
Notes:
1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
apportioned in any convenient way between the arguments uta and
utb. For example, JD(UT1)=2450123.7 could be expressed in any of
these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. In the case of uta,utb, the
date & time method is best matched to the Earth rotation angle
algorithm used: maximum precision is delivered when the uta
argument is for 0hrs UT1 on the day in question and the utb
argument lies in the range 0 to 1, or vice versa.
2) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
3) The matrix rc2t transforms from celestial to terrestrial
coordinates:
[TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), RC2I is the
celestial-to-intermediate matrix, ERA is the Earth rotation
angle and RPOM is the polar motion matrix.
4) The present function is faster, but slightly less accurate (about
1 mas), than the iauC2t00a function.
Called:
C2i00b celestial-to-intermediate matrix, IAU 2000B
Era00 Earth rotation angle, IAU 2000
Pom00 polar motion matrix
C2tcio form CIO-based celestial-to-terrestrial matrix
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2t00b(tta, ttb float64, uta, utb float64, xp, yp float64, rc2t *[3][3]float64) {
var rc2i, rpom [3][3]float64
var era float64
/* Form the celestial-to-intermediate matrix for this TT (IAU 2000B). */
C2i00b(tta, ttb, &rc2i)
/* Predict the Earth rotation angle for this UT1. */
era = Era00(uta, utb)
/* Form the polar motion matrix (neglecting s'). */
Pom00(xp, yp, 0.0, &rpom)
/* Combine to form the celestial-to-terrestrial matrix. */
C2tcio(rc2i, era, rpom, rc2t)
}
/*
C2t06a Celestial-to-terrestrial matrix, IAU 2006/2000A
Form the celestial to terrestrial matrix given the date, the UT1 and
the polar motion, using the IAU 2006/2000A precession-nutation
model.
Given:
tta,ttb float64 TT as a 2-part Julian Date (Note 1)
uta,utb float64 UT1 as a 2-part Julian Date (Note 1)
xp,yp float64 coordinates of the pole (radians, Note 2)
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 3)
Notes:
1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
apportioned in any convenient way between the two arguments. For
example, JD(UT1)=2450123.7 could be expressed in any of
these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. In the case of uta,utb, the
date & time method is best matched to the Earth rotation angle
algorithm used: maximum precision is delivered when the uta
argument is for 0hrs UT1 on the day in question and the utb
argument lies in the range 0 to 1, or vice versa.
2) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
3) The matrix rc2t transforms from celestial to terrestrial
coordinates:
[TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), RC2I is the
celestial-to-intermediate matrix, ERA is the Earth rotation
angle and RPOM is the polar motion matrix.
Called:
C2i06a celestial-to-intermediate matrix, IAU 2006/2000A
Era00 Earth rotation angle, IAU 2000
Sp00 the TIO locator s', IERS 2000
Pom00 polar motion matrix
C2tcio form CIO-based celestial-to-terrestrial matrix
Reference:
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
*/
func C2t06a(tta, ttb float64, uta, utb float64, xp, yp float64, rc2t *[3][3]float64) {
var rc2i, rpom [3][3]float64
var era, sp float64
/* Form the celestial-to-intermediate matrix for this TT. */
C2i06a(tta, ttb, &rc2i)
/* Predict the Earth rotation angle for this UT1. */
era = Era00(uta, utb)
/* Estimate s'. */
sp = Sp00(tta, ttb)
/* Form the polar motion matrix. */
Pom00(xp, yp, sp, &rpom)
/* Combine to form the celestial-to-terrestrial matrix. */
C2tcio(rc2i, era, rpom, rc2t)
}
/*
C2tcio Form CIO-based Celestial-to-terrestrial matrix
Assemble the celestial to terrestrial matrix from CIO-based
components (the celestial-to-intermediate matrix, the Earth Rotation
Angle and the polar motion matrix).
Given:
rc2i [3][3]float64 celestial-to-intermediate matrix
era float64 Earth rotation angle (radians)
rpom [3][3]float64 polar-motion matrix
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix
Notes:
1) This function constructs the rotation matrix that transforms
vectors in the celestial system into vectors in the terrestrial
system. It does so starting from precomputed components, namely
the matrix which rotates from celestial coordinates to the
intermediate frame, the Earth rotation angle and the polar motion
matrix. One use of the present function is when generating a
series of celestial-to-terrestrial matrices where only the Earth
Rotation Angle changes, avoiding the considerable overhead of
recomputing the precession-nutation more often than necessary to
achieve given accuracy objectives.
2) The relationship between the arguments is as follows:
[TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003).
Called:
Cr copy r-matrix
Rz rotate around Z-axis
Rxr product of two r-matrices
Reference:
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
*/
func C2tcio(rc2i [3][3]float64, era float64, rpom [3][3]float64, rc2t *[3][3]float64) {
var r [3][3]float64
/* Construct the matrix. */
Cr(rc2i, &r)
Rz(era, &r)
Rxr(rpom, r, rc2t)
}
/*
C2teqx Celestial-to-terrestrial matrix, classical
Assemble the celestial to terrestrial matrix from equinox-based
components (the celestial-to-true matrix, the Greenwich Apparent
Sidereal Time and the polar motion matrix).
Given:
rbpn [3][3]float64 celestial-to-true matrix
gst float64 Greenwich (apparent) Sidereal Time (radians)
rpom [3][3]float64 polar-motion matrix
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 2)
Notes:
1) This function constructs the rotation matrix that transforms
vectors in the celestial system into vectors in the terrestrial
system. It does so starting from precomputed components, namely
the matrix which rotates from celestial coordinates to the
true equator and equinox of date, the Greenwich Apparent Sidereal
Time and the polar motion matrix. One use of the present function
is when generating a series of celestial-to-terrestrial matrices
where only the Sidereal Time changes, avoiding the considerable
overhead of recomputing the precession-nutation more often than
necessary to achieve given accuracy objectives.
2) The relationship between the arguments is as follows:
[TRS] = rpom * R_3(gst) * rbpn * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003).
Called:
Cr copy r-matrix
Rz rotate around Z-axis
Rxr product of two r-matrices
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2teqx(rbpn [3][3]float64, gst float64, rpom [3][3]float64, rc2t *[3][3]float64) {
var r [3][3]float64
/* Construct the matrix. */
Cr(rbpn, &r)
Rz(gst, &r)
Rxr(rpom, r, rc2t)
}
/*
C2tpe Celestial-to-terrestrial matrix given nutation
Form the celestial to terrestrial matrix given the date, the UT1,
the nutation and the polar motion. IAU 2000.
Given:
tta,ttb float64 TT as a 2-part Julian Date (Note 1)
uta,utb float64 UT1 as a 2-part Julian Date (Note 1)
dpsi,deps float64 nutation (Note 2)
xp,yp float64 coordinates of the pole (radians, Note 3)
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 4)
Notes:
1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
apportioned in any convenient way between the arguments uta and
utb. For example, JD(UT1)=2450123.7 could be expressed in any of
these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. In the case of uta,utb, the
date & time method is best matched to the Earth rotation angle
algorithm used: maximum precision is delivered when the uta
argument is for 0hrs UT1 on the day in question and the utb
argument lies in the range 0 to 1, or vice versa.
2) The caller is responsible for providing the nutation components;
they are in longitude and obliquity, in radians and are with
respect to the equinox and ecliptic of date. For high-accuracy
applications, free core nutation should be included as well as
any other relevant corrections to the position of the CIP.
3) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
4) The matrix rc2t transforms from celestial to terrestrial
coordinates:
[TRS] = RPOM * R_3(GST) * RBPN * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), RBPN is the
bias-precession-nutation matrix, GST is the Greenwich (apparent)
Sidereal Time and RPOM is the polar motion matrix.
5) Although its name does not include "00", This function is in fact
specific to the IAU 2000 models.
Called:
Pn00 bias/precession/nutation results, IAU 2000
Gmst00 Greenwich mean sidereal time, IAU 2000
Sp00 the TIO locator s', IERS 2000
Ee00 equation of the equinoxes, IAU 2000
Pom00 polar motion matrix
C2teqx form equinox-based celestial-to-terrestrial matrix
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2tpe(tta, ttb float64, uta, utb float64, dpsi, deps float64, xp, yp float64, rc2t *[3][3]float64) {
var epsa, gmst, ee, sp float64
var rb, rp, rbp, rn, rbpn, rpom [3][3]float64
/* Form the celestial-to-true matrix for this TT. */
Pn00(tta, ttb, dpsi, deps, &epsa, &rb, &rp, &rbp, &rn, &rbpn)
/* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */
gmst = Gmst00(uta, utb, tta, ttb)
/* Predict the equation of the equinoxes given TT and nutation. */
ee = Ee00(tta, ttb, epsa, dpsi)
/* Estimate s'. */
sp = Sp00(tta, ttb)
/* Form the polar motion matrix. */
Pom00(xp, yp, sp, &rpom)
/* Combine to form the celestial-to-terrestrial matrix. */
C2teqx(rbpn, gmst+ee, rpom, rc2t)
}
/*
C2txy Celestial-to-terrestrial matrix given CIP
Form the celestial to terrestrial matrix given the date, the UT1,
the CIP coordinates and the polar motion. IAU 2000.
Given:
tta,ttb float64 TT as a 2-part Julian Date (Note 1)
uta,utb float64 UT1 as a 2-part Julian Date (Note 1)
x,y float64 Celestial Intermediate Pole (Note 2)
xp,yp float64 coordinates of the pole (radians, Note 3)
Returned:
rc2t [3][3]float64 celestial-to-terrestrial matrix (Note 4)
Notes:
1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
apportioned in any convenient way between the arguments uta and
utb. For example, JD(UT1)=2450123.7 could be expressed in any o
these ways, among others:
uta utb
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution is
acceptable. The J2000 and MJD methods are good compromises
between resolution and convenience. In the case of uta,utb, the
date & time method is best matched to the Earth rotation angle
algorithm used: maximum precision is delivered when the uta
argument is for 0hrs UT1 on the day in question and the utb
argument lies in the range 0 to 1, or vice versa.
2) The Celestial Intermediate Pole coordinates are the x,y
components of the unit vector in the Geocentric Celestial
Reference System.
3) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
4) The matrix rc2t transforms from celestial to terrestrial
coordinates:
[TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
= rc2t * [CRS]
where [CRS] is a vector in the Geocentric Celestial Reference
System and [TRS] is a vector in the International Terrestrial
Reference System (see IERS Conventions 2003), ERA is the Earth
Rotation Angle and RPOM is the polar motion matrix.
5) Although its name does not include "00", This function is in fact
specific to the IAU 2000 models.
Called:
C2ixy celestial-to-intermediate matrix, given X,Y
Era00 Earth rotation angle, IAU 2000
Sp00 the TIO locator s', IERS 2000
Pom00 polar motion matrix
C2tcio form CIO-based celestial-to-terrestrial matrix
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func C2txy(tta, ttb float64, uta, utb float64, x, y float64, xp, yp float64, rc2t *[3][3]float64) {
var rc2i, rpom [3][3]float64
var era, sp float64
/* Form the celestial-to-intermediate matrix for this TT. */
C2ixy(tta, ttb, x, y, &rc2i)
/* Predict the Earth rotation angle for this UT1. */
era = Era00(uta, utb)
/* Estimate s'. */
sp = Sp00(tta, ttb)
/* Form the polar motion matrix. */
Pom00(xp, yp, sp, &rpom)
/* Combine to form the celestial-to-terrestrial matrix. */
C2tcio(rc2i, era, rpom, rc2t)
}
/*
Eo06a Equation of the origins, IAU 2006/2000A
Equation of the origins, IAU 2006 precession and IAU 2000A nutation.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 the equation of the origins in radians
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The equation of the origins is the distance between the true
equinox and the celestial intermediate origin and, equivalently,
the difference between Earth rotation angle and Greenwich
apparent sidereal time (ERA-GST). It comprises the precession
(since J2000.0) in right ascension plus the equation of the
equinoxes (including the small correction terms).
Called:
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
Eors equation of the origins, given NPB matrix and s
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Eo06a(date1, date2 float64) float64 {
var r [3][3]float64
var x, y, s, eo float64
/* Classical nutation x precession x bias matrix. */
Pnm06a(date1, date2, &r)
/* Extract CIP coordinates. */
Bpn2xy(r, &x, &y)
/* The CIO locator, s. */
s = S06(date1, date2, x, y)
/* Solve for the EO. */
eo = Eors(r, s)
return eo
}
/*
Eors Equation of the origins, given NPB matrix and s
Equation of the origins, given the classical NPB matrix and the
quantity s.
Given:
rnpb [3][3]float64 classical nutation x precession x bias matrix
s float64 the quantity s (the CIO locator) in radians
Returned (function value):
float64 the equation of the origins in radians
Notes:
1) The equation of the origins is the distance between the true
equinox and the celestial intermediate origin and, equivalently,
the difference between Earth rotation angle and Greenwich
apparent sidereal time (ERA-GST). It comprises the precession
(since J2000.0) in right ascension plus the equation of the
equinoxes (including the small correction terms).
2) The algorithm is from Wallace & Capitaine (2006).
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Eors(rnpb [3][3]float64, s float64) float64 {
var x, ax, xs, ys, zs, p, q, eo float64
/* Evaluate Wallace & Capitaine (2006) expression (16). */
x = rnpb[2][0]
ax = x / (1.0 + rnpb[2][2])
xs = 1.0 - ax*x
ys = -ax * rnpb[2][1]
zs = -x
p = rnpb[0][0]*xs + rnpb[0][1]*ys + rnpb[0][2]*zs
q = rnpb[1][0]*xs + rnpb[1][1]*ys + rnpb[1][2]*zs
// eo = ((p != 0) || (q != 0)) ? s - atan2(q, p) : s;
if (p != 0) || (q != 0) {
eo = s - atan2(q, p)
} else {
eo = s
}
return eo
}
/*
Fw2m Fukushima-Williams angles to r-matrix
Form rotation matrix given the Fukushima-Williams angles.
Given:
gamb float64 F-W angle gamma_bar (radians)
phib float64 F-W angle phi_bar (radians)
psi float64 F-W angle psi (radians)
eps float64 F-W angle epsilon (radians)
Returned:
r [3][3]float64 rotation matrix
Notes:
1) Naming the following points:
e = J2000.0 ecliptic pole,
p = GCRS pole,
E = ecliptic pole of date,
and P = CIP,
the four Fukushima-Williams angles are as follows:
gamb = gamma = epE
phib = phi = pE
psi = psi = pEP
eps = epsilon = EP
2) The matrix representing the combined effects of frame bias,
precession and nutation is:
NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb)
3) The present function can construct three different matrices,
depending on which angles are supplied as the arguments gamb,
phib, psi and eps:
o To obtain the nutation x precession x frame bias matrix,
first generate the four precession angles known conventionally
as gamma_bar, phi_bar, psi_bar and epsilon_A, then generate
the nutation components Dpsi and Depsilon and add them to
psi_bar and epsilon_A, and finally call the present function
using those four angles as arguments.
o To obtain the precession x frame bias matrix, generate the
four precession angles and call the present function.
o To obtain the frame bias matrix, generate the four precession
angles for date J2000.0 and call the present function.
The nutation-only and precession-only matrices can if necessary
be obtained by combining these three appropriately.
Called:
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Rx rotate around X-axis
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
*/
func Fw2m(gamb, phib, psi, eps float64, r *[3][3]float64) {
Ir(r)
Rz(gamb, r)
Rx(phib, r)
Rz(-psi, r)
Rx(-eps, r)
}
/*
Fw2xy Fukushima-Williams angles to X,Y
CIP X,Y given Fukushima-Williams bias-precession-nutation angles.
Given:
gamb float64 F-W angle gamma_bar (radians)
phib float64 F-W angle phi_bar (radians)
psi float64 F-W angle psi (radians)
eps float64 F-W angle epsilon (radians)
Returned:
x,y float64 CIP unit vector X,Y
Notes:
1) Naming the following points:
e = J2000.0 ecliptic pole,
p = GCRS pole
E = ecliptic pole of date,
and P = CIP,
the four Fukushima-Williams angles are as follows:
gamb = gamma = epE
phib = phi = pE
psi = psi = pEP
eps = epsilon = EP
2) The matrix representing the combined effects of frame bias,
precession and nutation is:
NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
The returned values x,y are elements [2][0] and [2][1] of the
matrix. Near J2000.0, they are essentially angles in radians.
Called:
Fw2m F-W angles to r-matrix
Bpn2xy extract CIP X,Y coordinates from NPB matrix
Reference:
Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
*/
func Fw2xy(gamb, phib float64, psi, eps float64, x, y *float64) {
var r [3][3]float64
/* Form NxPxB matrix. */
Fw2m(gamb, phib, psi, eps, &r)
/* Extract CIP X,Y. */
Bpn2xy(r, x, y)
}
/*
Ltp Long-term precession matrix.
Given:
epj float64 Julian epoch (TT)
Returned:
rp [3][3]float64 precession matrix, J2000.0 to date
Notes:
1) The matrix is in the sense
P_date = rp x P_J2000,
where P_J2000 is a vector with respect to the J2000.0 mean
equator and equinox and P_date is the same vector with respect to
the equator and equinox of epoch epj.
2) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
Called:
Ltpequ equator pole, long term
Ltpecl ecliptic pole, long term
Pxp vector product
Pn normalize vector
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Ltp(epj float64, rp *[3][3]float64) {
var peqr, pecl, v, eqx [3]float64
var w float64
/* Equator pole (bottom row of matrix). */
Ltpequ(epj, &peqr)
/* Ecliptic pole. */
Ltpecl(epj, &pecl)
/* Equinox (top row of matrix). */
Pxp(peqr, pecl, &v)
Pn(v, &w, &eqx)
/* Middle row of matrix. */
Pxp(peqr, eqx, &v)
/* Assemble the matrix. */
for i := 0; i < 3; i++ {
rp[0][i] = eqx[i]
rp[1][i] = v[i]
rp[2][i] = peqr[i]
}
}
/*
Ltpb Long-term precession matrix, including ICRS frame bias.
Given:
epj float64 Julian epoch (TT)
Returned:
rpb [3][3]float64 precession-bias matrix, J2000.0 to date
Notes:
1) The matrix is in the sense
P_date = rpb x P_ICRS,
where P_ICRS is a vector in the Geocentric Celestial Reference
System, and P_date is the vector with respect to the Celestial
Intermediate Reference System at that date but with nutation
neglected.
2) A first order frame bias formulation is used, of sub-
microarcsecond accuracy compared with a full 3D rotation.
3) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Ltpb(epj float64, rpb *[3][3]float64) {
/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
dx := -0.016617 * DAS2R
de := -0.0068192 * DAS2R
dr := -0.0146 * DAS2R
var rp [3][3]float64
/* Precession matrix. */
Ltp(epj, &rp)
/* Apply the bias. */
for i := 0; i < 3; i++ {
rpb[i][0] = rp[i][0] - rp[i][1]*dr + rp[i][2]*dx
rpb[i][1] = rp[i][0]*dr + rp[i][1] + rp[i][2]*de
rpb[i][2] = -rp[i][0]*dx - rp[i][1]*de + rp[i][2]
}
}
/*
Ltpecl Long-term precession of the ecliptic.
Given:
epj float64 Julian epoch (TT)
Returned:
vec [3]float64 ecliptic pole unit vector
Notes:
1) The returned vector is with respect to the J2000.0 mean equator
and equinox.
2) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Ltpecl(epj float64, vec *[3]float64) {
/* Obliquity at J2000.0 (radians). */
const eps0 = 84381.406 * DAS2R
/* Polynomial coefficients */
const NPOL = 4
pqpol := [2][4]float64{
{5851.607687, -0.1189000, -0.00028913, 0.000000101},
{-1600.886300, 1.1689818, -0.00000020, -0.000000437},
}
/* Periodic coefficients */
pqper := [][5]float64{
{708.15, -5486.751211, -684.661560, 667.666730, -5523.863691},
{2309.00, -17.127623, 2446.283880, -2354.886252, -549.747450},
{1620.00, -617.517403, 399.671049, -428.152441, -310.998056},
{492.20, 413.442940, -356.652376, 376.202861, 421.535876},
{1183.00, 78.614193, -186.387003, 184.778874, -36.776172},
{622.00, -180.732815, -316.800070, 335.321713, -145.278396},
{882.00, -87.676083, 198.296701, -185.138669, -34.744450},
{547.00, 46.140315, 101.135679, -120.972830, 22.885731},
}
NPER := len(pqper)
/* Miscellaneous */
var t, p, q, w, a, s, c float64
/* Centuries since J2000. */
t = (epj - 2000.0) / 100.0
/* Initialize P_A and Q_A accumulators. */
p = 0.0
q = 0.0
/* Periodic terms. */
w = D2PI * t
for i := 0; i < NPER; i++ {
a = w / pqper[i][0]
s = sin(a)
c = cos(a)
p += c*pqper[i][1] + s*pqper[i][3]
q += c*pqper[i][2] + s*pqper[i][4]
}
/* Polynomial terms. */
w = 1.0
for i := 0; i < NPOL; i++ {
p += pqpol[0][i] * w
q += pqpol[1][i] * w
w *= t
}
/* P_A and Q_A (radians). */
p *= DAS2R
q *= DAS2R
/* Form the ecliptic pole vector. */
w = 1.0 - p*p - q*q
if w < 0.0 {
w = 0.0
} else {
w = sqrt(w)
}
s = sin(eps0)
c = cos(eps0)
vec[0] = p
vec[1] = -q*c - w*s
vec[2] = -q*s + w*c
}
/*
Ltpequ Long-term precession of the equator.
Given:
epj float64 Julian epoch (TT)
Returned:
veq [3]float64 equator pole unit vector
Notes:
1) The returned vector is with respect to the J2000.0 mean equator
and equinox.
2) The Vondrak et al. (2011, 2012) 400 millennia precession model
agrees with the IAU 2006 precession at J2000.0 and stays within
100 microarcseconds during the 20th and 21st centuries. It is
accurate to a few arcseconds throughout the historical period,
worsening to a few tenths of a degree at the end of the
+/- 200,000 year time span.
References:
Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
expressions, valid for long time intervals, Astron.Astrophys. 534,
A22
Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
expressions, valid for long time intervals (Corrigendum),
Astron.Astrophys. 541, C1
*/
func Ltpequ(epj float64, veq *[3]float64) {
/* Polynomial coefficients */
const NPOL = 4
xypol := [2][4]float64{
{5453.282155, 0.4252841, -0.00037173, -0.000000152},
{-73750.930350, -0.7675452, -0.00018725, 0.000000231},
}
/* Periodic coefficients */
xyper := [][5]float64{
{256.75, -819.940624, 75004.344875, 81491.287984, 1558.515853},
{708.15, -8444.676815, 624.033993, 787.163481, 7774.939698},
{274.20, 2600.009459, 1251.136893, 1251.296102, -2219.534038},
{241.45, 2755.175630, -1102.212834, -1257.950837, -2523.969396},
{2309.00, -167.659835, -2660.664980, -2966.799730, 247.850422},
{492.20, 871.855056, 699.291817, 639.744522, -846.485643},
{396.10, 44.769698, 153.167220, 131.600209, -1393.124055},
{288.90, -512.313065, -950.865637, -445.040117, 368.526116},
{231.10, -819.415595, 499.754645, 584.522874, 749.045012},
{1610.00, -538.071099, -145.188210, -89.756563, 444.704518},
{620.00, -189.793622, 558.116553, 524.429630, 235.934465},
{157.87, -402.922932, -23.923029, -13.549067, 374.049623},
{220.30, 179.516345, -165.405086, -210.157124, -171.330180},
{1200.00, -9.814756, 9.344131, -44.919798, -22.899655},
}
NPER := len(xyper)
/* Miscellaneous */
var t, x, y, w, a, s, c float64
/* Centuries since J2000. */
t = (epj - 2000.0) / 100.0
/* Initialize X and Y accumulators. */
x = 0.0
y = 0.0
/* Periodic terms. */
w = D2PI * t
for i := 0; i < NPER; i++ {
a = w / xyper[i][0]
s = sin(a)
c = cos(a)
x += c*xyper[i][1] + s*xyper[i][3]
y += c*xyper[i][2] + s*xyper[i][4]
}
/* Polynomial terms. */
w = 1.0
for i := 0; i < NPOL; i++ {
x += xypol[0][i] * w
y += xypol[1][i] * w
w *= t
}
/* X and Y (direction cosines). */
x *= DAS2R
y *= DAS2R
/* Form the equator pole vector. */
veq[0] = x
veq[1] = y
w = 1.0 - x*x - y*y
if w < 0.0 {
veq[2] = 0.0
} else {
veq[2] = sqrt(w)
}
}
/*
Num00a Nutation matrix, IAU 2000A
Form the matrix of nutation for a given date, IAU 2000A model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rmatn [3][3]float64 nutation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(true) = rmatn * V(mean), where
the p-vector V(true) is with respect to the true equatorial triad
of date and the p-vector V(mean) is with respect to the mean
equatorial triad of date.
3) A faster, but slightly less accurate, result (about 1 mas) can be
obtained by using instead the iauNum00b function.
Called:
Pn00a bias/precession/nutation, IAU 2000A
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.222-3 (p114).
*/
func Num00a(date1, date2 float64, rmatn *[3][3]float64) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rbpn [3][3]float64
/* Obtain the required matrix (discarding other results). */
Pn00a(date1, date2,
&dpsi, &deps, &epsa, &rb, &rp, &rbp, rmatn, &rbpn)
}
/*
Num00b Nutation matrix, IAU 2000B
Form the matrix of nutation for a given date, IAU 2000B model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rmatn [3][3]float64 nutation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(true) = rmatn * V(mean), where
the p-vector V(true) is with respect to the true equatorial triad
of date and the p-vector V(mean) is with respect to the mean
equatorial triad of date.
3) The present function is faster, but slightly less accurate (about
1 mas), than the iauNum00a function.
Called:
Pn00b bias/precession/nutation, IAU 2000B
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.222-3 (p114).
*/
func Num00b(date1, date2 float64, rmatn *[3][3]float64) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rbpn [3][3]float64
/* Obtain the required matrix (discarding other results). */
Pn00b(date1, date2,
&dpsi, &deps, &epsa, &rb, &rp, &rbp, rmatn, &rbpn)
}
/*
Num06a Nutation matrix, IAU 2006/2000A
Form the matrix of nutation for a given date, IAU 2006/2000A model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rmatn [3][3]float64 nutation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(true) = rmatn * V(mean), where
the p-vector V(true) is with respect to the true equatorial triad
of date and the p-vector V(mean) is with respect to the mean
equatorial triad of date.
Called:
Obl06 mean obliquity, IAU 2006
Nut06a nutation, IAU 2006/2000A
Numat form nutation matrix
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.222-3 (p114).
*/
func Num06a(date1, date2 float64, rmatn *[3][3]float64) {
var eps, dp, de float64
/* Mean obliquity. */
eps = Obl06(date1, date2)
/* Nutation components. */
Nut06a(date1, date2, &dp, &de)
/* Nutation matrix. */
Numat(eps, dp, de, rmatn)
}
/*
Numat Nutation matrix, generic Form the matrix of nutation.
Given:
epsa float64 mean obliquity of date (Note 1)
dpsi,deps float64 nutation (Note 2)
Returned:
rmatn [3][3]float64 nutation matrix (Note 3)
Notes:
1) The supplied mean obliquity epsa, must be consistent with the
precession-nutation models from which dpsi and deps were obtained.
2) The caller is responsible for providing the nutation components;
they are in longitude and obliquity, in radians and are with
respect to the equinox and ecliptic of date.
3) The matrix operates in the sense V(true) = rmatn * V(mean),
where the p-vector V(true) is with respect to the true
equatorial triad of date and the p-vector V(mean) is with
respect to the mean equatorial triad of date.
Called:
Ir initialize r-matrix to identity
Rx rotate around X-axis
Rz rotate around Z-axis
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.222-3 (p114).
*/
func Numat(epsa, dpsi, deps float64, rmatn *[3][3]float64) {
/* Build the rotation matrix. */
Ir(rmatn)
Rx(epsa, rmatn)
Rz(-dpsi, rmatn)
Rx(-(epsa + deps), rmatn)
}
/*
Nut00a Nutation, IAU 2000A Nutation, IAU 2000A model
(MHB2000 luni-solar and planetary nutation with free core nutation omitted).
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation, luni-solar + planetary (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components in longitude and obliquity are in radians
and with respect to the equinox and ecliptic of date. The
obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
value of 84381.448 arcsec.
Both the luni-solar and planetary nutations are included. The
latter are due to direct planetary nutations and the
perturbations of the lunar and terrestrial orbits.
3) The function computes the MHB2000 nutation series with the
associated corrections for planetary nutations. It is an
implementation of the nutation part of the IAU 2000A precession-
nutation model, formally adopted by the IAU General Assembly in
2000, namely MHB2000 (Mathews et al. 2002), but with the free
core nutation (FCN - see Note 4) omitted.
4) The full MHB2000 model also contains contributions to the
nutations in longitude and obliquity due to the free-excitation
of the free-core-nutation during the period 1979-2000. These FCN
terms, which are time-dependent and unpredictable, are NOT
included in the present function and, if required, must be
independently computed. With the FCN corrections included, the
present function delivers a pole which is at current epochs
accurate to a few hundred microarcseconds. The omission of FCN
introduces further errors of about that size.
5) The present function provides classical nutation. The MHB2000
algorithm, from which it is adapted, deals also with (i) the
offsets between the GCRS and mean poles and (ii) the adjustments
in longitude and obliquity due to the changed precession rates.
These additional functions, namely frame bias and precession
adjustments, are supported by the SOFA functions iauBi00 and
Pr00.
6) The MHB2000 algorithm also provides "total" nutations, comprising
the arithmetic sum of the frame bias, precession adjustments,
luni-solar nutation and planetary nutation. These total
nutations can be used in combination with an existing IAU 1976
precession implementation, such as iauPmat76, to deliver GCRS-
to-true predictions of sub-mas accuracy at current dates.
However, there are three shortcomings in the MHB2000 model that
must be taken into account if more accurate or definitive results
are required (see Wallace 2002):
(i) The MHB2000 total nutations are simply arithmetic sums,
yet in reality the various components are successive Euler
rotations. This slight lack of rigor leads to cross terms
that exceed 1 mas after a century. The rigorous procedure
is to form the GCRS-to-true rotation matrix by applying the
bias, precession and nutation in that order.
(ii) Although the precession adjustments are stated to be with
respect to Lieske et al. (1977), the MHB2000 model does
not specify which set of Euler angles are to be used and
how the adjustments are to be applied. The most literal
and straightforward procedure is to adopt the 4-rotation
epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
to psi_A and DEPSPR to both omega_A and eps_A.
(iii) The MHB2000 model predates the determination by Chapront
et al. (2002) of a 14.6 mas displacement between the
J2000.0 mean equinox and the origin of the ICRS frame. It
should, however, be noted that neglecting this displacement
when calculating star coordinates does not lead to a
14.6 mas change in right ascension, only a small second-
order distortion in the pattern of the precession-nutation
effect.
For these reasons, the SOFA functions do not generate the "total
nutations" directly, though they can of course easily be
generated by calling iauBi00, iauPr00 and the present function
and adding the results.
7) The MHB2000 model contains 41 instances where the same frequency
appears multiple times, of which 38 are duplicates and three are
triplicates. To keep the present code close to the original MHB
algorithm, this small inefficiency has not been corrected.
Called:
Fal03 mean anomaly of the Moon
Faf03 mean argument of the latitude of the Moon
Faom03 mean longitude of the Moon's ascending node
Fame03 mean longitude of Mercury
Fave03 mean longitude of Venus
Fae03 mean longitude of Earth
Fama03 mean longitude of Mars
Faju03 mean longitude of Jupiter
Fasa03 mean longitude of Saturn
Faur03 mean longitude of Uranus
Fapa03 general accumulated precession in longitude
References:
Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
Astron.Astrophys. 387, 700
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
Astron.Astrophys. 58, 1-16
Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
107, B4. The MHB_2000 code itself was obtained on 9th September
2002 from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
Wallace, P.T., "Software for Implementing the IAU 2000
Resolutions", in IERS Workshop 5.1 (2002)
*/
func Nut00a(date1, date2 float64, dpsi, deps *float64) {
var i int
var t, el, elp, f, d, om, arg, dp, de, sarg, carg,
al, af, ad, aom, alme, alve, alea, alma,
alju, alsa, alur, alne, apa, dpsils, depsls,
dpsipl, depspl float64
/* Units of 0.1 microarcsecond to radians */
const U2R = DAS2R / 1e7
/* ------------------------- */
/* Luni-Solar nutation model */
/* ------------------------- */
/* The units for the sine and cosine coefficients are */
/* 0.1 microarcsecond and the same per Julian century */
xls := []struct {
nl, nlp, nf, nd, nom int /* coefficients of l,l',F,D,Om */
sp, spt, cp float64 /* longitude sin, t*sin, cos coefficients */
ce, cet, se float64 /* obliquity cos, t*cos, sin coefficients */
}{
/* 1- 10 */
{0, 0, 0, 0, 1,
-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
{0, 0, 2, -2, 2,
-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
{0, 0, 2, 0, 2, -2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0},
{0, 0, 0, 0, 2, 2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0},
{0, 1, 0, 0, 0, 1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0},
{0, 1, 2, -2, 2, -516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0},
{1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
{0, 0, 2, 0, 1, -387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
{1, 0, 2, 0, 2, -301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
{0, -1, 2, -2, 2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
/* 11-20 */
{0, 0, 2, -2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
{-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
{-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
{1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
{-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
{-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
{1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
{-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
{0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
{0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
/* 21-30 */
{0, -2, 2, -2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
{-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
{2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
{1, 0, 2, -2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
{-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
{2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
{0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
{0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
{-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
{0, 2, 2, -2, 2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
/* 31-40 */
{0, 0, -2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
{1, 0, 0, -2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
{0, -1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
{-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
{0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
{1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
{-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
{0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
{0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
{0, -1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
/* 41-50 */
{0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
{1, 0, 2, -2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
{2, 0, 2, -2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
{-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
{2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
{0, -1, 2, -2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
{0, 0, 0, -2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
{-1, -1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
{2, 0, 0, -2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
{1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
/* 51-60 */
{0, 1, 2, -2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
{1, -1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
{-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
{3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
{0, -1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
{1, -1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
{0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
{-1, -1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
{-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
{0, -1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
/* 61-70 */
{-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
{1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
{2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
{-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
{1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
{1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
{-1, 0, 2, -2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
{1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
{-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0},
{0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
/* 71-80 */
{-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
{-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
{0, -2, 2, -2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
{1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
{-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
{-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
{1, 1, 2, -2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0},
{-2, 0, 2, 4, 2, -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0},
{-1, 0, 4, 0, 2, 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0},
{2, 0, 2, -2, 1, 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0},
/* 81-90 */
{2, 0, 2, 2, 2, -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0},
{1, 0, 0, 2, 1, -970.0, 0.0, 2.0, 496.0, 0.0, 1.0},
{3, 0, 0, 0, 0, 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0},
{3, 0, 2, -2, 2, 934.0, 0.0, -3.0, -399.0, 0.0, -1.0},
{0, 0, 4, -2, 2, 922.0, 0.0, -1.0, -395.0, 0.0, -1.0},
{0, 1, 2, 0, 1, 815.0, 0.0, -1.0, -422.0, 0.0, -1.0},
{0, 0, -2, 2, 1, 834.0, 0.0, 2.0, -440.0, 0.0, 1.0},
{0, 0, 2, -2, 3, 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0},
{-1, 0, 0, 4, 0, 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0},
{2, 0, -2, 0, 1, 716.0, 0.0, -2.0, -389.0, 0.0, -1.0},
/* 91-100 */
{-2, 0, 0, 4, 0, 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0},
{-1, -1, 0, 2, 1, 742.0, 0.0, 1.0, -391.0, 0.0, 0.0},
{-1, 0, 0, 1, 1, 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0},
{0, 1, 0, 0, 2, 715.0, 0.0, -4.0, -326.0, 0.0, 2.0},
{0, 0, -2, 0, 1, -666.0, 0.0, -3.0, 369.0, 0.0, -1.0},
{0, -1, 2, 0, 1, -667.0, 0.0, 1.0, 346.0, 0.0, 1.0},
{0, 0, 2, -1, 2, -704.0, 0.0, 0.0, 304.0, 0.0, 0.0},
{0, 0, 2, 4, 2, -694.0, 0.0, 5.0, 294.0, 0.0, 2.0},
{-2, -1, 0, 2, 0, -1014.0, 0.0, -1.0, 4.0, 0.0, -1.0},
{1, 1, 0, -2, 1, -585.0, 0.0, -2.0, 316.0, 0.0, -1.0},
/* 101-110 */
{-1, 1, 0, 2, 0, -949.0, 0.0, 1.0, 8.0, 0.0, -1.0},
{-1, 1, 0, 1, 2, -595.0, 0.0, 0.0, 258.0, 0.0, 0.0},
{1, -1, 0, 0, 1, 528.0, 0.0, 0.0, -279.0, 0.0, 0.0},
{1, -1, 2, 2, 2, -590.0, 0.0, 4.0, 252.0, 0.0, 2.0},
{-1, 1, 2, 2, 2, 570.0, 0.0, -2.0, -244.0, 0.0, -1.0},
{3, 0, 2, 0, 1, -502.0, 0.0, 3.0, 250.0, 0.0, 2.0},
{0, 1, -2, 2, 0, -875.0, 0.0, 1.0, 29.0, 0.0, 0.0},
{-1, 0, 0, -2, 1, -492.0, 0.0, -3.0, 275.0, 0.0, -1.0},
{0, 1, 2, 2, 2, 535.0, 0.0, -2.0, -228.0, 0.0, -1.0},
{-1, -1, 2, 2, 1, -467.0, 0.0, 1.0, 240.0, 0.0, 1.0},
/* 111-120 */
{0, -1, 0, 0, 2, 591.0, 0.0, 0.0, -253.0, 0.0, 0.0},
{1, 0, 2, -4, 1, -453.0, 0.0, -1.0, 244.0, 0.0, -1.0},
{-1, 0, -2, 2, 0, 766.0, 0.0, 1.0, 9.0, 0.0, 0.0},
{0, -1, 2, 2, 1, -446.0, 0.0, 2.0, 225.0, 0.0, 1.0},
{2, -1, 2, 0, 2, -488.0, 0.0, 2.0, 207.0, 0.0, 1.0},
{0, 0, 0, 2, 2, -468.0, 0.0, 0.0, 201.0, 0.0, 0.0},
{1, -1, 2, 0, 1, -421.0, 0.0, 1.0, 216.0, 0.0, 1.0},
{-1, 1, 2, 0, 2, 463.0, 0.0, 0.0, -200.0, 0.0, 0.0},
{0, 1, 0, 2, 0, -673.0, 0.0, 2.0, 14.0, 0.0, 0.0},
{0, -1, -2, 2, 0, 658.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 121-130 */
{0, 3, 2, -2, 2, -438.0, 0.0, 0.0, 188.0, 0.0, 0.0},
{0, 0, 0, 1, 1, -390.0, 0.0, 0.0, 205.0, 0.0, 0.0},
{-1, 0, 2, 2, 0, 639.0, -11.0, -2.0, -19.0, 0.0, 0.0},
{2, 1, 2, 0, 2, 412.0, 0.0, -2.0, -176.0, 0.0, -1.0},
{1, 1, 0, 0, 1, -361.0, 0.0, 0.0, 189.0, 0.0, 0.0},
{1, 1, 2, 0, 1, 360.0, 0.0, -1.0, -185.0, 0.0, -1.0},
{2, 0, 0, 2, 0, 588.0, 0.0, -3.0, -24.0, 0.0, 0.0},
{1, 0, -2, 2, 0, -578.0, 0.0, 1.0, 5.0, 0.0, 0.0},
{-1, 0, 0, 2, 2, -396.0, 0.0, 0.0, 171.0, 0.0, 0.0},
{0, 1, 0, 1, 0, 565.0, 0.0, -1.0, -6.0, 0.0, 0.0},
/* 131-140 */
{0, 1, 0, -2, 1, -335.0, 0.0, -1.0, 184.0, 0.0, -1.0},
{-1, 0, 2, -2, 2, 357.0, 0.0, 1.0, -154.0, 0.0, 0.0},
{0, 0, 0, -1, 1, 321.0, 0.0, 1.0, -174.0, 0.0, 0.0},
{-1, 1, 0, 0, 1, -301.0, 0.0, -1.0, 162.0, 0.0, 0.0},
{1, 0, 2, -1, 2, -334.0, 0.0, 0.0, 144.0, 0.0, 0.0},
{1, -1, 0, 2, 0, 493.0, 0.0, -2.0, -15.0, 0.0, 0.0},
{0, 0, 0, 4, 0, 494.0, 0.0, -2.0, -19.0, 0.0, 0.0},
{1, 0, 2, 1, 2, 337.0, 0.0, -1.0, -143.0, 0.0, -1.0},
{0, 0, 2, 1, 1, 280.0, 0.0, -1.0, -144.0, 0.0, 0.0},
{1, 0, 0, -2, 2, 309.0, 0.0, 1.0, -134.0, 0.0, 0.0},
/* 141-150 */
{-1, 0, 2, 4, 1, -263.0, 0.0, 2.0, 131.0, 0.0, 1.0},
{1, 0, -2, 0, 1, 253.0, 0.0, 1.0, -138.0, 0.0, 0.0},
{1, 1, 2, -2, 1, 245.0, 0.0, 0.0, -128.0, 0.0, 0.0},
{0, 0, 2, 2, 0, 416.0, 0.0, -2.0, -17.0, 0.0, 0.0},
{-1, 0, 2, -1, 1, -229.0, 0.0, 0.0, 128.0, 0.0, 0.0},
{-2, 0, 2, 2, 1, 231.0, 0.0, 0.0, -120.0, 0.0, 0.0},
{4, 0, 2, 0, 2, -259.0, 0.0, 2.0, 109.0, 0.0, 1.0},
{2, -1, 0, 0, 0, 375.0, 0.0, -1.0, -8.0, 0.0, 0.0},
{2, 1, 2, -2, 2, 252.0, 0.0, 0.0, -108.0, 0.0, 0.0},
{0, 1, 2, 1, 2, -245.0, 0.0, 1.0, 104.0, 0.0, 0.0},
/* 151-160 */
{1, 0, 4, -2, 2, 243.0, 0.0, -1.0, -104.0, 0.0, 0.0},
{-1, -1, 0, 0, 1, 208.0, 0.0, 1.0, -112.0, 0.0, 0.0},
{0, 1, 0, 2, 1, 199.0, 0.0, 0.0, -102.0, 0.0, 0.0},
{-2, 0, 2, 4, 1, -208.0, 0.0, 1.0, 105.0, 0.0, 0.0},
{2, 0, 2, 0, 0, 335.0, 0.0, -2.0, -14.0, 0.0, 0.0},
{1, 0, 0, 1, 0, -325.0, 0.0, 1.0, 7.0, 0.0, 0.0},
{-1, 0, 0, 4, 1, -187.0, 0.0, 0.0, 96.0, 0.0, 0.0},
{-1, 0, 4, 0, 1, 197.0, 0.0, -1.0, -100.0, 0.0, 0.0},
{2, 0, 2, 2, 1, -192.0, 0.0, 2.0, 94.0, 0.0, 1.0},
{0, 0, 2, -3, 2, -188.0, 0.0, 0.0, 83.0, 0.0, 0.0},
/* 161-170 */
{-1, -2, 0, 2, 0, 276.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 1, 0, 0, 0, -286.0, 0.0, 1.0, 6.0, 0.0, 0.0},
{0, 0, 4, 0, 2, 186.0, 0.0, -1.0, -79.0, 0.0, 0.0},
{0, 0, 0, 0, 3, -219.0, 0.0, 0.0, 43.0, 0.0, 0.0},
{0, 3, 0, 0, 0, 276.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 2, -4, 1, -153.0, 0.0, -1.0, 84.0, 0.0, 0.0},
{0, -1, 0, 2, 1, -156.0, 0.0, 0.0, 81.0, 0.0, 0.0},
{0, 0, 0, 4, 1, -154.0, 0.0, 1.0, 78.0, 0.0, 0.0},
{-1, -1, 2, 4, 2, -174.0, 0.0, 1.0, 75.0, 0.0, 0.0},
{1, 0, 2, 4, 2, -163.0, 0.0, 2.0, 69.0, 0.0, 1.0},
/* 171-180 */
{-2, 2, 0, 2, 0, -228.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-2, -1, 2, 0, 1, 91.0, 0.0, -4.0, -54.0, 0.0, -2.0},
{-2, 0, 0, 2, 2, 175.0, 0.0, 0.0, -75.0, 0.0, 0.0},
{-1, -1, 2, 0, 2, -159.0, 0.0, 0.0, 69.0, 0.0, 0.0},
{0, 0, 4, -2, 1, 141.0, 0.0, 0.0, -72.0, 0.0, 0.0},
{3, 0, 2, -2, 1, 147.0, 0.0, 0.0, -75.0, 0.0, 0.0},
{-2, -1, 0, 2, 1, -132.0, 0.0, 0.0, 69.0, 0.0, 0.0},
{1, 0, 0, -1, 1, 159.0, 0.0, -28.0, -54.0, 0.0, 11.0},
{0, -2, 0, 2, 0, 213.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{-2, 0, 0, 4, 1, 123.0, 0.0, 0.0, -64.0, 0.0, 0.0},
/* 181-190 */
{-3, 0, 0, 0, 1, -118.0, 0.0, -1.0, 66.0, 0.0, 0.0},
{1, 1, 2, 2, 2, 144.0, 0.0, -1.0, -61.0, 0.0, 0.0},
{0, 0, 2, 4, 1, -121.0, 0.0, 1.0, 60.0, 0.0, 0.0},
{3, 0, 2, 2, 2, -134.0, 0.0, 1.0, 56.0, 0.0, 1.0},
{-1, 1, 2, -2, 1, -105.0, 0.0, 0.0, 57.0, 0.0, 0.0},
{2, 0, 0, -4, 1, -102.0, 0.0, 0.0, 56.0, 0.0, 0.0},
{0, 0, 0, -2, 2, 120.0, 0.0, 0.0, -52.0, 0.0, 0.0},
{2, 0, 2, -4, 1, 101.0, 0.0, 0.0, -54.0, 0.0, 0.0},
{-1, 1, 0, 2, 1, -113.0, 0.0, 0.0, 59.0, 0.0, 0.0},
{0, 0, 2, -1, 1, -106.0, 0.0, 0.0, 61.0, 0.0, 0.0},
/* 191-200 */
{0, -2, 2, 2, 2, -129.0, 0.0, 1.0, 55.0, 0.0, 0.0},
{2, 0, 0, 2, 1, -114.0, 0.0, 0.0, 57.0, 0.0, 0.0},
{4, 0, 2, -2, 2, 113.0, 0.0, -1.0, -49.0, 0.0, 0.0},
{2, 0, 0, -2, 2, -102.0, 0.0, 0.0, 44.0, 0.0, 0.0},
{0, 2, 0, 0, 1, -94.0, 0.0, 0.0, 51.0, 0.0, 0.0},
{1, 0, 0, -4, 1, -100.0, 0.0, -1.0, 56.0, 0.0, 0.0},
{0, 2, 2, -2, 1, 87.0, 0.0, 0.0, -47.0, 0.0, 0.0},
{-3, 0, 0, 4, 0, 161.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-1, 1, 2, 0, 1, 96.0, 0.0, 0.0, -50.0, 0.0, 0.0},
{-1, -1, 0, 4, 0, 151.0, 0.0, -1.0, -5.0, 0.0, 0.0},
/* 201-210 */
{-1, -2, 2, 2, 2, -104.0, 0.0, 0.0, 44.0, 0.0, 0.0},
{-2, -1, 2, 4, 2, -110.0, 0.0, 0.0, 48.0, 0.0, 0.0},
{1, -1, 2, 2, 1, -100.0, 0.0, 1.0, 50.0, 0.0, 0.0},
{-2, 1, 0, 2, 0, 92.0, 0.0, -5.0, 12.0, 0.0, -2.0},
{-2, 1, 2, 0, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0},
{2, 1, 0, -2, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0},
{-3, 0, 2, 0, 1, -78.0, 0.0, 0.0, 41.0, 0.0, 0.0},
{-2, 0, 2, -2, 1, -77.0, 0.0, 0.0, 43.0, 0.0, 0.0},
{-1, 1, 0, 2, 2, 2.0, 0.0, 0.0, 54.0, 0.0, 0.0},
{0, -1, 2, -1, 2, 94.0, 0.0, 0.0, -40.0, 0.0, 0.0},
/* 211-220 */
{-1, 0, 4, -2, 2, -93.0, 0.0, 0.0, 40.0, 0.0, 0.0},
{0, -2, 2, 0, 2, -83.0, 0.0, 10.0, 40.0, 0.0, -2.0},
{-1, 0, 2, 1, 2, 83.0, 0.0, 0.0, -36.0, 0.0, 0.0},
{2, 0, 0, 0, 2, -91.0, 0.0, 0.0, 39.0, 0.0, 0.0},
{0, 0, 2, 0, 3, 128.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-2, 0, 4, 0, 2, -79.0, 0.0, 0.0, 34.0, 0.0, 0.0},
{-1, 0, -2, 0, 1, -83.0, 0.0, 0.0, 47.0, 0.0, 0.0},
{-1, 1, 2, 2, 1, 84.0, 0.0, 0.0, -44.0, 0.0, 0.0},
{3, 0, 0, 0, 1, 83.0, 0.0, 0.0, -43.0, 0.0, 0.0},
{-1, 0, 2, 3, 2, 91.0, 0.0, 0.0, -39.0, 0.0, 0.0},
/* 221-230 */
{2, -1, 2, 0, 1, -77.0, 0.0, 0.0, 39.0, 0.0, 0.0},
{0, 1, 2, 2, 1, 84.0, 0.0, 0.0, -43.0, 0.0, 0.0},
{0, -1, 2, 4, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0},
{2, -1, 2, 2, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0},
{0, 2, -2, 2, 0, -94.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 2, -1, 1, 68.0, 0.0, 0.0, -36.0, 0.0, 0.0},
{0, -2, 0, 0, 1, -61.0, 0.0, 0.0, 32.0, 0.0, 0.0},
{1, 0, 2, -4, 2, 71.0, 0.0, 0.0, -31.0, 0.0, 0.0},
{1, -1, 0, -2, 1, 62.0, 0.0, 0.0, -34.0, 0.0, 0.0},
{-1, -1, 2, 0, 1, -63.0, 0.0, 0.0, 33.0, 0.0, 0.0},
/* 231-240 */
{1, -1, 2, -2, 2, -73.0, 0.0, 0.0, 32.0, 0.0, 0.0},
{-2, -1, 0, 4, 0, 115.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 0, 0, 3, 0, -103.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, -1, 2, 2, 2, 63.0, 0.0, 0.0, -28.0, 0.0, 0.0},
{0, 2, 2, 0, 2, 74.0, 0.0, 0.0, -32.0, 0.0, 0.0},
{1, 1, 0, 2, 0, -103.0, 0.0, -3.0, 3.0, 0.0, -1.0},
{2, 0, 2, -1, 2, -69.0, 0.0, 0.0, 30.0, 0.0, 0.0},
{1, 0, 2, 1, 1, 57.0, 0.0, 0.0, -29.0, 0.0, 0.0},
{4, 0, 0, 0, 0, 94.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{2, 1, 2, 0, 1, 64.0, 0.0, 0.0, -33.0, 0.0, 0.0},
/* 241-250 */
{3, -1, 2, 0, 2, -63.0, 0.0, 0.0, 26.0, 0.0, 0.0},
{-2, 2, 0, 2, 1, -38.0, 0.0, 0.0, 20.0, 0.0, 0.0},
{1, 0, 2, -3, 1, -43.0, 0.0, 0.0, 24.0, 0.0, 0.0},
{1, 1, 2, -4, 1, -45.0, 0.0, 0.0, 23.0, 0.0, 0.0},
{-1, -1, 2, -2, 1, 47.0, 0.0, 0.0, -24.0, 0.0, 0.0},
{0, -1, 0, -1, 1, -48.0, 0.0, 0.0, 25.0, 0.0, 0.0},
{0, -1, 0, -2, 1, 45.0, 0.0, 0.0, -26.0, 0.0, 0.0},
{-2, 0, 0, 0, 2, 56.0, 0.0, 0.0, -25.0, 0.0, 0.0},
{-2, 0, -2, 2, 0, 88.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 0, -2, 4, 0, -75.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 251-260 */
{1, -2, 0, 0, 0, 85.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 0, 1, 1, 49.0, 0.0, 0.0, -26.0, 0.0, 0.0},
{-1, 2, 0, 2, 0, -74.0, 0.0, -3.0, -1.0, 0.0, -1.0},
{1, -1, 2, -2, 1, -39.0, 0.0, 0.0, 21.0, 0.0, 0.0},
{1, 2, 2, -2, 2, 45.0, 0.0, 0.0, -20.0, 0.0, 0.0},
{2, -1, 2, -2, 2, 51.0, 0.0, 0.0, -22.0, 0.0, 0.0},
{1, 0, 2, -1, 1, -40.0, 0.0, 0.0, 21.0, 0.0, 0.0},
{2, 1, 2, -2, 1, 41.0, 0.0, 0.0, -21.0, 0.0, 0.0},
{-2, 0, 0, -2, 1, -42.0, 0.0, 0.0, 24.0, 0.0, 0.0},
{1, -2, 2, 0, 2, -51.0, 0.0, 0.0, 22.0, 0.0, 0.0},
/* 261-270 */
{0, 1, 2, 1, 1, -42.0, 0.0, 0.0, 22.0, 0.0, 0.0},
{1, 0, 4, -2, 1, 39.0, 0.0, 0.0, -21.0, 0.0, 0.0},
{-2, 0, 4, 2, 2, 46.0, 0.0, 0.0, -18.0, 0.0, 0.0},
{1, 1, 2, 1, 2, -53.0, 0.0, 0.0, 22.0, 0.0, 0.0},
{1, 0, 0, 4, 0, 82.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{1, 0, 2, 2, 0, 81.0, 0.0, -1.0, -4.0, 0.0, 0.0},
{2, 0, 2, 1, 2, 47.0, 0.0, 0.0, -19.0, 0.0, 0.0},
{3, 1, 2, 0, 2, 53.0, 0.0, 0.0, -23.0, 0.0, 0.0},
{4, 0, 2, 0, 1, -45.0, 0.0, 0.0, 22.0, 0.0, 0.0},
{-2, -1, 2, 0, 0, -44.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 271-280 */
{0, 1, -2, 2, 1, -33.0, 0.0, 0.0, 16.0, 0.0, 0.0},
{1, 0, -2, 1, 0, -61.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{0, -1, -2, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0},
{2, -1, 0, -2, 1, -38.0, 0.0, 0.0, 19.0, 0.0, 0.0},
{-1, 0, 2, -1, 2, -33.0, 0.0, 0.0, 21.0, 0.0, 0.0},
{1, 0, 2, -3, 2, -60.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 2, -2, 3, 48.0, 0.0, 0.0, -10.0, 0.0, 0.0},
{0, 0, 2, -3, 1, 27.0, 0.0, 0.0, -14.0, 0.0, 0.0},
{-1, 0, -2, 2, 1, 38.0, 0.0, 0.0, -20.0, 0.0, 0.0},
{0, 0, 2, -4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0},
/* 281-290 */
{-2, 1, 0, 0, 1, -29.0, 0.0, 0.0, 15.0, 0.0, 0.0},
{-1, 0, 0, -1, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0},
{2, 0, 2, -4, 2, -32.0, 0.0, 0.0, 15.0, 0.0, 0.0},
{0, 0, 4, -4, 4, 45.0, 0.0, 0.0, -8.0, 0.0, 0.0},
{0, 0, 4, -4, 2, -44.0, 0.0, 0.0, 19.0, 0.0, 0.0},
{-1, -2, 0, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0},
{-2, 0, 0, 3, 0, -51.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, -2, 2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0},
{-3, 0, 2, 2, 2, 44.0, 0.0, 0.0, -19.0, 0.0, 0.0},
{-3, 0, 2, 2, 1, 26.0, 0.0, 0.0, -14.0, 0.0, 0.0},
/* 291-300 */
{-2, 0, 2, 2, 0, -60.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, -1, 0, 0, 1, 35.0, 0.0, 0.0, -18.0, 0.0, 0.0},
{-2, 1, 2, 2, 2, -27.0, 0.0, 0.0, 11.0, 0.0, 0.0},
{1, 1, 0, 1, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, 1, 4, -2, 2, 36.0, 0.0, 0.0, -15.0, 0.0, 0.0},
{-1, 1, 0, -2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0},
{0, 0, 0, -4, 1, -35.0, 0.0, 0.0, 19.0, 0.0, 0.0},
{1, -1, 0, 2, 1, -37.0, 0.0, 0.0, 19.0, 0.0, 0.0},
{1, 1, 0, 2, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0},
{-1, 2, 2, 2, 2, 35.0, 0.0, 0.0, -14.0, 0.0, 0.0},
/* 301-310 */
{3, 1, 2, -2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0},
{0, -1, 0, 4, 0, 65.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, -1, 0, 2, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, 0, 4, 0, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0},
{2, 0, 4, -2, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0},
{-1, -1, 2, 4, 1, -30.0, 0.0, 0.0, 15.0, 0.0, 0.0},
{1, 0, 0, 4, 1, -32.0, 0.0, 0.0, 16.0, 0.0, 0.0},
{1, -2, 2, 2, 2, -31.0, 0.0, 0.0, 13.0, 0.0, 0.0},
{0, 0, 2, 3, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0},
{-1, 1, 2, 4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0},
/* 311-320 */
{3, 0, 0, 2, 0, 49.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 0, 4, 2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0},
{1, 1, 2, 2, 1, 23.0, 0.0, 0.0, -12.0, 0.0, 0.0},
{-2, 0, 2, 6, 2, -43.0, 0.0, 0.0, 18.0, 0.0, 0.0},
{2, 1, 2, 2, 2, 26.0, 0.0, 0.0, -11.0, 0.0, 0.0},
{-1, 0, 2, 6, 2, -32.0, 0.0, 0.0, 14.0, 0.0, 0.0},
{1, 0, 2, 4, 1, -29.0, 0.0, 0.0, 14.0, 0.0, 0.0},
{2, 0, 2, 4, 2, -27.0, 0.0, 0.0, 12.0, 0.0, 0.0},
{1, 1, -2, 1, 0, 30.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, 1, 2, 1, 2, -11.0, 0.0, 0.0, 5.0, 0.0, 0.0},
/* 321-330 */
{2, 0, -2, 0, 2, -21.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{-1, 0, 0, 1, 2, -34.0, 0.0, 0.0, 15.0, 0.0, 0.0},
{-4, 0, 2, 2, 1, -10.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{-1, -1, 0, 1, 0, -36.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, -2, 2, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{1, 0, 0, -1, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{0, -1, 2, -2, 3, -21.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{-2, 1, 2, 0, 0, -29.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, 0, 2, -2, 4, -15.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-2, -2, 0, 2, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 331-340 */
{-2, 0, -2, 4, 0, 28.0, 0.0, 0.0, 0.0, 0.0, -2.0},
{0, -2, -2, 2, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 2, 0, -2, 1, -22.0, 0.0, 0.0, 12.0, 0.0, 0.0},
{3, 0, 0, -4, 1, -14.0, 0.0, 0.0, 7.0, 0.0, 0.0},
{-1, 1, 2, -2, 2, 24.0, 0.0, 0.0, -11.0, 0.0, 0.0},
{1, -1, 2, -4, 1, 11.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{1, 1, 0, -2, 2, 14.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{-3, 0, 2, 0, 0, 24.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, 0, 2, 0, 2, 18.0, 0.0, 0.0, -8.0, 0.0, 0.0},
{-2, 0, 0, 1, 0, -38.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 341-350 */
{0, 0, -2, 1, 0, -31.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, 0, 0, 2, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0},
{-1, -1, -2, 2, 0, 29.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 2, -4, 1, -18.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{2, 1, 0, -4, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{0, 2, 0, -2, 1, -17.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{1, 0, 0, -3, 1, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{-2, 0, 2, -2, 2, 16.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{-2, -1, 0, 0, 1, 22.0, 0.0, 0.0, -12.0, 0.0, 0.0},
{-4, 0, 0, 2, 0, 20.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 351-360 */
{1, 1, 0, -4, 1, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{-1, 0, 2, -4, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{0, 0, 4, -4, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0},
{0, 3, 2, -2, 2, 0.0, 0.0, 0.0, -7.0, 0.0, 0.0},
{-3, -1, 0, 4, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, 0, 0, 4, 1, 19.0, 0.0, 0.0, -10.0, 0.0, 0.0},
{1, -1, -2, 2, 0, -34.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 0, 2, 2, -20.0, 0.0, 0.0, 8.0, 0.0, 0.0},
{1, -2, 0, 0, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0},
{1, -1, 0, 0, 2, -18.0, 0.0, 0.0, 7.0, 0.0, 0.0},
/* 361-370 */
{0, 0, 0, 1, 2, 13.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{-1, -1, 2, 0, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, -2, 2, -2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{0, -1, 2, -1, 1, 15.0, 0.0, 0.0, -8.0, 0.0, 0.0},
{-1, 0, 2, 0, 3, -11.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{1, 1, 0, 0, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0},
{-1, 1, 2, 0, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 2, 0, 0, 0, -35.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 2, 2, 0, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{-1, 0, 4, -2, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0},
/* 371-380 */
{3, 0, 2, -4, 2, -26.0, 0.0, 0.0, 11.0, 0.0, 0.0},
{1, 2, 2, -2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{1, 0, 4, -4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{-2, -1, 0, 4, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{0, -1, 0, 2, 2, -21.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{-2, 1, 0, 4, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, -1, 2, 2, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0},
{2, 0, -2, 2, 0, -29.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 0, 1, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{0, 1, 0, 2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0},
/* 381-390 */
{1, -1, 2, -1, 2, 22.0, 0.0, 0.0, -9.0, 0.0, 0.0},
{-2, 0, 4, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{2, 1, 0, 0, 1, -20.0, 0.0, 0.0, 11.0, 0.0, 0.0},
{0, 1, 2, 0, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, -1, 4, -2, 2, -17.0, 0.0, 0.0, 7.0, 0.0, 0.0},
{0, 0, 4, -2, 4, 15.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{0, 2, 2, 0, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{-3, 0, 0, 6, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 0, 4, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{1, -2, 0, 2, 0, 25.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 391-400 */
{-1, 0, 0, 4, 2, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{-1, -2, 2, 2, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0},
{-1, 0, 0, -2, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0},
{1, 0, -2, -2, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{0, 0, -2, -2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{-2, 0, -2, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{0, 0, 0, 3, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0},
{0, 0, 0, 3, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 1, 0, 4, 0, -22.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 2, 2, 0, 28.0, 0.0, 0.0, -1.0, 0.0, 0.0},
/* 401-410 */
{-2, 0, 2, 3, 2, 15.0, 0.0, 0.0, -7.0, 0.0, 0.0},
{1, 0, 0, 2, 2, 23.0, 0.0, 0.0, -10.0, 0.0, 0.0},
{0, -1, 2, 1, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0},
{3, -1, 0, 0, 0, 29.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{2, 0, 0, 1, 0, -25.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{1, -1, 2, 0, 0, 22.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, 2, 1, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 2, 0, 3, 15.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{3, 1, 0, 0, 0, -23.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{3, -1, 2, -2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0},
/* 411-420 */
{2, 0, 2, -1, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{1, 1, 2, 0, 0, -19.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, 4, -1, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{1, 2, 2, 0, 2, 21.0, 0.0, 0.0, -9.0, 0.0, 0.0},
{-2, 0, 0, 6, 0, 23.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, -1, 0, 4, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0},
{-2, -1, 2, 4, 1, -19.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{0, -2, 2, 2, 1, -22.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{0, -1, 2, 2, 0, 27.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-1, 0, 2, 3, 1, 16.0, 0.0, 0.0, -8.0, 0.0, 0.0},
/* 421-430 */
{-2, 1, 2, 4, 2, 19.0, 0.0, 0.0, -8.0, 0.0, 0.0},
{2, 0, 0, 2, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{2, -2, 2, 0, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{-1, 1, 2, 3, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{3, 0, 2, -1, 2, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{4, 0, 2, -2, 1, 18.0, 0.0, 0.0, -9.0, 0.0, 0.0},
{-1, 0, 0, 6, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-1, -2, 2, 4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{-3, 0, 2, 6, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{-1, 0, 2, 4, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0},
/* 431-440 */
{3, 0, 0, 2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0},
{3, -1, 2, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{3, 0, 2, 0, 0, 30.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{1, 0, 4, 0, 2, 24.0, 0.0, 0.0, -10.0, 0.0, 0.0},
{5, 0, 2, -2, 2, 10.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{0, -1, 2, 4, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0},
{2, -1, 2, 2, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0},
{0, 1, 2, 4, 2, 17.0, 0.0, 0.0, -7.0, 0.0, 0.0},
{1, -1, 2, 4, 2, -24.0, 0.0, 0.0, 10.0, 0.0, 0.0},
{3, -1, 2, 2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0},
/* 441-450 */
{3, 0, 2, 2, 1, -24.0, 0.0, 0.0, 11.0, 0.0, 0.0},
{5, 0, 2, 0, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0},
{0, 0, 2, 6, 2, -13.0, 0.0, 0.0, 5.0, 0.0, 0.0},
{4, 0, 2, 2, 2, -15.0, 0.0, 0.0, 7.0, 0.0, 0.0},
{0, -1, 1, -1, 1, 0.0, 0.0, -1988.0, 0.0, 0.0, -1679.0},
{-1, 0, 1, 0, 3, 0.0, 0.0, -63.0, 0.0, 0.0, -27.0},
{0, -2, 2, -2, 3, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, -1, 0, 1, 0.0, 0.0, 5.0, 0.0, 0.0, 4.0},
{2, -2, 0, -2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-1, 0, 1, 0, 2, 0.0, 0.0, 364.0, 0.0, 0.0, 176.0},
/* 451-460 */
{-1, 0, 1, 0, 1, 0.0, 0.0, -1044.0, 0.0, 0.0, -891.0},
{-1, -1, 2, -1, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-2, 2, 0, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 0, 1, 0, 0, 0.0, 0.0, 330.0, 0.0, 0.0, 0.0},
{-4, 1, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-3, 0, 2, 1, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-2, -1, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{1, 0, -2, 1, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, -1, -2, 0, 1, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-4, 0, 2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 461-470 */
{-3, 1, 0, 3, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 0, -1, 2, 0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0},
{0, -2, 0, 0, 2, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{0, -2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-3, 0, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, -1, 0, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 0, -2, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-4, 0, 0, 4, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 1, -2, 0, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{2, -1, 0, -2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
/* 471-480 */
{0, 0, 1, -1, 0, -5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 2, 0, 1, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 1, 2, 0, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{1, 1, 0, -1, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{1, 0, 1, -2, 1, 0.0, 0.0, -12.0, 0.0, 0.0, -10.0},
{0, 2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{1, -1, 2, -3, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 1, 2, -1, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, 0, 4, -2, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-2, 0, 4, -2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
/* 481-490 */
{-2, -2, 0, 2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-2, 0, -2, 4, 0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 2, 2, -4, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{1, 1, 2, -4, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-1, 2, 2, -2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, 0, 0, -3, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 2, 0, 0, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{0, 0, 0, -2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 2, -2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 1, 0, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 491-500 */
{0, 0, 0, -1, 2, -8.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-2, 1, 0, 1, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, -2, 0, -2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{1, 0, -2, 0, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-3, 1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 1, -2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 0, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-3, 0, 0, 2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, -1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 0, 2, -6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
/* 501-510 */
{0, 1, 2, -4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 0, 0, -4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-2, 1, 2, -2, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, -1, 2, -4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{0, 1, 0, -2, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-1, 0, 0, -2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 0, -2, -2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-4, 0, 2, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, -1, 0, -1, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, -2, 0, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0},
/* 511-520 */
{-3, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 0, -2, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 0, -2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{0, 0, -4, 2, 0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, -1, -2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 2, -6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 0, 2, -4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{1, 0, 0, -4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{2, 1, 2, -4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{2, 1, 2, -4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
/* 521-530 */
{0, 1, 4, -4, 4, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 4, -4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-1, -1, -2, 4, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 0, -2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, -1, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, -2, 3, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 0, 0, 3, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{0, -1, 0, 1, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, 0, 2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 531-540 */
{1, 1, -2, 2, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 1, 0, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{1, -2, 2, -2, 1, 10.0, 0.0, 13.0, 6.0, 0.0, -5.0},
{0, 0, 1, 0, 2, 0.0, 0.0, 30.0, 0.0, 0.0, 14.0},
{0, 0, 1, 0, 1, 0.0, 0.0, -162.0, 0.0, 0.0, -138.0},
{0, 0, 1, 0, 0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0},
{-1, 2, 0, 2, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{0, 0, 2, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, 0, 2, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 0, 0, -1, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 541-550 */
{3, 0, 0, -2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{1, 0, 2, -2, 3, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 2, 0, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, 0, 2, -3, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 1, 4, -2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, -2, 0, 4, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, -3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, -2, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 0, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 0, 0, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
/* 551-560 */
{-1, 0, 0, 3, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, -2, 0, 0, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, -1, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, -2, 2, 0, 1, -6.0, 0.0, -3.0, 3.0, 0.0, 1.0},
{-1, 0, 1, 2, 1, 0.0, 0.0, -3.0, 0.0, 0.0, -2.0},
{-1, 1, 0, 3, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -1, 2, 1, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, -1, 2, 0, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 1, 2, 2, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
/* 561-570 */
{2, -2, 2, -2, 2, -1.0, 0.0, 3.0, 3.0, 0.0, -1.0},
{1, 1, 0, 1, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{1, 0, 1, 0, 1, 0.0, 0.0, -13.0, 0.0, 0.0, -11.0},
{1, 0, 1, 0, 0, 3.0, 0.0, 6.0, 0.0, 0.0, 0.0},
{0, 2, 0, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, -1, 2, -2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{0, -1, 4, -2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{0, 0, 4, -2, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 4, -2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{4, 0, 2, -4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0},
/* 571-580 */
{2, 2, 2, -2, 2, 8.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{2, 0, 4, -4, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, -2, 0, 4, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, -3, 2, 2, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-3, 0, 2, 4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-3, 0, 2, -2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, -1, 0, -2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{-3, 0, 0, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-3, 0, -2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 0, -4, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
/* 581-590 */
{-2, 1, 0, -2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-4, 0, 0, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0},
{-1, 0, 0, -4, 1, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-3, 0, 0, -2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 0, 3, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-1, 1, 0, 4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{1, -2, 2, 0, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{0, 1, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-1, 0, 2, 2, 3, 6.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{0, 0, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 591-600 */
{-2, 0, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{3, 0, 0, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, 1, 0, 1, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, -1, 2, -1, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{0, 0, 2, 0, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 3, 0, 3, 0.0, 0.0, -26.0, 0.0, 0.0, -11.0},
{0, 0, 3, 0, 2, 0.0, 0.0, -10.0, 0.0, 0.0, -5.0},
{-1, 2, 2, 2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-1, 0, 4, 0, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 601-610 */
{1, 2, 2, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{3, 1, 2, -2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{1, 1, 4, -2, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-2, -1, 0, 6, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, -2, 0, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-2, 0, 0, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, -2, 2, 4, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, -3, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 0, 4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-1, -1, 2, 3, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 611-620 */
{-2, 0, 2, 4, 0, 13.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, -1, 0, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{1, 0, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 0, 4, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{0, 1, 0, 4, 0, -11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, -1, 2, 1, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{0, 0, 2, 2, 3, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 2, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-1, 0, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-2, 0, 4, 2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
/* 621-630 */
{2, 1, 0, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 1, 0, 2, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, -1, 2, 0, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 2, 1, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 0, 2, 0, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{3, 0, 2, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{1, 0, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{1, 0, 3, 0, 3, 0.0, 0.0, -5.0, 0.0, 0.0, -2.0},
{1, 1, 2, 1, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0},
/* 631-640 */
{0, 2, 2, 2, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{2, 1, 2, 0, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 0, 4, -2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{4, 1, 2, -2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{-1, -1, 0, 6, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{-3, -1, 2, 6, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{-1, 0, 0, 6, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-3, 0, 2, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{1, -1, 0, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{1, -1, 0, 4, 0, 12.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 641-650 */
{-2, 0, 2, 5, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{1, -2, 2, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{3, -1, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, -1, 2, 2, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, 2, 3, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{-1, 1, 2, 4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{0, 1, 2, 3, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-1, 0, 4, 2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 0, 2, 1, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{5, 0, 0, 0, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 651-660 */
{2, 1, 2, 1, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{1, 0, 4, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{3, 1, 2, 0, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0},
{3, 0, 4, -2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{-2, -1, 2, 6, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 0, 6, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, -2, 2, 4, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{-2, 0, 2, 6, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0},
{2, 0, 0, 4, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{2, 0, 0, 4, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0},
/* 661-670 */
{2, -2, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{0, 0, 2, 4, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{1, 0, 2, 3, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0},
{4, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{2, 0, 2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0, 0, 4, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{4, -1, 2, 0, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{3, 0, 2, 1, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{2, 1, 2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{4, 1, 2, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0},
/* 671-678 */
{-1, -1, 2, 6, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{-1, 0, 2, 6, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{1, -1, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{1, 1, 2, 4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0},
{3, 1, 2, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0},
{5, 0, 2, 0, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{2, -1, 2, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0},
{2, 0, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0},
}
/* Number of terms in the luni-solar nutation model */
NLS := len(xls)
/* ------------------------ */
/* Planetary nutation model */
/* ------------------------ */
/* The units for the sine and cosine coefficients are */
/* 0.1 microarcsecond */
xpl := []struct {
nl, /* coefficients of l, F, D and Omega */
nf,
nd,
nom,
nme, /* coefficients of planetary longitudes */
nve,
nea,
nma,
nju,
nsa,
nur,
nne,
npa int /* coefficient of general precession */
sp, cp int /* longitude sin, cos coefficients */
se, ce int /* obliquity sin, cos coefficients */
}{
/* 1-10 */
{0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 0, 1440, 0, 0, 0},
{0, 0, 0, 0, 0, 0, -8, 16, -4, -5, 0, 0, 2, 56, -117, -42, -40},
{0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 2, 125, -43, 0, -54},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 0, 5, 0, 0},
{0, 0, 0, 0, 0, 0, -4, 8, -1, -5, 0, 0, 2, 3, -7, -3, 0},
{0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, 3, 0, 0, -2},
{0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, -114, 0, 0, 61},
{-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, -219, 89, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, -2, 6, -3, 0, 2, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, -462, 1604, 0, 0},
/* 11-20 */
{0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0, 99, 0, 0, -53},
{0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 1, -3, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, 0, 6, 2, 0},
{0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2, -12, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1, 14, -218, 117, 8},
{0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0, 31, -481, -257, -17},
{0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, -491, 128, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0, -3084, 5123, 2735, 1647},
{0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 1, -1444, 2409, -1286, -771},
/* 21-30 */
{0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 2, 11, -24, -11, -9},
{2, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, 26, -9, 0, 0},
{1, 0, -2, 0, 0, 19, -21, 3, 0, 0, 0, 0, 0, 103, -60, 0, 0},
{0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0, 0, -13, -7, 0},
{1, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -26, -29, -16, 14},
{0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0, 9, -27, -14, -5},
{-2, 0, 2, 1, 0, 0, 2, 0, 0, -5, 0, 0, 0, 12, 0, 0, -6},
{0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0},
{0, -1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 24, 0, 0},
{-2, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 284, 0, 0, -151},
/* 31-40 */
{-1, 0, 0, 0, 0, 18, -16, 0, 0, 0, 0, 0, 0, 226, 101, 0, 0},
{-2, 1, 1, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -8, -2, 0},
{-1, 1, -1, 1, 0, 18, -17, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0},
{-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -3},
{0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, -41, 175, 76, 17},
{0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 15, 6, 0},
{0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, 425, 212, -133, 269},
{0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, 1200, 598, 319, -641},
{0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 0, 235, 334, 0, 0},
{0, 1, -1, 1, 0, 8, -14, 0, 0, 0, 0, 0, 0, 11, -12, -7, -6},
/* 41-50 */
{0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 1, 5, -6, 3, 3},
{-2, 0, 2, 1, 0, 0, 2, 0, -4, 5, 0, 0, 0, -5, 0, 0, 3},
{-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3},
{-2, 0, 2, 0, 0, 0, 2, 0, -3, 1, 0, 0, 0, 15, 0, 0, 0},
{0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, 13, 0, 0, -7},
{-2, 0, 2, 0, 0, 0, 2, 0, -4, 3, 0, 0, 0, -6, -9, 0, 0},
{0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 266, -78, 0, 0},
{0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -460, -435, -232, 246},
{0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 15, 7, 0},
{-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2},
/* 51-60 */
{-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0},
{-2, 0, 2, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 4, 0, 0, 0},
{-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, 0, 3, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 4, 2, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -17, -19, -10, 9},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -9, -11, 6, -5},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, 0, 0, 3},
{-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -16, 8, 0, 0},
{0, -1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0},
/* 61-70 */
{0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 11, 24, 11, -5},
{0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, -3, -4, -2, 1},
{0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0, 0, -8, -4, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 3, 0, 0},
{1, 0, -2, 0, 0, 17, -16, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0, 0, 3, 2, 0},
{-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, -6, 4, 2, 3},
{0, -2, 2, 0, 0, 0, 9, -13, 0, 0, 0, 0, 0, -3, -5, 0, 0},
{0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, -5, 0, 0, 2},
/* 71-80 */
{0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 24, 13, -2},
{0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -42, 20, 0, 0},
{0, -2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, -10, 233, 0, 0},
{0, -1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1},
{-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 78, -18, 0, 0},
{2, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, -1, 0},
{0, -1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, -2, 1},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -8, -4, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -5, 3, 0},
/* 81-90 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -7, 0, 0, 3},
{0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, -14, 8, 3, 6},
{0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, 0, 8, -4, 0},
{0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, 0, 19, 10, 0},
{0, 0, 0, 0, 0, 0, 8, -15, 0, 0, 0, 0, 0, 45, -22, 0, 0},
{1, -1, -1, 0, 0, 0, 8, -15, 0, 0, 0, 0, 0, -3, 0, 0, 0},
{2, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0},
{-2, 0, 2, 0, 0, 0, 2, 0, -5, 5, 0, 0, 0, 0, 3, 0, 0},
{2, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, 3, 5, 3, -2},
{2, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 89, -16, -9, -48},
/* 91-100 */
{-2, 1, 1, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0},
{-2, 1, 1, 1, 0, 0, 1, 0, -3, 0, 0, 0, 0, -3, 7, 4, 2},
{-2, 0, 2, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, -349, -62, 0, 0},
{-2, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -15, 22, 0, 0},
{-2, 0, 2, 0, 0, 0, 2, 0, -1, -5, 0, 0, 0, -3, 0, 0, 0},
{-1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -53, 0, 0, 0},
{-1, 1, 1, 1, 0, -20, 20, 0, 0, 0, 0, 0, 0, 5, 0, 0, -3},
{1, 0, -2, 0, 0, 20, -21, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0},
{0, 0, 0, 1, 0, 0, 8, -15, 0, 0, 0, 0, 0, 15, -7, -4, -8},
{0, 2, -2, 1, 0, 0, -10, 15, 0, 0, 0, 0, 0, -3, 0, 0, 1},
/* 101-110 */
{0, -1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -21, -78, 0, 0},
{0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, -70, -37, -11},
{0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 3, 0},
{0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0, 5, 3, 2, -2},
{2, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, -17, -4, -2, 9},
{0, -2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 32, 15, -8, 17},
{0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 174, 84, 45, -93},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 11, 56, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -66, -12, -6, 35},
/* 111-120 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 47, 8, 4, -25},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 8, 4, 0},
{0, 2, -2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0, 10, -22, -12, -5},
{0, 0, 0, 1, 0, 0, 7, -13, 0, 0, 0, 0, 0, -3, 0, 0, 2},
{-2, 0, 2, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -24, 12, 0, 0},
{0, 0, 0, 0, 0, 0, 9, -17, 0, 0, 0, 0, 0, 5, -6, 0, 0},
{0, 0, 0, 0, 0, 0, -9, 17, 0, 0, 0, 0, 2, 3, 0, 0, -2},
{1, 0, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 4, 3, 1, -2},
{1, 0, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 29, 15, 0},
{0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, -5, -4, -2, 2},
/* 121-130 */
{0, -1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, -3, -1, -5},
{0, -2, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0},
{0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0},
{-2, 0, 2, 1, 0, 0, 2, 0, -3, 1, 0, 0, 0, 3, 0, 0, -2},
{-2, 0, 2, 1, 0, 3, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3},
{0, 0, 0, 1, 0, 8, -13, 0, 0, 0, 0, 0, 0, 46, 66, 35, -25},
{0, -1, 1, 0, 0, 8, -12, 0, 0, 0, 0, 0, 0, -14, 7, 0, 0},
{0, 2, -2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0},
{-1, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0},
{-1, 0, 0, 1, 0, 18, -16, 0, 0, 0, 0, 0, 0, -68, -34, -18, 36},
/* 131-140 */
{0, 1, -1, 1, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 14, 7, 0},
{0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0, 10, -6, -3, -5},
{-2, 1, 1, 1, 0, 0, -3, 7, 0, 0, 0, 0, 0, -5, -4, -2, 3},
{0, 1, -1, 2, 0, 0, -1, 0, -2, 5, 0, 0, 0, -3, 5, 2, 1},
{0, 0, 0, 1, 0, 0, 0, 0, -2, 5, 0, 0, 0, 76, 17, 9, -41},
{0, 0, 0, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0, 84, 298, 159, -45},
{1, 0, 0, 1, 0, -10, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 2, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2},
{-1, 0, 0, 1, 0, 10, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1},
{0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, -82, 292, 156, 44},
/* 141-150 */
{0, 0, 0, 1, 0, 0, 0, 0, 2, -5, 0, 0, 0, -73, 17, 9, 39},
{0, -1, 1, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0, -9, -16, 0, 0},
{2, -1, -1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0, 3, 0, -1, -2},
{-2, 0, 2, 0, 0, 0, 2, 0, 0, -5, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0, -9, -5, -3, 5},
{-2, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -439, 0, 0, 0},
{1, 0, 0, 1, 0, -18, 16, 0, 0, 0, 0, 0, 0, 57, -28, -15, -30},
{-2, 1, 1, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -6, -3, 0},
{0, 1, -1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2},
{0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0, -40, 57, 30, 21},
/* 151-160 */
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 23, 7, 3, -13},
{0, 1, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 273, 80, 43, -146},
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -449, 430, 0, 0},
{0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -8, -47, -25, 4},
{0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 6, 47, 25, -3},
{-1, 0, 1, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 23, 13, 0},
{-1, 0, 1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -3, 0, 0, 2},
{0, 1, -1, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0, 3, -4, -2, -2},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -48, -110, -59, 26},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 51, 114, 61, -27},
/* 161-170 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -133, 0, 0, 57},
{0, 1, -1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0},
{0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, -21, -6, -3, 11},
{0, 1, -1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0},
{0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0, -11, -21, -11, 6},
{0, 2, -2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, -18, -436, -233, 9},
{0, -1, 1, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 35, -7, 0, 0},
{0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0},
{-2, 0, 2, 1, 0, 6, -8, 0, 0, 0, 0, 0, 0, 11, -3, -1, -6},
{0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0, -5, -3, -1, 3},
/* 171-180 */
{-2, 0, 2, 1, 0, 0, 2, 0, -3, 0, 0, 0, 0, -53, -9, -5, 28},
{-2, 0, 2, 1, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 3, 2, 1},
{1, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -4, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -50, 194, 103, 27},
{0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, -13, 52, 28, 7},
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -91, 248, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 6, 49, 26, -3},
{0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -6, -47, -25, 3},
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 3, 0},
/* 181-190 */
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 52, 23, 10, -23},
{0, 1, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0, -3, 0, 0, 1},
{0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 5, 3, 0},
{0, -1, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0},
{0, 0, 0, 0, 0, 0, -7, 13, 0, 0, 0, 0, 2, -4, 8, 3, 2},
{0, 0, 0, 0, 0, 0, 7, -13, 0, 0, 0, 0, 0, 10, 0, 0, 0},
{2, 0, -2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0, 3, 0, 0, -2},
{0, 2, -2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0, 0, 8, 4, 0},
{0, 2, -2, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 1},
{-2, 0, 2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0},
/* 191-200 */
{0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -4, 0, 0, 0},
{0, 1, -1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0, -8, 4, 2, 4},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 8, -4, -2, -4},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 15, 7, 0},
{-2, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0},
{0, 0, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, 0, -7, -3, 0},
{0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -7, -3, 0},
{2, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 54, 0, 0, -29},
{0, 1, -1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 10, 4, 0},
{0, 1, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 3},
/* 201-210 */
{0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -37, 35, 19, 20},
{0, -1, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0},
{0, -1, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -4, 9, 0, 0},
{0, 2, -2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 0, 0, -4},
{0, 1, -1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0, -9, -14, -8, 5},
{0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1, -3, -9, -5, 3},
{0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0, -145, 47, 0, 0},
{0, 1, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, -10, 40, 21, 5},
{0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 1, 11, -49, -26, -7},
{0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, -2150, 0, 0, 932},
/* 211-220 */
{0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -12, 0, 0, 5},
{0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, 85, 0, 0, -37},
{0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1, 4, 0, 0, -2},
{0, 1, -1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0, 3, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -86, 153, 0, 0},
{0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -6, 9, 5, 3},
{0, 1, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 9, -13, -7, -5},
{0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -8, 12, 6, 4},
{0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -51, 0, 0, 22},
{0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, -11, -268, -116, 5},
/* 221-230 */
{0, 2, -2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 12, 5, 0},
{0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, 0, 7, 3, 0},
{0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 31, 6, 3, -17},
{0, 1, -1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0, 140, 27, 14, -75},
{0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 57, 11, 6, -30},
{0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, -14, -39, 0, 0},
{0, 1, -1, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -6, -2, 0},
{0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 4, 15, 8, -2},
{0, -1, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0},
{0, 2, -2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, 0, 1},
/* 231-240 */
{0, 0, 0, 0, 0, 0, -6, 11, 0, 0, 0, 0, 2, 0, 11, 5, 0},
{0, 0, 0, 0, 0, 0, 6, -11, 0, 0, 0, 0, 0, 9, 6, 0, 0},
{0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 2, -4, 10, 4, 2},
{0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 5, 3, 0, 0},
{2, 0, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 16, 0, 0, -9},
{-2, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0},
{0, 2, -2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0, 0, 3, 2, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 2, 7, 0, 0, -3},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -25, 22, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 42, 223, 119, -22},
/* 241-250 */
{0, 1, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -27, -143, -77, 14},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 9, 49, 26, -5},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -1166, 0, 0, 505},
{0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, -6, 0, 0, 3},
{0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -8, 0, 1, 4},
{0, -1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0},
{0, 2, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 117, 0, 0, -63},
{0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 8, 4, 2},
{0, 2, -2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 3, 0, 0, -2},
/* 251-260 */
{0, 1, -1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 31, 0, 0},
{0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -5, 0, 1, 3},
{0, 1, -1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0, 4, 0, 0, -2},
{0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -4, 0, 0, 2},
{0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 2, -24, -13, -6, 10},
{0, -1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0},
{0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -32, -17, 0},
{0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 2, 8, 12, 5, -3},
{0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 1, 3, 0, 0, -1},
/* 261-270 */
{0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, 7, 13, 0, 0},
{0, -1, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, -3, 16, 0, 0},
{0, 2, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 50, 0, 0, -27},
{-2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, -3, 0},
{0, -2, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0},
{0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 1, 0, 5, 3, 1},
{0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 2, 24, 5, 2, -11},
{0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 2, 5, -11, -5, -2},
{0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 30, -3, -2, -16},
{0, 1, -1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 18, 0, 0, -9},
/* 271-280 */
{0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 8, 614, 0, 0},
{0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1, 3, -3, -1, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 17, 9, -3},
{0, 1, -1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, -9, -5, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 6, 3, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, -127, 21, 9, 55},
{0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 3, 5, 0, 0},
{0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, -6, -10, -4, 3},
{0, -2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 2, 16, 9, 4, -7},
/* 281-290 */
{0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 1, 3, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0},
{0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 19, 10, 0},
{0, 2, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 7, 0, 0, -4},
{0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, 0, -5, -2, 0},
{0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, -9, 3, 1, 4},
{0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, 17, 0, 0, -7},
{0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, 0, -3, -2, -1},
{0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -20, 34, 0, 0},
/* 291-300 */
{0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -10, 0, 1, 5},
{0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2},
{0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 22, -87, 0, 0},
{0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2},
{0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, -3, -6, -2, 1},
{0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, -16, -3, -1, 7},
{0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0},
{0, -2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -68, 39, 0, 0},
{0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, 27, 0, 0, -14},
/* 301-310 */
{0, -1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -25, 0, 0, 0},
{0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, -12, -3, -2, 6},
{0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, 3, 66, 29, -1},
{0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, 490, 0, 0, -213},
{0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -22, 93, 49, 12},
{0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, -7, 28, 15, 4},
{0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -3, 13, 7, 2},
{0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, -46, 14, 0, 0},
/* 311-320 */
{-2, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0},
{0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0},
{0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -28, 0, 0, 15},
{0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0},
{0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, -11, 0, 0, 5},
{0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, 0, 3, 1, 0},
{0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 25, 106, 57, -13},
/* 321-330 */
{0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 21, 11, -3},
{0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1485, 0, 0, 0},
{0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -7, -32, -17, 4},
{0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0},
{0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, -6, -3, -2, 3},
{0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 30, -6, -2, -13},
{0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, -4, 4, 0, 0},
{0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -19, 0, 0, 10},
{0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, 0, 4, 2, -1},
{0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0},
/* 331-340 */
{0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, 4, 0, 0, -2},
{0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, 0, -3, -1, 0},
{-2, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, 5, 3, 1, -2},
{0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, 11, 0, 0},
{0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 118, 0, 0, -52},
{0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, -5, -3, 0},
{0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, -28, 36, 0, 0},
{0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0},
{0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, 14, -59, -31, -8},
/* 341-350 */
{0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 9, 5, 1},
{0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, -458, 0, 0, 198},
{0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, 0, -45, -20, 0},
{0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, 9, 0, 0, -5},
{0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0},
{0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -4, -2, -1},
{0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 11, 0, 0, -6},
{0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, 6, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -16, 23, 0, 0},
{0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0},
/* 351-360 */
{0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, -166, 269, 0, 0},
{0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 15, 0, 0, -8},
{0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, 10, 0, 0, -4},
{0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -78, 45, 0, 0},
{0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, 0, -5, -2, 0},
{0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, -4},
{0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -5, 328, 0, 0},
{0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2},
{0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2},
/* 361-370 */
{0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, -2, 0},
{0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1223, -26, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 7, 3, 0},
{0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 3, 0, 0, 0},
{0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -6, 20, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -368, 0, 0, 0},
/* 371-380 */
{0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -75, 0, 0, 0},
{0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 11, 0, 0, -6},
{0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 3, 0, 0, -2},
{0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0, -13, -30, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, 21, 3, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, -27, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, -19, -11, 0, 0},
/* 381-390 */
{0, 0, 0, 0, 0, 0, -3, 8, -3, 0, 0, 0, 2, -4, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2, 0, 5, 2, 0},
{0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, -6, 0, 0, 2},
{0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, -1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, -14, 0, 0, 6},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -74, 0, 0, 32},
{0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -3, -1, 0},
{0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2},
/* 391-400 */
{0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 8, 11, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -262, 0, 0, 114},
{0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0},
{0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, -7, 0, 0, 4},
{0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, 0, -27, -12, 0},
{0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, -19, -8, -4, 8},
{0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, 202, 0, 0, -87},
{0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, -8, 35, 19, 5},
{0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0},
/* 401-410 */
{0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 16, -5, 0, 0},
{0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 5, 0, 0, -3},
{0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0},
{0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -35, -48, -21, 15},
{0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, -3, -5, -2, 1},
{0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3},
{0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0},
{0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 12, 55, 29, -6},
/* 411-420 */
{0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0},
{0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -598, 0, 0, 0},
{0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -3, -13, -7, 1},
{0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, -5, -7, -3, 2},
{0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 5, -7, 0, 0},
{0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 16, -6, 0, 0},
{0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0},
{0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, 8, -31, -16, -4},
/* 421-430 */
{0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 113, 0, 0, -49},
{0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, 0, -24, -10, 0},
{0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, 4, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 27, 0, 0, 0},
{0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, 0, -4, -2, 0},
{0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -13, 0, 0, 6},
/* 431-440 */
{0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, -18, -10, -4, 8},
{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, -28, 0, 0},
{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -5, 6, 3, 2},
{0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, -5, -9, -4, 2},
{0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 17, 0, 0, -7},
{0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 11, 4, 0, 0},
{0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, 0, -6, -2, 0},
{0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 83, 15, 0, 0},
/* 441-450 */
{0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2},
{0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0, -114, -49, 0},
{0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, 117, 0, 0, -51},
{0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, -5, 19, 10, 2},
{0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 2},
{0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, 0, -3, -1, 0},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, 0, -6, -2, 0},
{0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 393, 3, 0, 0},
/* 451-460 */
{0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1, -4, 21, 11, 2},
{0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, -6, 0, -1, 3},
{0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, -3, 8, 4, 1},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 18, -29, -13, -8},
{0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, 8, 34, 18, -4},
{0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0},
{0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, 3, 12, 6, -1},
{0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, 54, -15, -7, -24},
{0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0},
/* 461-470 */
{0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 35, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, -154, -30, -13, 67},
{0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 15, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1, 0, 4, 2, 0},
{0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 9, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, 80, -71, -31, -35},
{0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2, 0, -20, -9, 0},
{0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, 11, 5, 2, -5},
{0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, 61, -96, -42, -27},
/* 471-480 */
{0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, 14, 9, 4, -6},
{0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2, -11, -6, -3, 5},
{0, 0, 0, 0, 0, 0, -2, 8, -1, -5, 0, 0, 2, 0, -3, -1, 0},
{0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, 123, -415, -180, -53},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 7, -32, -17, -4},
{0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -9, -5, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 2, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -89, 0, 0, 38},
/* 481-490 */
{0, 0, 0, 0, 0, 0, -6, 16, -4, -5, 0, 0, 2, 0, -86, -19, -6},
{0, 0, 0, 0, 0, 0, -2, 8, -3, 0, 0, 0, 2, 0, 0, -19, 6},
{0, 0, 0, 0, 0, 0, -2, 8, -3, 0, 0, 0, 2, -123, -416, -180, 53},
{0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, 0, -3, -1, 0},
{0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2, 12, -6, -3, -5},
{0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, -13, 9, 4, 6},
{0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, 0, -15, -7, 0},
{0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1},
{0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, -62, -97, -42, 27},
{0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, -11, 5, 2, 5},
/* 491-500 */
{0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, -19, -8, 0},
{0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 4, 2, 0},
{0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0},
{0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0, 0, 4, 2, 0},
{0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, -85, -70, -31, 37},
{0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 163, -12, -5, -72},
{0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, -63, -16, -7, 28},
{0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -21, -32, -14, 9},
{0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, 0, -3, -1, 0},
/* 501-510 */
{0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2},
{0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0},
{0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, 3, 10, 4, -1},
{0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, -7, -3, 0},
{0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, 0, -4, -2, 0},
{0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 6, 19, 0, 0},
{0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 5, -173, -75, -2},
{0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, 0, -7, -3, 0},
{0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, 7, -12, -5, -3},
/* 511-520 */
{0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, -3, 0, 0, 2},
{0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, 3, -4, -2, -1},
{0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, 74, 0, 0, -32},
{0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, -3, 12, 6, 2},
{0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, 26, -14, -6, -11},
{0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 19, 0, 0, -8},
{0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, 6, 24, 13, -3},
{0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0},
{0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, 0, -10, -5, 0},
{0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 11, -3, -1, -5},
/* 521-530 */
{0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, -1},
{0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0},
{0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 5, -23, -12, -3},
{0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -339, 0, 0, 147},
{0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, 0, -10, -5, 0},
{0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0, 5, 0, 0, 0},
{0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, 0, -4, -2, 0},
{0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 18, -3, 0, 0},
/* 531-540 */
{0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2, 9, -11, -5, -4},
{0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4},
{0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1},
{0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, 6, -9, -4, -2},
{0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, -4, -12, 0, 0},
{0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2, 67, -91, -39, -29},
{0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, 30, -18, -8, -13},
{0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, 0, -114, -50, 0},
/* 541-550 */
{0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2, 0, 0, 0, 23},
{0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2, 517, 16, 7, -224},
{0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2, 0, -7, -3, 0},
{0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 143, -3, -1, -62},
{0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2, 29, 0, 0, -13},
{0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -4, 0, 0, 2},
{0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, -6, 0, 0, 3},
{0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2, 5, 12, 5, -2},
{0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, -25, 0, 0, 11},
{0, 0, 0, 0, 0, 0, -5, 16, -4, -5, 0, 0, 2, -3, 0, 0, 1},
/* 551-560 */
{0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0},
{0, 0, 0, 0, 0, 0, -1, 8, -3, 0, 0, 0, 2, -22, 12, 5, 10},
{0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 50, 0, 0, -22},
{0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0},
{0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0},
{0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, -4, 4, 2, 2},
{0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, -5, -11, -5, 2},
{0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0},
{0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, 4, 17, 9, -2},
{0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0},
/* 561-570 */
{0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, 0, -4, -2, 0},
{0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4},
{0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, -15, -8, -2},
{0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 370, -8, 0, -160},
{0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 0, -3, 0},
{0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 3, 1, 0},
{0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, -6, 3, 1, 3},
{0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, -10, 0, 0, 4},
/* 571-580 */
{0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, 0, 9, 4, 0},
{0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 4, 17, 7, -2},
{0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, 34, 0, 0, -15},
{0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0},
{0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2, -37, -7, -3, 16},
{0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, 3, 13, 7, -2},
{0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0},
{0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0},
{0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2, -184, -3, -1, 80},
/* 581-590 */
{0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, -3, 0, 0, 1},
{0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, -10, -6, -1},
{0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 31, -6, 0, -13},
{0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2, -3, -32, -14, 1},
{0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2, -7, 0, 0, 3},
{0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, 0, -8, -4, 0},
{0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0},
{0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0},
{0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0},
/* 591-600 */
{0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 19, -23, -10, 2},
{0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -10},
{0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0},
{0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, 0, 9, 5, -1},
{0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0},
{0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, 0, -7, -4, 0},
{0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 8, -4, 0, -4},
{0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0},
{0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0},
{0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2, -3, 0, 0, 1},
/* 601-610 */
{0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2, -9, 0, 1, 4},
{0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2, 3, 12, 5, -1},
{0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 17, -3, -1, 0},
{0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0},
{0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0},
{0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, 0, -5, -3, 0},
{0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, 14, -3, 0, -1},
{0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0},
{0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5},
{0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0},
/* 611-620 */
{0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0},
{0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 9, 4, 3},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, 0, 0, -3},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0},
{0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 5, 0, 0, -2},
/* 621-630 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -1},
{1, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0},
{1, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0},
{1, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0},
{1, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0},
{-1, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0},
{-1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 6, 0, 0, 0},
{-1, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0},
{1, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0},
{-2, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 5, 0, 0, 0},
/* 631-640 */
{-1, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0},
{-1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0},
{-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0},
{-1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0},
{1, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0},
{-1, 0, 2, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 13, 0, 0, 0},
{-2, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 21, 11, 0, 0},
{1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0},
{-1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0},
{1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0},
/* 641-650 */
{-1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0},
{-1, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 20, 10, 0, 0},
{-1, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -34, 0, 0, 0},
{-1, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0},
{1, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 3, 0, 0, -2},
{1, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1},
{1, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -6, 0, 0, 3},
{1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0},
/* 651-660 */
{0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0},
{0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0},
{0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 6, 0, 0, -3},
{0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 3},
{0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0},
{0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0},
{1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 126, -63, -27, -55},
{-1, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, -5, 0, 1, 2},
/* 661-670 */
{0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 28, 15, 2},
{1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 1, -2},
{0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 9, 4, 1},
{0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, 0, 9, 4, -1},
{-1, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, -126, -63, -27, 55},
{2, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1},
{1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 21, -11, -6, -11},
{0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0},
{-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -21, -11, -6, 11},
{-2, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 1},
/* 671-680 */
{0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0},
{0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4},
{0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0, -6, 0, 0, 3},
{0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1},
{-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, -1},
{1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1},
{-1, 2, 2, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0, -5, 0, 0, 2},
{2, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0, 24, -12, -5, -11},
{1, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, 0, 3, 1, 0},
{1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 3, 1, 0},
/* 681-687 */
{1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0},
{0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -24, -12, -5, 10},
{2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, -1, -2},
{-1, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 13, 0, 0, -6},
{-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3},
{1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1},
{0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 3, 0, 0, -1},
}
/* Number of terms in the planetary nutation model */
NPL := len(xpl)
/* ------------------------------------------------------------------ */
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* ------------------- */
/* LUNI-SOLAR NUTATION */
/* ------------------- */
/* Fundamental (Delaunay) arguments */
/* Mean anomaly of the Moon (IERS 2003). */
el = Fal03(t)
/* Mean anomaly of the Sun (MHB2000). */
elp = fmod(1287104.79305+
t*(129596581.0481+
t*(-0.5532+
t*(0.000136+
t*(-0.00001149)))), TURNAS) * DAS2R
/* Mean longitude of the Moon minus that of the ascending node */
/* (IERS 2003. */
f = Faf03(t)
/* Mean elongation of the Moon from the Sun (MHB2000). */
d = fmod(1072260.70369+
t*(1602961601.2090+
t*(-6.3706+
t*(0.006593+
t*(-0.00003169)))), TURNAS) * DAS2R
/* Mean longitude of the ascending node of the Moon (IERS 2003). */
om = Faom03(t)
/* Initialize the nutation values. */
dp = 0.0
de = 0.0
/* Summation of luni-solar nutation series (in reverse order). */
for i = NLS - 1; i >= 0; i-- {
/* Argument and functions. */
arg = fmod(float64(xls[i].nl)*el+
float64(xls[i].nlp)*elp+
float64(xls[i].nf)*f+
float64(xls[i].nd)*d+
float64(xls[i].nom)*om, D2PI)
sarg = sin(arg)
carg = cos(arg)
/* Term. */
dp += (xls[i].sp+xls[i].spt*t)*sarg + xls[i].cp*carg
de += (xls[i].ce+xls[i].cet*t)*carg + xls[i].se*sarg
}
/* Convert from 0.1 microarcsec units to radians. */
dpsils = dp * U2R
depsls = de * U2R
/* ------------------ */
/* PLANETARY NUTATION */
/* ------------------ */
/* n.b. The MHB2000 code computes the luni-solar and planetary nutation */
/* in different functions, using slightly different Delaunay */
/* arguments in the two cases. This behaviour is faithfully */
/* reproduced here. Use of the IERS 2003 expressions for both */
/* cases leads to negligible changes, well below */
/* 0.1 microarcsecond. */
/* Mean anomaly of the Moon (MHB2000). */
al = fmod(2.35555598+8328.6914269554*t, D2PI)
/* Mean longitude of the Moon minus that of the ascending node */
/*(MHB2000). */
af = fmod(1.627905234+8433.466158131*t, D2PI)
/* Mean elongation of the Moon from the Sun (MHB2000). */
ad = fmod(5.198466741+7771.3771468121*t, D2PI)
/* Mean longitude of the ascending node of the Moon (MHB2000). */
aom = fmod(2.18243920-33.757045*t, D2PI)
/* General accumulated precession in longitude (IERS 2003). */
apa = Fapa03(t)
/* Planetary longitudes, Mercury through Uranus (IERS 2003). */
alme = Fame03(t)
alve = Fave03(t)
alea = Fae03(t)
alma = Fama03(t)
alju = Faju03(t)
alsa = Fasa03(t)
alur = Faur03(t)
/* Neptune longitude (MHB2000). */
alne = fmod(5.321159000+3.8127774000*t, D2PI)
/* Initialize the nutation values. */
dp = 0.0
de = 0.0
/* Summation of planetary nutation series (in reverse order). */
for i = NPL - 1; i >= 0; i-- {
/* Argument and functions. */
arg = fmod(float64(xpl[i].nl)*al+
float64(xpl[i].nf)*af+
float64(xpl[i].nd)*ad+
float64(xpl[i].nom)*aom+
float64(xpl[i].nme)*alme+
float64(xpl[i].nve)*alve+
float64(xpl[i].nea)*alea+
float64(xpl[i].nma)*alma+
float64(xpl[i].nju)*alju+
float64(xpl[i].nsa)*alsa+
float64(xpl[i].nur)*alur+
float64(xpl[i].nne)*alne+
float64(xpl[i].npa)*apa, D2PI)
sarg = sin(arg)
carg = cos(arg)
/* Term. */
dp += float64(xpl[i].sp)*sarg + float64(xpl[i].cp)*carg
de += float64(xpl[i].se)*sarg + float64(xpl[i].ce)*carg
}
/* Convert from 0.1 microarcsec units to radians. */
dpsipl = dp * U2R
depspl = de * U2R
/* ------- */
/* RESULTS */
/* ------- */
/* Add luni-solar and planetary components. */
*dpsi = dpsils + dpsipl
*deps = depsls + depspl
}
/*
Nut00b Nutation, IAU 2000B Nutation, IAU 2000B model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation, luni-solar + planetary (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components in longitude and obliquity are in radians
and with respect to the equinox and ecliptic of date. The
obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
value of 84381.448 arcsec. (The errors that result from using
this function with the IAU 2006 value of 84381.406 arcsec can be
neglected.)
The nutation model consists only of luni-solar terms, but
includes also a fixed offset which compensates for certain long-
period planetary terms (Note 7).
3) This function is an implementation of the IAU 2000B abridged
nutation model formally adopted by the IAU General Assembly in
2000. The function computes the MHB_2000_SHORT luni-solar
nutation series (Luzum 2001), but without the associated
corrections for the precession rate adjustments and the offset
between the GCRS and J2000.0 mean poles.
4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
77 terms, plus additional simplifications, yet still delivers
results of 1 mas accuracy at present epochs. This combination of
accuracy and size makes the IAU 2000B abridged nutation model
suitable for most practical applications.
The function delivers a pole accurate to 1 mas from 1900 to 2100
(usually better than 1 mas, very occasionally just outside
1 mas). The full IAU 2000A model, which is implemented in the
function iauNut00a (q.v.), delivers considerably greater accuracy
at current dates; however, to realize this improved accuracy,
corrections for the essentially unpredictable free-core-nutation
(FCN) must also be included.
5) The present function provides classical nutation. The
MHB_2000_SHORT algorithm, from which it is adapted, deals also
with (i) the offsets between the GCRS and mean poles and (ii) the
adjustments in longitude and obliquity due to the changed
precession rates. These additional functions, namely frame bias
and precession adjustments, are supported by the SOFA functions
Bi00 and iauPr00.
6) The MHB_2000_SHORT algorithm also provides "total" nutations,
comprising the arithmetic sum of the frame bias, precession
adjustments, and nutation (luni-solar + planetary). These total
nutations can be used in combination with an existing IAU 1976
precession implementation, such as iauPmat76, to deliver GCRS-
to-true predictions of mas accuracy at current epochs. However,
for symmetry with the iauNut00a function (q.v. for the reasons),
the SOFA functions do not generate the "total nutations"
directly. Should they be required, they could of course easily
be generated by calling iauBi00, iauPr00 and the present function
and adding the results.
7) The IAU 2000B model includes "planetary bias" terms that are
fixed in size but compensate for long-period nutations. The
amplitudes quoted in McCarthy & Luzum (2003), namely
Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
the "total nutations" method described in Note 6. The Luzum
(2001) values used in this SOFA implementation, namely -0.135 mas
and +0.388 mas, are optimized for the "rigorous" method, where
frame bias, precession and nutation are applied separately and in
that order. During the interval 1995-2050, the SOFA
implementation delivers a maximum error of 1.001 mas (not
including FCN).
References:
Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
for the precession quantities based upon the IAU /1976/ system of
astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
Luzum, B., private communication, 2001 (Fortran code
MHB_2000_SHORT)
McCarthy, D.D. & Luzum, B.J., "An abridged model of the
precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
85, 37-49 (2003)
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
*/
func Nut00b(date1, date2 float64, dpsi, deps *float64) {
var t, el, elp, f, d, om, arg, dp, de, sarg, carg,
dpsils, depsls, dpsipl, depspl float64
var i int
/* Units of 0.1 microarcsecond to radians */
const U2R = DAS2R / 1e7
/* ---------------------------------------- */
/* Fixed offsets in lieu of planetary terms */
/* ---------------------------------------- */
const DPPLAN = -0.135 * DMAS2R
const DEPLAN = 0.388 * DMAS2R
/* --------------------------------------------------- */
/* Luni-solar nutation: argument and term coefficients */
/* --------------------------------------------------- */
/* The units for the sine and cosine coefficients are */
/* 0.1 microarcsec and the same per Julian century */
x := []struct {
nl, nlp, nf, nd, nom int /* coefficients of l,l',F,D,Om */
ps, pst, pc float64 /* longitude sin, t*sin, cos coefficients */
ec, ect, es float64 /* obliquity cos, t*cos, sin coefficients */
}{
/* 1-10 */
{0, 0, 0, 0, 1,
-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
{0, 0, 2, -2, 2,
-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
{0, 0, 2, 0, 2, -2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0},
{0, 0, 0, 0, 2, 2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0},
{0, 1, 0, 0, 0, 1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0},
{0, 1, 2, -2, 2, -516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0},
{1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
{0, 0, 2, 0, 1, -387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
{1, 0, 2, 0, 2, -301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
{0, -1, 2, -2, 2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
/* 11-20 */
{0, 0, 2, -2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
{-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
{-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
{1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
{-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
{-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
{1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
{-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
{0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
{0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
/* 21-30 */
{0, -2, 2, -2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
{-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
{2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
{1, 0, 2, -2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
{-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
{2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
{0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
{0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
{-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
{0, 2, 2, -2, 2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
/* 31-40 */
{0, 0, -2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
{1, 0, 0, -2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
{0, -1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
{-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
{0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
{1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
{-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
{0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
{0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
{0, -1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
/* 41-50 */
{0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
{1, 0, 2, -2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
{2, 0, 2, -2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
{-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
{2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
{0, -1, 2, -2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
{0, 0, 0, -2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
{-1, -1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
{2, 0, 0, -2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
{1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
/* 51-60 */
{0, 1, 2, -2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
{1, -1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
{-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
{3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
{0, -1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
{1, -1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
{0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
{-1, -1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
{-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
{0, -1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
/* 61-70 */
{-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
{1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
{2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
{-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
{1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
{1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
{-1, 0, 2, -2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
{1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
{-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0},
{0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
/* 71-77 */
{-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
{-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
{0, -2, 2, -2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
{1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
{-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
{-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
{1, 1, 2, -2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0},
}
/* Number of terms in the series */
NLS := len(x)
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* --------------------*/
/* LUNI-SOLAR NUTATION */
/* --------------------*/
/* Fundamental (Delaunay) arguments from Simon et al. (1994) */
/* Mean anomaly of the Moon. */
el = fmod(485868.249036+(1717915923.2178)*t, TURNAS) * DAS2R
/* Mean anomaly of the Sun. */
elp = fmod(1287104.79305+(129596581.0481)*t, TURNAS) * DAS2R
/* Mean argument of the latitude of the Moon. */
f = fmod(335779.526232+(1739527262.8478)*t, TURNAS) * DAS2R
/* Mean elongation of the Moon from the Sun. */
d = fmod(1072260.70369+(1602961601.2090)*t, TURNAS) * DAS2R
/* Mean longitude of the ascending node of the Moon. */
om = fmod(450160.398036+(-6962890.5431)*t, TURNAS) * DAS2R
/* Initialize the nutation values. */
dp = 0.0
de = 0.0
/* Summation of luni-solar nutation series (smallest terms first). */
for i = NLS - 1; i >= 0; i-- {
/* Argument and functions. */
arg = fmod(float64(x[i].nl)*el+
float64(x[i].nlp)*elp+
float64(x[i].nf)*f+
float64(x[i].nd)*d+
float64(x[i].nom)*om, D2PI)
sarg = sin(arg)
carg = cos(arg)
/* Term. */
dp += (x[i].ps+x[i].pst*t)*sarg + x[i].pc*carg
de += (x[i].ec+x[i].ect*t)*carg + x[i].es*sarg
}
/* Convert from 0.1 microarcsec units to radians. */
dpsils = dp * U2R
depsls = de * U2R
/* ------------------------------*/
/* IN LIEU OF PLANETARY NUTATION */
/* ------------------------------*/
/* Fixed offset to correct for missing terms in truncated series. */
dpsipl = DPPLAN
depspl = DEPLAN
/* --------*/
/* RESULTS */
/* --------*/
/* Add luni-solar and planetary components. */
*dpsi = dpsils + dpsipl
*deps = depsls + depspl
}
/*
Nut06a Nutation, IAU 2006/2000A
IAU 2000A nutation with adjustments to match the IAU 2006
precession.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation, luni-solar + planetary (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components in longitude and obliquity are in radians
and with respect to the mean equinox and ecliptic of date,
2006 precession model (Hilton et al. 2006, Capitaine et al.
2005).
3) The function first computes the IAU 2000A nutation, then applies
adjustments for (i) the consequences of the change in obliquity
from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the
secular variation in the Earth's dynamical form factor J2.
4) The present function provides classical nutation, complementing
the IAU 2000 frame bias and IAU 2006 precession. It delivers a
pole which is at current epochs accurate to a few tens of
microarcseconds, apart from the free core nutation.
Called:
Nut00a nutation, IAU 2000A
References:
Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
Astron.Astrophys. 387, 700
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
Astron.Astrophys. 58, 1-16
Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
107, B4. The MHB_2000 code itself was obtained on 9th September
2002 from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
Astron.Astrophys.Supp.Ser. 135, 111
Wallace, P.T., "Software for Implementing the IAU 2000
Resolutions", in IERS Workshop 5.1 (2002)
*/
func Nut06a(date1, date2 float64, dpsi, deps *float64) {
var t, fj2, dp, de float64
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Factor correcting for secular variation of J2. */
fj2 = -2.7774e-6 * t
/* Obtain IAU 2000A nutation. */
Nut00a(date1, date2, &dp, &de)
/* Apply P03 adjustments (Wallace & Capitaine, 2006, Eqs.5). */
*dpsi = dp + dp*(0.4697e-6+fj2)
*deps = de + de*fj2
}
/*
Nut80 Nutation, IAU 1980 Nutation, IAU 1980 model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi float64 nutation in longitude (radians)
deps float64 nutation in obliquity (radians)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components are with respect to the ecliptic of
date.
Called:
Anpm normalize angle into range +/- pi
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.222 (p111).
*/
func Nut80(date1, date2 float64, dpsi, deps *float64) {
var t, el, elp, f, d, om, dp, de, arg, s, c float64
var j int
/* Units of 0.1 milliarcsecond to radians */
const U2R = DAS2R / 1e4
/* ------------------------------------------------ */
/* Table of multiples of arguments and coefficients */
/* ------------------------------------------------ */
/* The units for the sine and cosine coefficients are 0.1 mas and */
/* the same per Julian century */
x := []struct {
nl, nlp, nf, nd, nom int /* coefficients of l,l',F,D,Om */
sp, spt float64 /* longitude sine, 1 and t coefficients */
ce, cet float64 /* obliquity cosine, 1 and t coefficients */
}{
/* 1-10 */
{0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9},
{0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5},
{-2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0},
{2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0},
{-2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0},
{1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0},
{0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0},
{2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0},
{0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1},
{0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1},
/* 11-20 */
{0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6},
{0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3},
{0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0},
{2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0},
{0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0},
{0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0},
{0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0},
{0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0},
{0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0},
{-2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0},
/* 21-30 */
{0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0},
{2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0},
{0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0},
{1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0},
{2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0},
{0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0},
{0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0},
{0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0},
{-1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0},
{0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0},
/* 31-40 */
{0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5},
{1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0},
{0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0},
{1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1},
{1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0},
{-1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0},
{0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0},
{1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0},
{-1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0},
{-1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0},
/* 41-50 */
{1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0},
{0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0},
{2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0},
{1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0},
{2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0},
{0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0},
{-1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0},
{-1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0},
{1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0},
{-1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0},
/* 51-60 */
{1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0},
{0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0},
{0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0},
{1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0},
{1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0},
{2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0},
{0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0},
{0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0},
{1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0},
{0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0},
/* 61-70 */
{1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0},
{2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0},
{0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0},
{1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0},
{0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0},
{1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0},
{1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0},
{1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0},
{-1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0},
{-2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0},
/* 71-80 */
{3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0},
{0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0},
{1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0},
{-1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0},
{2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0},
{1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0},
{3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0},
{0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0},
{-1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0},
{1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0},
/* 81-90 */
{-2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0},
{-1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0},
{2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0},
{1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0},
{1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0},
{-2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0},
{-1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0},
{1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0},
{2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0},
{2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0},
/* 91-100 */
{1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0},
{0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0},
{3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0},
{1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0},
{0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0},
{-1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0},
{0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0},
{0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0},
{0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0},
{1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0},
/* 101-106 */
{0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0},
{1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0},
{1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0},
{2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0},
{0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0},
{0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0},
}
/* Number of terms in the series */
NT := len(x)
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* --------------------- */
/* Fundamental arguments */
/* --------------------- */
/* Mean longitude of Moon minus mean longitude of Moon's perigee. */
el = Anpm((485866.733+(715922.633+(31.310+0.064*t)*t)*t)*DAS2R + fmod(1325.0*t, 1.0)*D2PI)
/* Mean longitude of Sun minus mean longitude of Sun's perigee. */
elp = Anpm((1287099.804+(1292581.224+(-0.577-0.012*t)*t)*t)*DAS2R + fmod(99.0*t, 1.0)*D2PI)
/* Mean longitude of Moon minus mean longitude of Moon's node. */
f = Anpm((335778.877+(295263.137+(-13.257+0.011*t)*t)*t)*DAS2R + fmod(1342.0*t, 1.0)*D2PI)
/* Mean elongation of Moon from Sun. */
d = Anpm((1072261.307+(1105601.328+(-6.891+0.019*t)*t)*t)*DAS2R + fmod(1236.0*t, 1.0)*D2PI)
/* Longitude of the mean ascending node of the lunar orbit on the */
/* ecliptic, measured from the mean equinox of date. */
om = Anpm((450160.280+(-482890.539+(7.455+0.008*t)*t)*t)*DAS2R + fmod(-5.0*t, 1.0)*D2PI)
/* --------------- */
/* Nutation series */
/* --------------- */
/* Initialize nutation components. */
dp = 0.0
de = 0.0
/* Sum the nutation terms, ending with the biggest. */
for j = NT - 1; j >= 0; j-- {
/* Form argument for current term. */
arg = float64(x[j].nl)*el +
float64(x[j].nlp)*elp +
float64(x[j].nf)*f +
float64(x[j].nd)*d +
float64(x[j].nom)*om
/* Accumulate current nutation term. */
s = x[j].sp + x[j].spt*t
c = x[j].ce + x[j].cet*t
if s != 0.0 {
dp += s * sin(arg)
}
if c != 0.0 {
de += c * cos(arg)
}
}
/* Convert results from 0.1 mas units to radians. */
*dpsi = dp * U2R
*deps = de * U2R
}
/*
Nutm80 Nutation matrix, IAU 1980
Form the matrix of nutation for a given date, IAU 1980 model.
Given:
date1,date2 float64 TDB date (Note 1)
Returned:
rmatn [3][3]float64 nutation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(true) = rmatn * V(mean),
where the p-vector V(true) is with respect to the true
equatorial triad of date and the p-vector V(mean) is with
respect to the mean equatorial triad of date.
Called:
Nut80 nutation, IAU 1980
Obl80 mean obliquity, IAU 1980
Numat form nutation matrix
*/
func Nutm80(date1, date2 float64, rmatn *[3][3]float64) {
var dpsi, deps, epsa float64
/* Nutation components and mean obliquity. */
Nut80(date1, date2, &dpsi, &deps)
epsa = Obl80(date1, date2)
/* Build the rotation matrix. */
Numat(epsa, dpsi, deps, rmatn)
}
/*
Obl06 Mean obliquity, IAU 2006
Mean obliquity of the ecliptic, IAU 2006 precession model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 obliquity of the ecliptic (radians, Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result is the angle between the ecliptic and mean equator of
date date1+date2.
Reference:
Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
*/
func Obl06(date1, date2 float64) float64 {
var t, eps0 float64
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Mean obliquity. */
eps0 = (84381.406 + (-46.836769+(-0.0001831+(0.00200340+(-0.000000576+(-0.0000000434)*t)*t)*t)*t)*t) * DAS2R
return eps0
}
/*
Obl80 Mean obliquity, IAU 1980 Mean obliquity of the ecliptic, IAU 1980 model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 obliquity of the ecliptic (radians, Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The result is the angle between the ecliptic and mean equator of
date date1+date2.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Expression 3.222-1 (p114).
*/
func Obl80(date1, date2 float64) float64 {
var t, eps0 float64
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Mean obliquity of date. */
eps0 = DAS2R * (84381.448 +
(-46.8150+
(-0.00059+
(0.001813)*t)*t)*t)
return eps0
}
/*
Pb06 Zeta, z, theta precession angles, IAU 2006, including bias
This function forms three Euler angles which implement general
precession from epoch J2000.0, using the IAU 2006 model. Frame
bias (the offset between ICRS and mean J2000.0) is included.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
bzeta float64 1st rotation: radians cw around z
bz float64 3rd rotation: radians cw around z
btheta float64 2nd rotation: radians ccw around y
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The traditional accumulated precession angles zeta_A, z_A,
theta_A cannot be obtained in the usual way, namely through
polynomial expressions, because of the frame bias. The latter
means that two of the angles undergo rapid changes near this
date. They are instead the results of decomposing the
precession-bias matrix obtained by using the Fukushima-Williams
method, which does not suffer from the problem. The
decomposition returns values which can be used in the
conventional formulation and which include frame bias.
3) The three angles are returned in the conventional order, which
is not the same as the order of the corresponding Euler
rotations. The precession-bias matrix is
R_3(-z) x R_2(+theta) x R_3(-zeta).
4) Should zeta_A, z_A, theta_A angles be required that do not
contain frame bias, they are available by calling the SOFA
function iauP06e.
Called:
Pmat06 PB matrix, IAU 2006
Rz rotate around Z-axis
*/
func Pb06(date1, date2 float64, bzeta, bz, btheta *float64) {
var r [3][3]float64
var y, x float64
/* Precession matrix via Fukushima-Williams angles. */
Pmat06(date1, date2, &r)
/* Solve for z, choosing the +/- pi alternative. */
y = r[1][2]
x = -r[0][2]
if x < 0.0 {
y = -y
x = -x
}
// *bz = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
if x != 0.0 || y != 0.0 {
*bz = -atan2(y, x)
} else {
*bz = 0.0
}
/* Derotate it out of the matrix. */
Rz(*bz, &r)
/* Solve for the remaining two angles. */
y = r[0][2]
x = r[2][2]
// *btheta = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
if x != 0.0 || y != 0.0 {
*btheta = -atan2(y, x)
} else {
*btheta = 0.0
}
y = -r[1][0]
x = r[1][1]
// *bzeta = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
if x != 0.0 || y != 0.0 {
*bzeta = -atan2(y, x)
} else {
*bzeta = 0.0
}
}
/*
Pfw06 Bias-precession Fukushima-Williams angles, IAU 2006
Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
gamb float64 F-W angle gamma_bar (radians)
phib float64 F-W angle phi_bar (radians)
psib float64 F-W angle psi_bar (radians)
epsa float64 F-W angle epsilon_A (radians)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) Naming the following points:
e = J2000.0 ecliptic pole,
p = GCRS pole,
E = mean ecliptic pole of date,
and P = mean pole of date,
the four Fukushima-Williams angles are as follows:
gamb = gamma_bar = epE
phib = phi_bar = pE
psib = psi_bar = pEP
epsa = epsilon_A = EP
3) The matrix representing the combined effects of frame bias and
precession is:
PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)
4) The matrix representing the combined effects of frame bias,
precession and nutation is simply:
NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)
where dP and dE are the nutation components with respect to the
ecliptic of date.
Reference:
Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
Called:
Obl06 mean obliquity, IAU 2006
*/
func Pfw06(date1, date2 float64, gamb, phib, psib, epsa *float64) {
var t float64
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* P03 bias+precession angles. */
*gamb = (-0.052928 + (10.556378+(0.4932044+(-0.00031238+(-0.000002788+(0.0000000260)*t)*t)*t)*t)*t) * DAS2R
*phib = (84381.412819 + (-46.811016+(0.0511268+(0.00053289+(-0.000000440+(-0.0000000176)*t)*t)*t)*t)*t) * DAS2R
*psib = (-0.041775 + (5038.481484+(1.5584175+(-0.00018522+(-0.000026452+(-0.0000000148)*t)*t)*t)*t)*t) * DAS2R
*epsa = Obl06(date1, date2)
}
/*
Pmat00 Precession matrix (including frame bias), IAU 2000
Precession matrix (including frame bias) from GCRS to a specified
date, IAU 2000 model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rbp [3][3]float64 bias-precession matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rbp * V(GCRS), where
the p-vector V(GCRS) is with respect to the Geocentric Celestial
Reference System (IAU, 2000) and the p-vector V(date) is with
respect to the mean equatorial triad of the given date.
Called:
Bp00 frame bias and precession matrices, IAU 2000
Reference:
: Trans. International Astronomical Union, Vol. XXIVB; Proc.
24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
(2000)
*/
func Pmat00(date1, date2 float64, rbp *[3][3]float64) {
var rb, rp [3][3]float64
/* Obtain the required matrix (discarding others). */
Bp00(date1, date2, &rb, &rp, rbp)
}
/*
Pmat06 Precession matrix (including frame bias), IAU 2006
Precession matrix (including frame bias) from GCRS to a specified
date, IAU 2006 model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rbp [3][3]float64 bias-precession matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rbp * V(GCRS), where
the p-vector V(GCRS) is with respect to the Geocentric Celestial
Reference System (IAU, 2000) and the p-vector V(date) is with
respect to the mean equatorial triad of the given date.
Called:
Pfw06 bias-precession F-W angles, IAU 2006
Fw2m F-W angles to r-matrix
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
: Trans. International Astronomical Union, Vol. XXIVB; Proc.
24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
(2000)
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Pmat06(date1, date2 float64, rbp *[3][3]float64) {
var gamb, phib, psib, epsa float64
/* Bias-precession Fukushima-Williams angles. */
Pfw06(date1, date2, &gamb, &phib, &psib, &epsa)
/* Form the matrix. */
Fw2m(gamb, phib, psib, epsa, rbp)
}
/*
Pmat76 Precession matrix, IAU 1976
Precession matrix from J2000.0 to a specified date, IAU 1976 model.
Given:
date1,date2 float64 ending date, TT (Note 1)
Returned:
rmatp [3][3]float64 precession matrix, J2000.0 -> date1+date2
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = RMATP * V(J2000),
where the p-vector V(J2000) is with respect to the mean
equatorial triad of epoch J2000.0 and the p-vector V(date)
is with respect to the mean equatorial triad of the given
date.
3) Though the matrix method itself is rigorous, the precession
angles are expressed through canonical polynomials which are
valid only for a limited time span. In addition, the IAU 1976
precession rate is known to be imperfect. The absolute accuracy
of the present formulation is better than 0.1 arcsec from
1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
and remains below 3 arcsec for the whole of the period
500BC to 3000AD. The errors exceed 10 arcsec outside the
range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
Called:
Prec76 accumulated precession angles, IAU 1976
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Ry rotate around Y-axis
Cr copy r-matrix
References:
Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
equations (6) & (7), p283.
Kaplan,G.H., 1981. USNO circular no. 163, pA2.
*/
func Pmat76(date1, date2 float64, rmatp *[3][3]float64) {
var zeta, z, theta float64
var wmat [3][3]float64
/* Precession Euler angles, J2000.0 to specified date. */
Prec76(DJ00, 0.0, date1, date2, &zeta, &z, &theta)
/* Form the rotation matrix. */
Ir(&wmat)
Rz(-zeta, &wmat)
Ry(theta, &wmat)
Rz(-z, &wmat)
Cr(wmat, rmatp)
}
/*
Pn00 B,P,N matrices, IAU 2000, given nutation
Precession-nutation, IAU 2000 model: a multi-purpose function,
supporting classical (equinox-based) use directly and CIO-based
use indirectly.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
dpsi,deps float64 nutation (Note 2)
Returned:
epsa float64 mean obliquity (Note 3)
rb [3][3]float64 frame bias matrix (Note 4)
rp [3][3]float64 precession matrix (Note 5)
rbp [3][3]float64 bias-precession matrix (Note 6)
rn [3][3]float64 nutation matrix (Note 7)
rbpn [3][3]float64 GCRS-to-true matrix (Note 8)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The caller is responsible for providing the nutation components;
they are in longitude and obliquity, in radians and are with
respect to the equinox and ecliptic of date. For high-accuracy
applications, free core nutation should be included as well as
any other relevant corrections to the position of the CIP.
3) The returned mean obliquity is consistent with the IAU 2000
precession-nutation models.
4) The matrix rb transforms vectors from GCRS to J2000.0 mean
equator and equinox by applying frame bias.
5) The matrix rp transforms vectors from J2000.0 mean equator and
equinox to mean equator and equinox of date by applying
precession.
6) The matrix rbp transforms vectors from GCRS to mean equator and
equinox of date by applying frame bias then precession. It is
the product rp x rb.
7) The matrix rn transforms vectors from mean equator and equinox of
date to true equator and equinox of date by applying the nutation
(luni-solar + planetary).
8) The matrix rbpn transforms vectors from GCRS to true equator and
equinox of date. It is the product rn x rbp, applying frame
bias, precession and nutation in that order.
9) It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the order given.
Called:
Pr00 IAU 2000 precession adjustments
Obl80 mean obliquity, IAU 1980
Bp00 frame bias and precession matrices, IAU 2000
Cr copy r-matrix
Numat form nutation matrix
Rxr product of two r-matrices
Reference:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
*/
func Pn00(date1, date2 float64, dpsi, deps float64, epsa *float64, rb, rp, rbp, rn, rbpn *[3][3]float64) {
var dpsipr, depspr float64
var rbpw, rnw [3][3]float64
/* IAU 2000 precession-rate adjustments. */
Pr00(date1, date2, &dpsipr, &depspr)
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
*epsa = Obl80(date1, date2) + depspr
/* Frame bias and precession matrices and their product. */
Bp00(date1, date2, rb, rp, &rbpw)
Cr(rbpw, rbp)
/* Nutation matrix. */
Numat(*epsa, dpsi, deps, &rnw)
Cr(rnw, rn)
/* Bias-precession-nutation matrix (classical). */
Rxr(rnw, rbpw, rbpn)
}
/*
Pn00a B,P,N matrices, IAU 2000A
Precession-nutation, IAU 2000A model: a multi-purpose function,
supporting classical (equinox-based) use directly and CIO-based
use indirectly.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation (Note 2)
epsa float64 mean obliquity (Note 3)
rb [3][3]float64 frame bias matrix (Note 4)
rp [3][3]float64 precession matrix (Note 5)
rbp [3][3]float64 bias-precession matrix (Note 6)
rn [3][3]float64 nutation matrix (Note 7)
rbpn [3][3]float64 GCRS-to-true matrix (Notes 8,9)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components (luni-solar + planetary, IAU 2000A) in
longitude and obliquity are in radians and with respect to the
equinox and ecliptic of date. Free core nutation is omitted;
for the utmost accuracy, use the iauPn00 function, where the
nutation components are caller-specified. For faster but
slightly less accurate results, use the iauPn00b function.
3) The mean obliquity is consistent with the IAU 2000 precession.
4) The matrix rb transforms vectors from GCRS to J2000.0 mean
equator and equinox by applying frame bias.
5) The matrix rp transforms vectors from J2000.0 mean equator and
equinox to mean equator and equinox of date by applying
precession.
6) The matrix rbp transforms vectors from GCRS to mean equator and
equinox of date by applying frame bias then precession. It is
the product rp x rb.
7) The matrix rn transforms vectors from mean equator and equinox
of date to true equator and equinox of date by applying the
nutation (luni-solar + planetary).
8) The matrix rbpn transforms vectors from GCRS to true equator and
equinox of date. It is the product rn x rbp, applying frame
bias, precession and nutation in that order.
9) The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate
Pole are elements (3,1-3) of the GCRS-to-true matrix,
i.e. rbpn[2][0-2].
10)It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the stated order.
Called:
Nut00a nutation, IAU 2000A
Pn00 bias/precession/nutation results, IAU 2000
Reference:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
*/
func Pn00a(date1, date2 float64, dpsi, deps, epsa *float64, rb, rp, rbp, rn, rbpn *[3][3]float64) {
/* Nutation. */
Nut00a(date1, date2, dpsi, deps)
/* Remaining results. */
Pn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn)
}
/*
Pn00b B,P,N matrices, IAU 2000B
Precession-nutation, IAU 2000B model: a multi-purpose function,
supporting classical (equinox-based) use directly and CIO-based
use indirectly.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation (Note 2)
epsa float64 mean obliquity (Note 3)
rb [3][3]float64 frame bias matrix (Note 4)
rp [3][3]float64 precession matrix (Note 5)
rbp [3][3]float64 bias-precession matrix (Note 6)
rn [3][3]float64 nutation matrix (Note 7)
rbpn [3][3]float64 GCRS-to-true matrix (Notes 8,9)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components (luni-solar + planetary, IAU 2000B) in
longitude and obliquity are in radians and with respect to the
equinox and ecliptic of date. For more accurate results, but
at the cost of increased computation, use the iauPn00a function.
For the utmost accuracy, use the iauPn00 function, where the
nutation components are caller-specified.
3) The mean obliquity is consistent with the IAU 2000 precession.
4) The matrix rb transforms vectors from GCRS to J2000.0 mean
equator and equinox by applying frame bias.
5) The matrix rp transforms vectors from J2000.0 mean equator and
equinox to mean equator and equinox of date by applying
precession.
6) The matrix rbp transforms vectors from GCRS to mean equator and
equinox of date by applying frame bias then precession. It is
the product rp x rb.
7) The matrix rn transforms vectors from mean equator and equinox
of date to true equator and equinox of date by applying the
nutation (luni-solar + planetary).
8) The matrix rbpn transforms vectors from GCRS to true equator and
equinox of date. It is the product rn x rbp, applying frame
bias, precession and nutation in that order.
9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
Pole are elements (3,1-3) of the GCRS-to-true matrix,
i.e. rbpn[2][0-2].
10)It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the stated order.
Called:
Nut00b nutation, IAU 2000B
Pn00 bias/precession/nutation results, IAU 2000
Reference:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003).
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
*/
func Pn00b(date1, date2 float64, dpsi, deps, epsa *float64, rb, rp, rbp, rn, rbpn *[3][3]float64) {
/* Nutation. */
Nut00b(date1, date2, dpsi, deps)
/* Remaining results. */
Pn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn)
}
/*
Pn06 Bias precession nutation results, IAU 2006
Precession-nutation, IAU 2006 model: a multi-purpose function,
supporting classical (equinox-based) use directly and CIO-based use
indirectly.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
dpsi,deps float64 nutation (Note 2)
Returned:
epsa float64 mean obliquity (Note 3)
rb [3][3]float64 frame bias matrix (Note 4)
rp [3][3]float64 precession matrix (Note 5)
rbp [3][3]float64 bias-precession matrix (Note 6)
rn [3][3]float64 nutation matrix (Note 7)
rbpn [3][3]float64 GCRS-to-true matrix (Notes 8,9)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The caller is responsible for providing the nutation components;
they are in longitude and obliquity, in radians and are with
respect to the equinox and ecliptic of date. For high-accuracy
applications, free core nutation should be included as well as
any other relevant corrections to the position of the CIP.
3) The returned mean obliquity is consistent with the IAU 2006
precession.
4) The matrix rb transforms vectors from GCRS to J2000.0 mean
equator and equinox by applying frame bias.
5) The matrix rp transforms vectors from J2000.0 mean equator and
equinox to mean equator and equinox of date by applying
precession.
6) The matrix rbp transforms vectors from GCRS to mean equator and
equinox of date by applying frame bias then precession. It is
the product rp x rb.
7) The matrix rn transforms vectors from mean equator and equinox
of date to true equator and equinox of date by applying the
nutation (luni-solar + planetary).
8) The matrix rbpn transforms vectors from GCRS to true equator and
equinox of date. It is the product rn x rbp, applying frame
bias, precession and nutation in that order.
9) The X,Y,Z coordinates of the Celestial Intermediate Pole are
elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].
10)It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the stated order.
Called:
Pfw06 bias-precession F-W angles, IAU 2006
Fw2m F-W angles to r-matrix
Cr copy r-matrix
Tr transpose r-matrix
Rxr product of two r-matrices
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Pn06(date1, date2 float64, dpsi, deps float64, epsa *float64, rb, rp, rbp, rn, rbpn *[3][3]float64) {
var gamb, phib, psib, eps float64
var r1, r2, rt [3][3]float64
/* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
Pfw06(DJM0, DJM00, &gamb, &phib, &psib, &eps)
/* B matrix. */
Fw2m(gamb, phib, psib, eps, &r1)
Cr(r1, rb)
/* Bias-precession Fukushima-Williams angles of date. */
Pfw06(date1, date2, &gamb, &phib, &psib, &eps)
/* Bias-precession matrix. */
Fw2m(gamb, phib, psib, eps, &r2)
Cr(r2, rbp)
/* Solve for precession matrix. */
Tr(r1, &rt)
Rxr(r2, rt, rp)
/* Equinox-based bias-precession-nutation matrix. */
Fw2m(gamb, phib, psib+dpsi, eps+deps, &r1)
Cr(r1, rbpn)
/* Solve for nutation matrix. */
Tr(r2, &rt)
Rxr(r1, rt, rn)
/* Obliquity, mean of date. */
*epsa = eps
}
/*
Pn06a Bias precession nutation results, IAU 2006/2000A
Precession-nutation, IAU 2006/2000A models: a multi-purpose function,
supporting classical (equinox-based) use directly and CIO-based use
indirectly.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsi,deps float64 nutation (Note 2)
epsa float64 mean obliquity (Note 3)
rb [3][3]float64 frame bias matrix (Note 4)
rp [3][3]float64 precession matrix (Note 5)
rbp [3][3]float64 bias-precession matrix (Note 6)
rn [3][3]float64 nutation matrix (Note 7)
rbpn [3][3]float64 GCRS-to-true matrix (Notes 8,9)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The nutation components (luni-solar + planetary, IAU 2000A) in
longitude and obliquity are in radians and with respect to the
equinox and ecliptic of date. Free core nutation is omitted;
for the utmost accuracy, use the iauPn06 function, where the
nutation components are caller-specified.
3) The mean obliquity is consistent with the IAU 2006 precession.
4) The matrix rb transforms vectors from GCRS to mean J2000.0 by
applying frame bias.
5) The matrix rp transforms vectors from mean J2000.0 to mean of
date by applying precession.
6) The matrix rbp transforms vectors from GCRS to mean of date by
applying frame bias then precession. It is the product rp x rb.
7) The matrix rn transforms vectors from mean of date to true of
date by applying the nutation (luni-solar + planetary).
8) The matrix rbpn transforms vectors from GCRS to true of date
(CIP/equinox). It is the product rn x rbp, applying frame bias,
precession and nutation in that order.
9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial
Intermediate Pole are elements (3,1-3) of the GCRS-to-true
matrix, i.e. rbpn[2][0-2].
10)It is permissible to re-use the same array in the returned
arguments. The arrays are filled in the stated order.
Called:
Nut06a nutation, IAU 2006/2000A
Pn06 bias/precession/nutation results, IAU 2006
Reference:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
*/
func Pn06a(date1, date2 float64, dpsi, deps, epsa *float64, rb, rp, rbp, rn, rbpn *[3][3]float64) {
/* Nutation. */
Nut06a(date1, date2, dpsi, deps)
/* Remaining results. */
Pn06(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn)
}
/*
Pnm00a Classical NPB matrix, IAU 2000A
Form the matrix of precession-nutation for a given date (including
frame bias), equinox based, IAU 2000A model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rbpn [3][3]float64 bias-precession-nutation matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where
the p-vector V(date) is with respect to the true equatorial triad
of date date1+date2 and the p-vector V(GCRS) is with respect to
the Geocentric Celestial Reference System (IAU, 2000).
3) A faster, but slightly less accurate, result (about 1 mas) can be
obtained by using instead the iauPnm00b function.
Called:
Pn00a bias/precession/nutation, IAU 2000A
Reference:
: Trans. International Astronomical Union, Vol. XXIVB; Proc.
24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
(2000)
*/
func Pnm00a(date1, date2 float64, rbpn *[3][3]float64) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn [3][3]float64
/* Obtain the required matrix (discarding other results). */
Pn00a(date1, date2, &dpsi, &deps, &epsa, &rb, &rp, &rbp, &rn, rbpn)
}
/*
Pnm00b Classical NPB matrix, IAU 2000B
Form the matrix of precession-nutation for a given date (including
frame bias), equinox-based, IAU 2000B model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rbpn [3][3]float64 bias-precession-nutation matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where
the p-vector V(date) is with respect to the true equatorial triad
of date date1+date2 and the p-vector V(GCRS) is with respect to
the Geocentric Celestial Reference System (IAU, 2000).
3) The present function is faster, but slightly less accurate (about
1 mas), than the iauPnm00a function.
Called:
Pn00b bias/precession/nutation, IAU 2000B
Reference:
: Trans. International Astronomical Union, Vol. XXIVB; Proc.
24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
(2000)
*/
func Pnm00b(date1, date2 float64, rbpn *[3][3]float64) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn [3][3]float64
/* Obtain the required matrix (discarding other results). */
Pn00b(date1, date2, &dpsi, &deps, &epsa, &rb, &rp, &rbp, &rn, rbpn)
}
/*
Pnm06a Classical NPB matrix, IAU 2006/2000A
Form the matrix of precession-nutation for a given date (including
frame bias), equinox based, IAU 2006 precession and IAU 2000A
nutation models.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rbpn [3][3]float64 bias-precession-nutation matrix (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways, among
others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where
the p-vector V(date) is with respect to the true equatorial triad
of date date1+date2 and the p-vector V(GCRS) is with respect to
the Geocentric Celestial Reference System (IAU, 2000).
Called:
Pfw06 bias-precession F-W angles, IAU 2006
Nut06a nutation, IAU 2006/2000A
Fw2m F-W angles to r-matrix
Reference:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855.
*/
func Pnm06a(date1, date2 float64, rbpn *[3][3]float64) {
var gamb, phib, psib, epsa, dp, de float64
/* Fukushima-Williams angles for frame bias and precession. */
Pfw06(date1, date2, &gamb, &phib, &psib, &epsa)
/* Nutation components. */
Nut06a(date1, date2, &dp, &de)
/* Equinox based nutation x precession x bias matrix. */
Fw2m(gamb, phib, psib+dp, epsa+de, rbpn)
}
/*
Pnm80 Precession/nutation matrix, IAU 1976/1980
Form the matrix of precession/nutation for a given date, IAU 1976
precession model, IAU 1980 nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
rmatpn [3][3]float64 combined precession/nutation matrix
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The matrix operates in the sense V(date) = rmatpn * V(J2000),
where the p-vector V(date) is with respect to the true equatorial
triad of date date1+date2 and the p-vector V(J2000) is with
respect to the mean equatorial triad of epoch J2000.0.
Called:
Pmat76 precession matrix, IAU 1976
Nutm80 nutation matrix, IAU 1980
Rxr product of two r-matrices
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992),
Section 3.3 (p145).
*/
func Pnm80(date1, date2 float64, rmatpn *[3][3]float64) {
var rmatp, rmatn [3][3]float64
/* Precession matrix, J2000.0 to date. */
Pmat76(date1, date2, &rmatp)
/* Nutation matrix. */
Nutm80(date1, date2, &rmatn)
/* Combine the matrices: PN = N x P. */
Rxr(rmatn, rmatp, rmatpn)
}
/*
P06e Precession angles, IAU 2006, equinox based
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (see Note 2):
eps0 float64 epsilon_0
psia float64 psi_A
oma float64 omega_A
bpa float64 P_A
bqa float64 Q_A
pia float64 pi_A
bpia float64 Pi_A
epsa float64 obliquity epsilon_A
chia float64 chi_A
za float64 z_A
zetaa float64 zeta_A
thetaa float64 theta_A
pa float64 p_A
gam float64 F-W angle gamma_J2000
phi float64 F-W angle phi_J2000
psi float64 F-W angle psi_J2000
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) This function returns the set of equinox based angles for the
Capitaine et al. "P03" precession theory, adopted by the IAU in
2006. The angles are set out in Table 1 of Hilton et al. (2006):
eps0 epsilon_0 obliquity at J2000.0
psia psi_A luni-solar precession
oma omega_A inclination of equator wrt J2000.0 ecliptic
bpa P_A ecliptic pole x, J2000.0 ecliptic triad
bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
pia pi_A angle between moving and J2000.0 ecliptics
bpia Pi_A longitude of ascending node of the ecliptic
epsa epsilon_A obliquity of the ecliptic
chia chi_A planetary precession
za z_A equatorial precession: -3rd 323 Euler angle
zetaa zeta_A equatorial precession: -1st 323 Euler angle
thetaa theta_A equatorial precession: 2nd 323 Euler angle
pa p_A general precession (n.b. see below)
gam gamma_J2000 J2000.0 RA difference of ecliptic poles
phi phi_J2000 J2000.0 codeclination of ecliptic pole
psi psi_J2000 longitude difference of equator poles, J2000.0
The returned values are all radians.
Note that the t^5 coefficient in the series for p_A from
Capitaine et al. (2003) is incorrectly signed in Hilton et al.
(2006).
3) Hilton et al. (2006) Table 1 also contains angles that depend on
models distinct from the P03 precession theory itself, namely the
2000A frame bias and nutation. The quoted polynomials are
used in other SOFA functions:
. iauXy06 contains the polynomial parts of the X and Y series.
. iauS06 contains the polynomial part of the s+XY/2 series.
. iauPfw06 implements the series for the Fukushima-Williams
angles that are with respect to the GCRS pole (i.e. the variants
that include frame bias).
4) The IAU resolution stipulated that the choice of parameterization
was left to the user, and so an IAU compliant precession
implementation can be constructed using various combinations of
the angles returned by the present function.
5) The parameterization used by SOFA is the version of the Fukushima-
Williams angles that refers directly to the GCRS pole. These
angles may be calculated by calling the function iauPfw06. SOFA
also supports the direct computation of the CIP GCRS X,Y by
series, available by calling iauXy06.
6) The agreement between the different parameterizations is at the
1 microarcsecond level in the present era.
7) When constructing a precession formulation that refers to the GCRS
pole rather than the dynamical pole, it may (depending on the
choice of angles) be necessary to introduce the frame bias
explicitly.
8) It is permissible to re-use the same variable in the returned
arguments. The quantities are stored in the stated order.
References:
Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
Astron.Astrophys., 412, 567
Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
Called:
Obl06 mean obliquity, IAU 2006
*/
func P06e(date1, date2 float64, eps0, psia, oma, bpa *float64, bqa, pia, bpia *float64, epsa, chia, za, zetaa *float64,
thetaa, pa *float64, gam, phi, psi *float64) {
var t float64
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Obliquity at J2000.0. */
*eps0 = 84381.406 * DAS2R
/* Luni-solar precession. */
*psia = (5038.481507 +
(-1.0790069+
(-0.00114045+
(0.000132851+
(-0.0000000951)*
t)*t)*t)*t) * t * DAS2R
/* Inclination of mean equator with respect to the J2000.0 ecliptic. */
*oma = *eps0 + (-0.025754+
(0.0512623+
(-0.00772503+
(-0.000000467+
(0.0000003337)*
t)*t)*t)*t)*t*DAS2R
/* Ecliptic pole x, J2000.0 ecliptic triad. */
*bpa = (4.199094 +
(0.1939873+
(-0.00022466+
(-0.000000912+
(0.0000000120)*
t)*t)*t)*t) * t * DAS2R
/* Ecliptic pole -y, J2000.0 ecliptic triad. */
*bqa = (-46.811015 +
(0.0510283+
(0.00052413+
(-0.000000646+
(-0.0000000172)*
t)*t)*t)*t) * t * DAS2R
/* Angle between moving and J2000.0 ecliptics. */
*pia = (46.998973 +
(-0.0334926+
(-0.00012559+
(0.000000113+
(-0.0000000022)*
t)*t)*t)*t) * t * DAS2R
/* Longitude of ascending node of the moving ecliptic. */
*bpia = (629546.7936 +
(-867.95758+
(0.157992+
(-0.0005371+
(-0.00004797+
(0.000000072)*
t)*t)*t)*t)*t) * DAS2R
/* Mean obliquity of the ecliptic. */
*epsa = Obl06(date1, date2)
/* Planetary precession. */
*chia = (10.556403 +
(-2.3814292+
(-0.00121197+
(0.000170663+
(-0.0000000560)*
t)*t)*t)*t) * t * DAS2R
/* Equatorial precession: minus the third of the 323 Euler angles. */
*za = (-2.650545 +
(2306.077181+
(1.0927348+
(0.01826837+
(-0.000028596+
(-0.0000002904)*
t)*t)*t)*t)*t) * DAS2R
/* Equatorial precession: minus the first of the 323 Euler angles. */
*zetaa = (2.650545 +
(2306.083227+
(0.2988499+
(0.01801828+
(-0.000005971+
(-0.0000003173)*
t)*t)*t)*t)*t) * DAS2R
/* Equatorial precession: second of the 323 Euler angles. */
*thetaa = (2004.191903 +
(-0.4294934+
(-0.04182264+
(-0.000007089+
(-0.0000001274)*
t)*t)*t)*t) * t * DAS2R
/* General precession. */
*pa = (5028.796195 +
(1.1054348+
(0.00007964+
(-0.000023857+
(-0.0000000383)*
t)*t)*t)*t) * t * DAS2R
/* Fukushima-Williams angles for precession. */
*gam = (10.556403 +
(0.4932044+
(-0.00031238+
(-0.000002788+
(0.0000000260)*
t)*t)*t)*t) * t * DAS2R
*phi = *eps0 + (-46.811015+
(0.0511269+
(0.00053289+
(-0.000000440+
(-0.0000000176)*
t)*t)*t)*t)*t*DAS2R
*psi = (5038.481507 +
(1.5584176+
(-0.00018522+
(-0.000026452+
(-0.0000000148)*
t)*t)*t)*t) * t * DAS2R
}
/*
Pom00 Polar-motion matrix, IAU 2000
Form the matrix of polar motion for a given date, IAU 2000.
Given:
xp,yp float64 coordinates of the pole (radians, Note 1)
sp float64 the TIO locator s' (radians, Note 2)
Returned:
rpom [3][3]float64 polar-motion matrix (Note 3)
Notes:
1) The arguments xp and yp are the coordinates (in radians) of the
Celestial Intermediate Pole with respect to the International
Terrestrial Reference System (see IERS Conventions 2003),
measured along the meridians 0 and 90 deg west respectively.
2) The argument sp is the TIO locator s', in radians, which
positions the Terrestrial Intermediate Origin on the equator. It
is obtained from polar motion observations by numerical
integration, and so is in essence unpredictable. However, it is
dominated by a secular drift of about 47 microarcseconds per
century, and so can be taken into account by using s' = -47*t,
where t is centuries since J2000.0. The function iauSp00
implements this approximation.
3) The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning
that it is the final rotation when computing the pointing
direction to a celestial source.
Called:
Ir initialize r-matrix to identity
Rz rotate around Z-axis
Ry rotate around Y-axis
Rx rotate around X-axis
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Pom00(xp, yp, sp float64, rpom *[3][3]float64) {
/* Construct the matrix. */
Ir(rpom)
Rz(sp, rpom)
Ry(-xp, rpom)
Rx(-yp, rpom)
}
/*
Pr00 Adjustments to IAU 1976 precession, IAU 2000
Precession-rate part of the IAU 2000 precession-nutation models
(part of MHB2000).
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
dpsipr,depspr float64 precession corrections (Notes 2,3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The precession adjustments are expressed as "nutation
components", corrections in longitude and obliquity with respect
to the J2000.0 equinox and ecliptic.
3) Although the precession adjustments are stated to be with respect
to Lieske et al. (1977), the MHB2000 model does not specify which
set of Euler angles are to be used and how the adjustments are to
be applied. The most literal and straightforward procedure is to
adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and
to add dpsipr to psi_A and depspr to both omega_A and eps_A.
4) This is an implementation of one aspect of the IAU 2000A nutation
model, formally adopted by the IAU General Assembly in 2000,
namely MHB2000 (Mathews et al. 2002).
References:
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions
for the precession quantities based upon the IAU (1976) System of
Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977)
Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
and precession New nutation series for nonrigid Earth and
insights into the Earth's interior", J.Geophys.Res., 107, B4,
2002. The MHB2000 code itself was obtained on 9th September 2002
from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
Wallace, P.T., "Software for Implementing the IAU 2000
Resolutions", in IERS Workshop 5.1 (2002).
*/
func Pr00(date1, date2 float64, dpsipr, depspr *float64) {
var t float64
/* Precession and obliquity corrections (radians per century) */
const PRECOR = -0.29965 * DAS2R
const OBLCOR = -0.02524 * DAS2R
/* Interval between fundamental epoch J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Precession rate contributions with respect to IAU 1976/80. */
*dpsipr = PRECOR * t
*depspr = OBLCOR * t
}
/*
Prec76 Precession, IAU 1976
IAU 1976 precession model.
This function forms the three Euler angles which implement general
precession between two dates, using the IAU 1976 model (as for the
FK5 catalog).
Given:
date01,date02 float64 TDB starting date (Note 1)
date11,date12 float64 TDB ending date (Note 1)
Returned:
zeta float64 1st rotation: radians cw around z
z float64 3rd rotation: radians cw around z
theta float64 2nd rotation: radians ccw around y
Notes:
1) The dates date01+date02 and date11+date12 are Julian Dates,
apportioned in any convenient way between the arguments daten1
and daten2. For example, JD(TDB)=2450123.7 could be expressed in
any of these ways, among others:
daten1 daten2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases
where the loss of several decimal digits of resolution is
acceptable. The J2000 method is best matched to the way the
argument is handled internally and will deliver the optimum
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
The two dates may be expressed using different methods, but at
the risk of losing some resolution.
2) The accumulated precession angles zeta, z, theta are expressed
through canonical polynomials which are valid only for a limited
time span. In addition, the IAU 1976 precession rate is known to
be imperfect. The absolute accuracy of the present formulation
is better than 0.1 arcsec from 1960AD to 2040AD, better than
1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
the whole of the period 500BC to 3000AD. The errors exceed
10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
8200AD.
3) The three angles are returned in the conventional order, which
is not the same as the order of the corresponding Euler
rotations. The precession matrix is
R_3(-z) x R_2(+theta) x R_3(-zeta).
Reference:
Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
(6) & (7), p283.
*/
func Prec76(date01, date02 float64, date11, date12 float64, zeta, z, theta *float64) {
var t0, t, tas2r, w float64
/* Interval between fundamental epoch J2000.0 and start date (JC). */
t0 = ((date01 - DJ00) + date02) / DJC
/* Interval over which precession required (JC). */
t = ((date11 - date01) + (date12 - date02)) / DJC
/* Euler angles. */
tas2r = t * DAS2R
w = 2306.2181 + (1.39656-0.000139*t0)*t0
*zeta = (w + ((0.30188-0.000344*t0)+0.017998*t)*t) * tas2r
*z = (w + ((1.09468+0.000066*t0)+0.018203*t)*t) * tas2r
*theta = ((2004.3109 + (-0.85330-0.000217*t0)*t0) + ((-0.42665-0.000217*t0)-0.041833*t)*t) * tas2r
}
/*
S00 The CIO locator s, given X,Y, IAU 2000
The CIO locator s, positioning the Celestial Intermediate Origin on
the equator of the Celestial Intermediate Pole, given the CIP's X,Y
coordinates. Compatible with IAU 2000A precession-nutation.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
x,y float64 CIP coordinates (Note 3)
Returned (function value):
float64 the CIO locator s in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The CIO locator s is the difference between the right ascensions
of the same point in two systems: the two systems are the GCRS
and the CIP,CIO, and the point is the ascending node of the
CIP equator. The quantity s remains below 0.1 arcsecond
throughout 1900-2100.
3) The series used to compute s is in fact for s+XY/2, where X and Y
are the x and y components of the CIP unit vector; this series
is more compact than a direct series for s would be. This
function requires X,Y to be supplied by the caller, who is
responsible for providing values that are consistent with the
supplied date.
4) The model is consistent with the IAU 2000A precession-nutation.
Called:
Fal03 mean anomaly of the Moon
Falp03 mean anomaly of the Sun
Faf03 mean argument of the latitude of the Moon
Fad03 mean elongation of the Moon from the Sun
Faom03 mean longitude of the Moon's ascending node
Fave03 mean longitude of Venus
Fae03 mean longitude of Earth
Fapa03 general accumulated precession in longitude
References:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func S00(date1, date2 float64, x, y float64) float64 {
/* Time since J2000.0, in Julian centuries */
var t float64
/* Miscellaneous */
var i, j int
var a, w0, w1, w2, w3, w4, w5 float64
/* Fundamental arguments */
var fa [8]float64
/* Returned value */
var s float64
/* --------------------- */
/* The series for s+XY/2 */
/* --------------------- */
type TERM struct {
nfa [8]int /* coefficients of l,l',F,D,Om,LVe,LE,pA */
s, c float64 /* sine and cosine coefficients */
}
/* Polynomial coefficients */
sp := []float64{
/* 1-6 */
94.00e-6,
3808.35e-6,
-119.94e-6,
-72574.09e-6,
27.70e-6,
15.61e-6,
}
/* Terms of order t^0 */
s0 := []TERM{
/* 1-10 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6},
{[8]int{0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6},
{[8]int{0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6},
{[8]int{0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6},
{[8]int{0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6},
/* 11-20 */
{[8]int{1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6},
{[8]int{0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6},
{[8]int{0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6},
{[8]int{0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6},
/* 21-30 */
{[8]int{0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 0, 8, -13, -1}, 0.10e-6, -0.05e-6},
{[8]int{0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6},
{[8]int{2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6},
/* 31-33 */
{[8]int{0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6},
}
/* Terms of order t^1 */
s1 := []TERM{
/* 1-3 */
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6},
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6},
{[8]int{0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6},
}
/* Terms of order t^2 */
s2 := []TERM{
/* 1-10 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6},
{[8]int{0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6},
{[8]int{1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6},
/* 11-20 */
{[8]int{1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6},
{[8]int{0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6},
{[8]int{0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6},
{[8]int{2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6},
{[8]int{2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6},
/* 21-25 */
{[8]int{0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6},
{[8]int{2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6},
{[8]int{2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6},
{[8]int{1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6},
}
/* Terms of order t^3 */
s3 := []TERM{
/* 1-4 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6},
}
/* Terms of order t^4 */
s4 := []TERM{
/* 1-1 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6},
}
/* Number of terms in the series */
NS0 := len(s0)
NS1 := len(s1)
NS2 := len(s2)
NS3 := len(s3)
NS4 := len(s4)
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = Fal03(t)
/* Mean anomaly of the Sun. */
fa[1] = Falp03(t)
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = Faf03(t)
/* Mean elongation of the Moon from the Sun. */
fa[3] = Fad03(t)
/* Mean longitude of the ascending node of the Moon. */
fa[4] = Faom03(t)
/* Mean longitude of Venus. */
fa[5] = Fave03(t)
/* Mean longitude of Earth. */
fa[6] = Fae03(t)
/* General precession in longitude. */
fa[7] = Fapa03(t)
/* Evaluate s. */
w0 = sp[0]
w1 = sp[1]
w2 = sp[2]
w3 = sp[3]
w4 = sp[4]
w5 = sp[5]
for i = NS0 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s0[i].nfa[j]) * fa[j]
}
w0 += s0[i].s*sin(a) + s0[i].c*cos(a)
}
for i = NS1 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s1[i].nfa[j]) * fa[j]
}
w1 += s1[i].s*sin(a) + s1[i].c*cos(a)
}
for i = NS2 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s2[i].nfa[j]) * fa[j]
}
w2 += s2[i].s*sin(a) + s2[i].c*cos(a)
}
for i = NS3 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s3[i].nfa[j]) * fa[j]
}
w3 += s3[i].s*sin(a) + s3[i].c*cos(a)
}
for i = NS4 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s4[i].nfa[j]) * fa[j]
}
w4 += s4[i].s*sin(a) + s4[i].c*cos(a)
}
s = (w0+
(w1+
(w2+
(w3+
(w4+
w5*t)*t)*t)*t)*t)*DAS2R - x*y/2.0
return s
}
/*
S00a The CIO locator s, IAU 2000A
The CIO locator s, positioning the Celestial Intermediate Origin on
the equator of the Celestial Intermediate Pole, using the IAU 2000A
precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 the CIO locator s in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The CIO locator s is the difference between the right ascensions
of the same point in two systems. The two systems are the GCRS
and the CIP,CIO, and the point is the ascending node of the
CIP equator. The CIO locator s remains a small fraction of
1 arcsecond throughout 1900-2100.
3) The series used to compute s is in fact for s+XY/2, where X and Y
are the x and y components of the CIP unit vector; this series
is more compact than a direct series for s would be. The present
function uses the full IAU 2000A nutation model when predicting
the CIP position. Faster results, with no significant loss of
accuracy, can be obtained via the function iauS00b, which uses
instead the IAU 2000B truncated model.
Called:
Pnm00a classical NPB matrix, IAU 2000A
Bnp2xy extract CIP X,Y from the BPN matrix
S00 the CIO locator s, given X,Y, IAU 2000A
References:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func S00a(date1, date2 float64) float64 {
var rbpn [3][3]float64
var x, y, s float64
/* Bias-precession-nutation-matrix, IAU 2000A. */
Pnm00a(date1, date2, &rbpn)
/* Extract the CIP coordinates. */
Bpn2xy(rbpn, &x, &y)
/* Compute the CIO locator s, given the CIP coordinates. */
s = S00(date1, date2, x, y)
return s
}
/*
S00b The CIO locator s, IAU 2000B
The CIO locator s, positioning the Celestial Intermediate Origin on
the equator of the Celestial Intermediate Pole, using the IAU 2000B
precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 the CIO locator s in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The CIO locator s is the difference between the right ascensions
of the same point in two systems. The two systems are the GCRS
and the CIP,CIO, and the point is the ascending node of the
CIP equator. The CIO locator s remains a small fraction of
1 arcsecond throughout 1900-2100.
3) The series used to compute s is in fact for s+XY/2, where X and Y
are the x and y components of the CIP unit vector; this series
is more compact than a direct series for s would be. The present
function uses the IAU 2000B truncated nutation model when
predicting the CIP position. The function iauS00a uses instead
the full IAU 2000A model, but with no significant increase in
accuracy and at some cost in speed.
Called:
Pnm00b classical NPB matrix, IAU 2000B
Bnp2xy extract CIP X,Y from the BPN matrix
S00 the CIO locator s, given X,Y, IAU 2000A
References:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func S00b(date1, date2 float64) float64 {
var rbpn [3][3]float64
var x, y, s float64
/* Bias-precession-nutation-matrix, IAU 2000B. */
Pnm00b(date1, date2, &rbpn)
/* Extract the CIP coordinates. */
Bpn2xy(rbpn, &x, &y)
/* Compute the CIO locator s, given the CIP coordinates. */
s = S00(date1, date2, x, y)
return s
}
/*
S06 The CIO locator s, given X,Y, IAU 2006
The CIO locator s, positioning the Celestial Intermediate Origin on
the equator of the Celestial Intermediate Pole, given the CIP's X,Y
coordinates. Compatible with IAU 2006/2000A precession-nutation.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
x,y float64 CIP coordinates (Note 3)
Returned (function value):
float64 the CIO locator s in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The CIO locator s is the difference between the right ascensions
of the same point in two systems: the two systems are the GCRS
and the CIP,CIO, and the point is the ascending node of the
CIP equator. The quantity s remains below 0.1 arcsecond
throughout 1900-2100.
3) The series used to compute s is in fact for s+XY/2, where X and Y
are the x and y components of the CIP unit vector; this series
is more compact than a direct series for s would be. This
function requires X,Y to be supplied by the caller, who is
responsible for providing values that are consistent with the
supplied date.
4) The model is consistent with the "P03" precession (Capitaine et
al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
2000A nutation (with P03 adjustments).
Called:
Fal03 mean anomaly of the Moon
Falp03 mean anomaly of the Sun
Faf03 mean argument of the latitude of the Moon
Fad03 mean elongation of the Moon from the Sun
Faom03 mean longitude of the Moon's ascending node
Fave03 mean longitude of Venus
Fae03 mean longitude of Earth
Fapa03 general accumulated precession in longitude
References:
Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron.
Astrophys. 432, 355
McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
*/
func S06(date1, date2 float64, x, y float64) float64 {
/* Time since J2000.0, in Julian centuries */
var t float64
/* Miscellaneous */
var i, j int
var a, w0, w1, w2, w3, w4, w5 float64
/* Fundamental arguments */
var fa [8]float64
/* Returned value */
var s float64
/* --------------------- */
/* The series for s+XY/2 */
/* --------------------- */
type TERM struct {
nfa [8]int /* coefficients of l,l',F,D,Om,LVe,LE,pA */
s, c float64 /* sine and cosine coefficients */
}
/* Polynomial coefficients */
sp := []float64{
/* 1-6 */
94.00e-6,
3808.65e-6,
-122.68e-6,
-72574.11e-6,
27.98e-6,
15.62e-6,
}
/* Terms of order t^0 */
s0 := []TERM{
/* 1-10 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6},
{[8]int{0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6},
{[8]int{0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6},
{[8]int{0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6},
{[8]int{0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6},
/* 11-20 */
{[8]int{1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6},
{[8]int{0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6},
{[8]int{0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6},
{[8]int{0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6},
/* 21-30 */
{[8]int{0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6},
{[8]int{0, 0, 0, 0, 0, 8, -13, -1}, 0.10e-6, -0.05e-6},
{[8]int{0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6},
{[8]int{2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6},
{[8]int{0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6},
/* 31-33 */
{[8]int{0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6},
}
/* Terms of order t^1 */
s1 := []TERM{
/* 1 - 3 */
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6},
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6},
{[8]int{0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6},
}
/* Terms of order t^2 */
s2 := []TERM{
/* 1-10 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6},
{[8]int{0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6},
{[8]int{1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6},
{[8]int{0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6},
{[8]int{0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6},
/* 11-20 */
{[8]int{1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6},
{[8]int{0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6},
{[8]int{1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6},
{[8]int{0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6},
{[8]int{1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6},
{[8]int{1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6},
{[8]int{1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6},
{[8]int{2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6},
{[8]int{2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6},
/* 21-25 */
{[8]int{0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6},
{[8]int{2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6},
{[8]int{2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6},
{[8]int{1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6},
{[8]int{0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6},
}
/* Terms of order t^3 */
s3 := []TERM{
/* 1-4 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6},
{[8]int{0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6},
{[8]int{0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6},
{[8]int{0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6},
}
/* Terms of order t^4 */
s4 := []TERM{
/* 1-1 */
{[8]int{0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6},
}
/* Number of terms in the series */
NS0 := len(s0)
NS1 := len(s1)
NS2 := len(s2)
NS3 := len(s3)
NS4 := len(s4)
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = Fal03(t)
/* Mean anomaly of the Sun. */
fa[1] = Falp03(t)
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = Faf03(t)
/* Mean elongation of the Moon from the Sun. */
fa[3] = Fad03(t)
/* Mean longitude of the ascending node of the Moon. */
fa[4] = Faom03(t)
/* Mean longitude of Venus. */
fa[5] = Fave03(t)
/* Mean longitude of Earth. */
fa[6] = Fae03(t)
/* General precession in longitude. */
fa[7] = Fapa03(t)
/* Evaluate s. */
w0 = sp[0]
w1 = sp[1]
w2 = sp[2]
w3 = sp[3]
w4 = sp[4]
w5 = sp[5]
for i = NS0 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s0[i].nfa[j]) * fa[j]
}
w0 += s0[i].s*sin(a) + s0[i].c*cos(a)
}
for i = NS1 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s1[i].nfa[j]) * fa[j]
}
w1 += s1[i].s*sin(a) + s1[i].c*cos(a)
}
for i = NS2 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s2[i].nfa[j]) * fa[j]
}
w2 += s2[i].s*sin(a) + s2[i].c*cos(a)
}
for i = NS3 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s3[i].nfa[j]) * fa[j]
}
w3 += s3[i].s*sin(a) + s3[i].c*cos(a)
}
for i = NS4 - 1; i >= 0; i-- {
a = 0.0
for j = 0; j < 8; j++ {
a += float64(s4[i].nfa[j]) * fa[j]
}
w4 += s4[i].s*sin(a) + s4[i].c*cos(a)
}
s = (w0+(w1+(w2+(w3+(w4+w5*t)*t)*t)*t)*t)*DAS2R - x*y/2.0
return s
}
/*
S06a The CIO locator s, IAU 2006/2000A
The CIO locator s, positioning the Celestial Intermediate Origin on
the equator of the Celestial Intermediate Pole, using the IAU 2006
precession and IAU 2000A nutation models.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 the CIO locator s in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The CIO locator s is the difference between the right ascensions
of the same point in two systems. The two systems are the GCRS
and the CIP,CIO, and the point is the ascending node of the
CIP equator. The CIO locator s remains a small fraction of
1 arcsecond throughout 1900-2100.
3) The series used to compute s is in fact for s+XY/2, where X and Y
are the x and y components of the CIP unit vector; this series is
more compact than a direct series for s would be. The present
function uses the full IAU 2000A nutation model when predicting
the CIP position.
Called:
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
References:
Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
n.b. The celestial ephemeris origin (CEO) was renamed "celestial
intermediate origin" (CIO) by IAU 2006 Resolution 2.
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func S06a(date1, date2 float64) float64 {
var rnpb [3][3]float64
var x, y, s float64
/* Bias-precession-nutation-matrix, IAU 20006/2000A. */
Pnm06a(date1, date2, &rnpb)
/* Extract the CIP coordinates. */
Bpn2xy(rnpb, &x, &y)
/* Compute the CIO locator s, given the CIP coordinates. */
s = S06(date1, date2, x, y)
return s
}
/*
Sp00 The TIO locator s', IERS 2003
The TIO locator s', positioning the Terrestrial Intermediate Origin
on the equator of the Celestial Intermediate Pole.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned (function value):
float64 the TIO locator s' in radians (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The TIO locator s' is obtained from polar motion observations by
numerical integration, and so is in essence unpredictable.
However, it is dominated by a secular drift of about
47 microarcseconds per century, which is the approximation
evaluated by the present function.
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Sp00(date1, date2 float64) float64 {
var t, sp float64
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Approximate s'. */
sp = -47e-6 * t * DAS2R
return sp
}
/*
Xy06 CIP, IAU 2006/2000A, from series
X,Y coordinates of celestial intermediate pole from series based
on IAU 2006 precession and IAU 2000A nutation.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
x,y float64 CIP X,Y coordinates (Note 2)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The X,Y coordinates are those of the unit vector towards the
celestial intermediate pole. They represent the combined effects
of frame bias, precession and nutation.
3) The fundamental arguments used are as adopted in IERS Conventions
(2003) and are from Simon et al. (1994) and Souchay et al.
(1999).
4) This is an alternative to the angles-based method, via the SOFA
function iauFw2xy and as used in iauXys06a for example. The two
methods agree at the 1 microarcsecond level (at present), a
negligible amount compared with the intrinsic accuracy of the
models. However, it would be unwise to mix the two methods
(angles-based and series-based) in a single application.
Called:
Fal03 mean anomaly of the Moon
Falp03 mean anomaly of the Sun
Faf03 mean argument of the latitude of the Moon
Fad03 mean elongation of the Moon from the Sun
Faom03 mean longitude of the Moon's ascending node
Fame03 mean longitude of Mercury
Fave03 mean longitude of Venus
Fae03 mean longitude of Earth
Fama03 mean longitude of Mars
Faju03 mean longitude of Jupiter
Fasa03 mean longitude of Saturn
Faur03 mean longitude of Uranus
Fane03 mean longitude of Neptune
Fapa03 general accumulated precession in longitude
References:
Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
Astron.Astrophys., 412, 567
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
IERS Technical Note No. 32, BKG
Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999,
Astron.Astrophys.Supp.Ser. 135, 111
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Xy06(date1, date2 float64, x, y *float64) {
/* Maximum power of T in the polynomials for X and Y */
const MAXPT = 5
/* Polynomial coefficients (arcsec, X then Y). */
xyp := [2][MAXPT + 1]float64{
{-0.016617,
2004.191898,
-0.4297829,
-0.19861834,
0.000007578,
0.0000059285,
},
{-0.006951,
-0.025896,
-22.4072747,
0.00190059,
0.001112526,
0.0000001358,
},
}
/* Fundamental-argument multipliers: luni-solar terms */
mfals := [][5]int{
/* 1-10 */
{0, 0, 0, 0, 1},
{0, 0, 2, -2, 2},
{0, 0, 2, 0, 2},
{0, 0, 0, 0, 2},
{0, 1, 0, 0, 0},
{0, 1, 2, -2, 2},
{1, 0, 0, 0, 0},
{0, 0, 2, 0, 1},
{1, 0, 2, 0, 2},
{0, 1, -2, 2, -2},
/* 11-20 */
{0, 0, 2, -2, 1},
{1, 0, -2, 0, -2},
{1, 0, 0, -2, 0},
{1, 0, 0, 0, 1},
{1, 0, 0, 0, -1},
{1, 0, -2, -2, -2},
{1, 0, 2, 0, 1},
{2, 0, -2, 0, -1},
{0, 0, 0, 2, 0},
{0, 0, 2, 2, 2},
/* 21-30 */
{2, 0, 0, -2, 0},
{0, 2, -2, 2, -2},
{2, 0, 2, 0, 2},
{1, 0, 2, -2, 2},
{1, 0, -2, 0, -1},
{2, 0, 0, 0, 0},
{0, 0, 2, 0, 0},
{0, 1, 0, 0, 1},
{1, 0, 0, -2, -1},
{0, 2, 2, -2, 2},
/* 31-40 */
{0, 0, 2, -2, 0},
{1, 0, 0, -2, 1},
{0, 1, 0, 0, -1},
{0, 2, 0, 0, 0},
{1, 0, -2, -2, -1},
{1, 0, 2, 2, 2},
{0, 1, 2, 0, 2},
{2, 0, -2, 0, 0},
{0, 0, 2, 2, 1},
{0, 1, -2, 0, -2},
/* 41-50 */
{0, 0, 0, 2, 1},
{1, 0, 2, -2, 1},
{2, 0, 0, -2, -1},
{2, 0, 2, -2, 2},
{2, 0, 2, 0, 1},
{0, 0, 0, 2, -1},
{0, 1, -2, 2, -1},
{1, 1, 0, -2, 0},
{2, 0, 0, -2, 1},
{1, 0, 0, 2, 0},
/* 51-60 */
{0, 1, 2, -2, 1},
{1, -1, 0, 0, 0},
{0, 1, -1, 1, -1},
{2, 0, -2, 0, -2},
{0, 1, 0, -2, 0},
{1, 0, 0, -1, 0},
{3, 0, 2, 0, 2},
{0, 0, 0, 1, 0},
{1, -1, 2, 0, 2},
{1, 1, -2, -2, -2},
/* 61-70 */
{1, 0, -2, 0, 0},
{2, 0, 0, 0, -1},
{0, 1, -2, -2, -2},
{1, 1, 2, 0, 2},
{2, 0, 0, 0, 1},
{1, 1, 0, 0, 0},
{1, 0, -2, 2, -1},
{1, 0, 2, 0, 0},
{1, -1, 0, -1, 0},
{1, 0, 0, 0, 2},
/* 71-80 */
{1, 0, -1, 0, -1},
{0, 0, 2, 1, 2},
{1, 0, -2, -4, -2},
{1, -1, 0, -1, -1},
{1, 0, 2, 2, 1},
{0, 2, -2, 2, -1},
{1, 0, 0, 0, -2},
{2, 0, -2, -2, -2},
{1, 1, 2, -2, 2},
{2, 0, -2, -4, -2},
/* 81-90 */
{1, 0, -4, 0, -2},
{2, 0, 2, -2, 1},
{1, 0, 0, -1, -1},
{2, 0, 2, 2, 2},
{3, 0, 0, 0, 0},
{1, 0, 0, 2, 1},
{0, 0, 2, -2, -1},
{3, 0, 2, -2, 2},
{0, 0, 4, -2, 2},
{1, 0, 0, -4, 0},
/* 91-100 */
{0, 1, 2, 0, 1},
{2, 0, 0, -4, 0},
{1, 1, 0, -2, -1},
{2, 0, -2, 0, 1},
{0, 0, 2, 0, -1},
{0, 1, -2, 0, -1},
{0, 1, 0, 0, 2},
{0, 0, 2, -1, 2},
{0, 0, 2, 4, 2},
{2, 1, 0, -2, 0},
/* 101-110 */
{1, 1, 0, -2, 1},
{1, -1, 0, -2, 0},
{1, -1, 0, -1, -2},
{1, -1, 0, 0, 1},
{0, 1, -2, 2, 0},
{0, 1, 0, 0, -2},
{1, -1, 2, 2, 2},
{1, 0, 0, 2, -1},
{1, -1, -2, -2, -2},
{3, 0, 2, 0, 1},
/* 111-120 */
{0, 1, 2, 2, 2},
{1, 0, 2, -2, 0},
{1, 1, -2, -2, -1},
{1, 0, 2, -4, 1},
{0, 1, -2, -2, -1},
{2, -1, 2, 0, 2},
{0, 0, 0, 2, 2},
{1, -1, 2, 0, 1},
{1, -1, -2, 0, -2},
{0, 1, 0, 2, 0},
/* 121-130 */
{0, 1, 2, -2, 0},
{0, 0, 0, 1, 1},
{1, 0, -2, -2, 0},
{0, 3, 2, -2, 2},
{2, 1, 2, 0, 2},
{1, 1, 0, 0, 1},
{2, 0, 0, 2, 0},
{1, 1, 2, 0, 1},
{1, 0, 0, -2, -2},
{1, 0, -2, 2, 0},
/* 131-140 */
{1, 0, -1, 0, -2},
{0, 1, 0, -2, 1},
{0, 1, 0, 1, 0},
{0, 0, 0, 1, -1},
{1, 0, -2, 2, -2},
{1, -1, 0, 0, -1},
{0, 0, 0, 4, 0},
{1, -1, 0, 2, 0},
{1, 0, 2, 1, 2},
{1, 0, 2, -1, 2},
/* 141-150 */
{0, 0, 2, 1, 1},
{1, 0, 0, -2, 2},
{1, 0, -2, 0, 1},
{1, 0, -2, -4, -1},
{0, 0, 2, 2, 0},
{1, 1, 2, -2, 1},
{1, 0, -2, 1, -1},
{0, 0, 1, 0, 1},
{2, 0, -2, -2, -1},
{4, 0, 2, 0, 2},
/* 151-160 */
{2, -1, 0, 0, 0},
{2, 1, 2, -2, 2},
{0, 1, 2, 1, 2},
{1, 0, 4, -2, 2},
{1, 1, 0, 0, -1},
{2, 0, 2, 0, 0},
{2, 0, -2, -4, -1},
{1, 0, -1, 0, 0},
{1, 0, 0, 1, 0},
{0, 1, 0, 2, 1},
/* 161-170 */
{1, 0, -4, 0, -1},
{1, 0, 0, -4, -1},
{2, 0, 2, 2, 1},
{2, 1, 0, 0, 0},
{0, 0, 2, -3, 2},
{1, 2, 0, -2, 0},
{0, 3, 0, 0, 0},
{0, 0, 4, 0, 2},
{0, 0, 2, -4, 1},
{2, 0, 0, -2, -2},
/* 171-180 */
{1, 1, -2, -4, -2},
{0, 1, 0, -2, -1},
{0, 0, 0, 4, 1},
{3, 0, 2, -2, 1},
{1, 0, 2, 4, 2},
{1, 1, -2, 0, -2},
{0, 0, 4, -2, 1},
{2, -2, 0, -2, 0},
{2, 1, 0, -2, -1},
{0, 2, 0, -2, 0},
/* 181-190 */
{1, 0, 0, -1, 1},
{1, 1, 2, 2, 2},
{3, 0, 0, 0, -1},
{2, 0, 0, -4, -1},
{3, 0, 2, 2, 2},
{0, 0, 2, 4, 1},
{0, 2, -2, -2, -2},
{1, -1, 0, -2, -1},
{0, 0, 2, -1, 1},
{2, 0, 0, 2, 1},
/* 191-200 */
{1, -1, -2, 2, -1},
{0, 0, 0, 2, -2},
{2, 0, 0, -4, 1},
{1, 0, 0, -4, 1},
{2, 0, 2, -4, 1},
{4, 0, 2, -2, 2},
{2, 1, -2, 0, -1},
{2, 1, -2, -4, -2},
{3, 0, 0, -4, 0},
{1, -1, 2, 2, 1},
/* 201-210 */
{1, -1, -2, 0, -1},
{0, 2, 0, 0, 1},
{1, 2, -2, -2, -2},
{1, 1, 0, -4, 0},
{2, 0, 0, -2, 2},
{0, 2, 2, -2, 1},
{1, 0, 2, 0, -1},
{2, 1, 0, -2, 1},
{2, -1, -2, 0, -1},
{1, -1, -2, -2, -1},
/* 211-220 */
{0, 1, -2, 1, -2},
{1, 0, -4, 2, -2},
{0, 1, 2, 2, 1},
{3, 0, 0, 0, 1},
{2, -1, 2, 2, 2},
{0, 1, -2, -4, -2},
{1, 0, -2, -3, -2},
{2, 0, 0, 0, 2},
{1, -1, 0, -2, -2},
{2, 0, -2, 2, -1},
/* 221-230 */
{0, 2, -2, 0, -2},
{3, 0, -2, 0, -1},
{2, -1, 2, 0, 1},
{1, 0, -2, -1, -2},
{0, 0, 2, 0, 3},
{2, 0, -4, 0, -2},
{2, 1, 0, -4, 0},
{1, 1, -2, 1, -1},
{0, 2, 2, 0, 2},
{1, -1, 2, -2, 2},
/* 231-240 */
{1, -1, 0, -2, 1},
{2, 1, 2, 0, 1},
{1, 0, 2, -4, 2},
{1, 1, -2, 0, -1},
{1, 1, 0, 2, 0},
{1, 0, 0, -3, 0},
{2, 0, 2, -1, 2},
{0, 2, 0, 0, -1},
{2, -1, 0, -2, 0},
{4, 0, 0, 0, 0},
/* 241-250 */
{2, 1, -2, -2, -2},
{0, 2, -2, 2, 0},
{1, 0, 2, 1, 1},
{1, 0, -1, 0, -3},
{3, -1, 2, 0, 2},
{2, 0, 2, -2, 0},
{1, -2, 0, 0, 0},
{2, 0, 0, 0, -2},
{1, 0, 0, 4, 0},
{0, 1, 0, 1, 1},
/* 251-260 */
{1, 0, 2, 2, 0},
{0, 1, 0, 2, -1},
{0, 1, 0, 1, -1},
{0, 0, 2, -2, 3},
{3, 1, 2, 0, 2},
{1, 1, 2, 1, 2},
{1, 1, -2, 2, -1},
{2, -1, 2, -2, 2},
{1, -2, 2, 0, 2},
{1, 0, 2, -4, 0},
/* 261-270 */
{0, 0, 1, 0, 0},
{1, 0, 2, -3, 1},
{1, -2, 0, -2, 0},
{2, 0, 0, 2, -1},
{1, 1, 2, -4, 1},
{4, 0, 2, 0, 1},
{0, 1, 2, 1, 1},
{1, 2, 2, -2, 2},
{2, 0, 2, 1, 2},
{2, 1, 2, -2, 1},
/* 271-280 */
{1, 0, 2, -1, 1},
{1, 0, 4, -2, 1},
{1, -1, 2, -2, 1},
{0, 1, 0, -4, 0},
{3, 0, -2, -2, -2},
{0, 0, 4, -4, 2},
{2, 0, -4, -2, -2},
{2, -2, 0, -2, -1},
{1, 0, 2, -2, -1},
{2, 0, -2, -6, -2},
/* 281-290 */
{1, 0, -2, 1, -2},
{1, 0, -2, 2, 1},
{1, -1, 0, 2, -1},
{1, 0, -2, 1, 0},
{2, -1, 0, -2, 1},
{1, -1, 0, 2, 1},
{2, 0, -2, -2, 0},
{1, 0, 2, -3, 2},
{0, 0, 0, 4, -1},
{2, -1, 0, 0, 1},
/* 291-300 */
{2, 0, 4, -2, 2},
{0, 0, 2, 3, 2},
{0, 1, 4, -2, 2},
{0, 1, -2, 2, 1},
{1, 1, 0, 2, 1},
{1, 0, 0, 4, 1},
{0, 0, 4, 0, 1},
{2, 0, 0, -3, 0},
{1, 0, 0, -1, -2},
{1, -2, -2, -2, -2},
/* 301-310 */
{3, 0, 0, 2, 0},
{2, 0, 2, -4, 2},
{1, 1, -2, -4, -1},
{1, 0, -2, -6, -2},
{2, -1, 0, 0, -1},
{2, -1, 0, 2, 0},
{0, 1, 2, -2, -1},
{1, 1, 0, 1, 0},
{1, 2, 0, -2, -1},
{1, 0, 0, 1, -1},
/* 311-320 */
{0, 0, 1, 0, 2},
{3, 1, 2, -2, 2},
{1, 0, -4, -2, -2},
{1, 0, 2, 4, 1},
{1, -2, 2, 2, 2},
{1, -1, -2, -4, -2},
{0, 0, 2, -4, 2},
{0, 0, 2, -3, 1},
{2, 1, -2, 0, 0},
{3, 0, -2, -2, -1},
/* 321-330 */
{2, 0, 2, 4, 2},
{0, 0, 0, 0, 3},
{2, -1, -2, -2, -2},
{2, 0, 0, -1, 0},
{3, 0, 2, -4, 2},
{2, 1, 2, 2, 2},
{0, 0, 3, 0, 3},
{1, 1, 2, 2, 1},
{2, 1, 0, 0, -1},
{1, 2, 0, -2, 1},
/* 331-340 */
{3, 0, 2, 2, 1},
{1, -1, -2, 2, -2},
{1, 1, 0, -1, 0},
{1, 2, 0, 0, 0},
{1, 0, 4, 0, 2},
{1, -1, 2, 4, 2},
{2, 1, 0, 0, 1},
{1, 0, 0, 2, 2},
{1, -1, -2, 2, 0},
{0, 2, -2, -2, -1},
/* 341-350 */
{2, 0, -2, 0, 2},
{5, 0, 2, 0, 2},
{3, 0, -2, -6, -2},
{1, -1, 2, -1, 2},
{3, 0, 0, -4, -1},
{1, 0, 0, 1, 1},
{1, 0, -4, 2, -1},
{0, 1, 2, -4, 1},
{1, 2, 2, 0, 2},
{0, 1, 0, -2, -2},
/* 351-360 */
{0, 0, 2, -1, 0},
{1, 0, 1, 0, 1},
{0, 2, 0, -2, 1},
{3, 0, 2, 0, 0},
{1, 1, -2, 1, 0},
{2, 1, -2, -4, -1},
{3, -1, 0, 0, 0},
{2, -1, -2, 0, 0},
{4, 0, 2, -2, 1},
{2, 0, -2, 2, 0},
/* 361-370 */
{1, 1, 2, -2, 0},
{1, 0, -2, 4, -1},
{1, 0, -2, -2, 1},
{2, 0, 2, -4, 0},
{1, 1, 0, -2, -2},
{1, 1, -2, -2, 0},
{1, 0, 1, -2, 1},
{2, -1, -2, -4, -2},
{3, 0, -2, 0, -2},
{0, 1, -2, -2, 0},
/* 371-380 */
{3, 0, 0, -2, -1},
{1, 0, -2, -3, -1},
{0, 1, 0, -4, -1},
{1, -2, 2, -2, 1},
{0, 1, -2, 1, -1},
{1, -1, 0, 0, 2},
{2, 0, 0, 1, 0},
{1, -2, 0, 2, 0},
{1, 2, -2, -2, -1},
{0, 0, 4, -4, 1},
/* 381-390 */
{0, 1, 2, 4, 2},
{0, 1, -4, 2, -2},
{3, 0, -2, 0, 0},
{2, -1, 2, 2, 1},
{0, 1, -2, -4, -1},
{4, 0, 2, 2, 2},
{2, 0, -2, -3, -2},
{2, 0, 0, -6, 0},
{1, 0, 2, 0, 3},
{3, 1, 0, 0, 0},
/* 391-400 */
{3, 0, 0, -4, 1},
{1, -1, 2, 0, 0},
{1, -1, 0, -4, 0},
{2, 0, -2, 2, -2},
{1, 1, 0, -2, 2},
{4, 0, 0, -2, 0},
{2, 2, 0, -2, 0},
{0, 1, 2, 0, 0},
{1, 1, 0, -4, 1},
{1, 0, 0, -4, -2},
/* 401-410 */
{0, 0, 0, 1, 2},
{3, 0, 0, 2, 1},
{1, 1, 0, -4, -1},
{0, 0, 2, 2, -1},
{1, 1, 2, 0, 0},
{1, -1, 2, -4, 1},
{1, 1, 0, 0, 2},
{0, 0, 2, 6, 2},
{4, 0, -2, -2, -1},
{2, 1, 0, -4, -1},
/* 411-420 */
{0, 0, 0, 3, 1},
{1, -1, -2, 0, 0},
{0, 0, 2, 1, 0},
{1, 0, 0, 2, -2},
{3, -1, 2, 2, 2},
{3, -1, 2, -2, 2},
{1, 0, 0, -1, 2},
{1, -2, 2, -2, 2},
{0, 1, 0, 2, 2},
{0, 1, -2, -1, -2},
/* 421-430 */
{1, 1, -2, 0, 0},
{0, 2, 2, -2, 0},
{3, -1, -2, -1, -2},
{1, 0, 0, -6, 0},
{1, 0, -2, -4, 0},
{2, 1, 0, -4, 1},
{2, 0, 2, 0, -1},
{2, 0, -4, 0, -1},
{0, 0, 3, 0, 2},
{2, 1, -2, -2, -1},
/* 431-440 */
{1, -2, 0, 0, 1},
{2, -1, 0, -4, 0},
{0, 0, 0, 3, 0},
{5, 0, 2, -2, 2},
{1, 2, -2, -4, -2},
{1, 0, 4, -4, 2},
{0, 0, 4, -1, 2},
{3, 1, 0, -4, 0},
{3, 0, 0, -6, 0},
{2, 0, 0, 2, 2},
/* 441-450 */
{2, -2, 2, 0, 2},
{1, 0, 0, -3, 1},
{1, -2, -2, 0, -2},
{1, -1, -2, -3, -2},
{0, 0, 2, -2, -2},
{2, 0, -2, -4, 0},
{1, 0, -4, 0, 0},
{0, 1, 0, -1, 0},
{4, 0, 0, 0, -1},
{3, 0, 2, -1, 2},
/* 451-460 */
{3, -1, 2, 0, 1},
{2, 0, 2, -1, 1},
{1, 2, 2, -2, 1},
{1, 1, 0, 2, -1},
{0, 2, 2, 0, 1},
{3, 1, 2, 0, 1},
{1, 1, 2, 1, 1},
{1, 1, 0, -1, 1},
{1, -2, 0, -2, -1},
{4, 0, 0, -4, 0},
/* 461-470 */
{2, 1, 0, 2, 0},
{1, -1, 0, 4, 0},
{0, 1, 0, -2, 2},
{0, 0, 2, 0, -2},
{1, 0, -1, 0, 1},
{3, 0, 2, -2, 0},
{2, 0, 2, 2, 0},
{1, 2, 0, -4, 0},
{1, -1, 0, -3, 0},
{0, 1, 0, 4, 0},
/* 471 - 480 */
{0, 1, -2, 0, 0},
{2, 2, 2, -2, 2},
{0, 0, 0, 1, -2},
{0, 2, -2, 0, -1},
{4, 0, 2, -4, 2},
{2, 0, -4, 2, -2},
{2, -1, -2, 0, -2},
{1, 1, 4, -2, 2},
{1, 1, 2, -4, 2},
{1, 0, 2, 3, 2},
/* 481-490 */
{1, 0, 0, 4, -1},
{0, 0, 0, 4, 2},
{2, 0, 0, 4, 0},
{1, 1, -2, 2, 0},
{2, 1, 2, 1, 2},
{2, 1, 2, -4, 1},
{2, 0, 2, 1, 1},
{2, 0, -4, -2, -1},
{2, 0, -2, -6, -1},
{2, -1, 2, -1, 2},
/* 491-500 */
{1, -2, 2, 0, 1},
{1, -2, 0, -2, 1},
{1, -1, 0, -4, -1},
{0, 2, 2, 2, 2},
{0, 2, -2, -4, -2},
{0, 1, 2, 3, 2},
{0, 1, 0, -4, 1},
{3, 0, 0, -2, 1},
{2, 1, -2, 0, 1},
{2, 0, 4, -2, 1},
/* 501-510 */
{2, 0, 0, -3, -1},
{2, -2, 0, -2, 1},
{2, -1, 2, -2, 1},
{1, 0, 0, -6, -1},
{1, -2, 0, 0, -1},
{1, -2, -2, -2, -1},
{0, 1, 4, -2, 1},
{0, 0, 2, 3, 1},
{2, -1, 0, -1, 0},
{1, 3, 0, -2, 0},
/* 511-520 */
{0, 3, 0, -2, 0},
{2, -2, 2, -2, 2},
{0, 0, 4, -2, 0},
{4, -1, 2, 0, 2},
{2, 2, -2, -4, -2},
{4, 1, 2, 0, 2},
{4, -1, -2, -2, -2},
{2, 1, 0, -2, -2},
{2, 1, -2, -6, -2},
{2, 0, 0, -1, 1},
/* 521-530 */
{2, -1, -2, 2, -1},
{1, 1, -2, 2, -2},
{1, 1, -2, -3, -2},
{1, 0, 3, 0, 3},
{1, 0, -2, 1, 1},
{1, 0, -2, 0, 2},
{1, -1, 2, 1, 2},
{1, -1, 0, 0, -2},
{1, -1, -4, 2, -2},
{0, 3, -2, -2, -2},
/* 531-540 */
{0, 1, 0, 4, 1},
{0, 0, 4, 2, 2},
{3, 0, -2, -2, 0},
{2, -2, 0, 0, 0},
{1, 1, 2, -4, 0},
{1, 1, 0, -3, 0},
{1, 0, 2, -3, 0},
{1, -1, 2, -2, 0},
{0, 2, 0, 2, 0},
{0, 0, 2, 4, 0},
/* 541-550 */
{1, 0, 1, 0, 0},
{3, 1, 2, -2, 1},
{3, 0, 4, -2, 2},
{3, 0, 2, 1, 2},
{3, 0, 0, 2, -1},
{3, 0, 0, 0, 2},
{3, 0, -2, 2, -1},
{2, 0, 4, -4, 2},
{2, 0, 2, -3, 2},
{2, 0, 0, 4, 1},
/* 551-560 */
{2, 0, 0, -3, 1},
{2, 0, -4, 2, -1},
{2, 0, -2, -2, 1},
{2, -2, 2, 2, 2},
{2, -2, 0, -2, -2},
{2, -1, 0, 2, 1},
{2, -1, 0, 2, -1},
{1, 1, 2, 4, 2},
{1, 1, 0, 1, 1},
{1, 1, 0, 1, -1},
/* 561-570 */
{1, 1, -2, -6, -2},
{1, 0, 0, -3, -1},
{1, 0, -4, -2, -1},
{1, 0, -2, -6, -1},
{1, -2, 2, 2, 1},
{1, -2, -2, 2, -1},
{1, -1, -2, -4, -1},
{0, 2, 0, 0, 2},
{0, 1, 2, -4, 2},
{0, 1, -2, 4, -1},
/* 571-580 */
{5, 0, 0, 0, 0},
{3, 0, 0, -3, 0},
{2, 2, 0, -4, 0},
{1, -1, 2, 2, 0},
{0, 1, 0, 3, 0},
{4, 0, -2, 0, -1},
{3, 0, -2, -6, -1},
{3, 0, -2, -1, -1},
{2, 1, 2, 2, 1},
{2, 1, 0, 2, 1},
/* 581-590 */
{2, 0, 2, 4, 1},
{2, 0, 2, -6, 1},
{2, 0, 2, -2, -1},
{2, 0, 0, -6, -1},
{2, -1, -2, -2, -1},
{1, 2, 2, 0, 1},
{1, 2, 0, 0, 1},
{1, 0, 4, 0, 1},
{1, 0, 2, -6, 1},
{1, 0, 2, -4, -1},
/* 591-600 */
{1, 0, -1, -2, -1},
{1, -1, 2, 4, 1},
{1, -1, 2, -3, 1},
{1, -1, 0, 4, 1},
{1, -1, -2, 1, -1},
{0, 1, 2, -2, 3},
{3, 0, 0, -2, 0},
{1, 0, 1, -2, 0},
{0, 2, 0, -4, 0},
{0, 0, 2, -4, 0},
/* 601-610 */
{0, 0, 1, -1, 0},
{0, 0, 0, 6, 0},
{0, 2, 0, 0, -2},
{0, 1, -2, 2, -3},
{4, 0, 0, 2, 0},
{3, 0, 0, -1, 0},
{3, -1, 0, 2, 0},
{2, 1, 0, 1, 0},
{2, 1, 0, -6, 0},
{2, -1, 2, 0, 0},
/* 611-620 */
{1, 0, 2, -1, 0},
{1, -1, 0, 1, 0},
{1, -1, -2, -2, 0},
{0, 1, 2, 2, 0},
{0, 0, 2, -3, 0},
{2, 2, 0, -2, -1},
{2, -1, -2, 0, 1},
{1, 2, 2, -4, 1},
{0, 1, 4, -4, 2},
{0, 0, 0, 3, 2},
/* 621-630 */
{5, 0, 2, 0, 1},
{4, 1, 2, -2, 2},
{4, 0, -2, -2, 0},
{3, 1, 2, 2, 2},
{3, 1, 0, -2, 0},
{3, 1, -2, -6, -2},
{3, 0, 0, 0, -2},
{3, 0, -2, -4, -2},
{3, -1, 0, -3, 0},
{3, -1, 0, -2, 0},
/* 631-640 */
{2, 1, 2, 0, 0},
{2, 1, 2, -4, 2},
{2, 1, 2, -2, 0},
{2, 1, 0, -3, 0},
{2, 1, -2, 0, -2},
{2, 0, 0, -4, 2},
{2, 0, 0, -4, -2},
{2, 0, -2, -5, -2},
{2, -1, 2, 4, 2},
{2, -1, 0, -2, 2},
/* 641-650 */
{1, 3, -2, -2, -2},
{1, 1, 0, 0, -2},
{1, 1, 0, -6, 0},
{1, 1, -2, 1, -2},
{1, 1, -2, -1, -2},
{1, 0, 2, 1, 0},
{1, 0, 0, 3, 0},
{1, 0, 0, -4, 2},
{1, 0, -2, 4, -2},
{1, -2, 0, -1, 0},
/* 651-NFLS */
{0, 1, -4, 2, -1},
{1, 0, -2, 0, -3},
{0, 0, 4, -4, 4},
}
/* Number of frequencies: luni-solar */
NFLS := len(mfals)
/* Fundamental-argument multipliers: planetary terms */
mfapl := [][14]int{
/* 1-10 */
{0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0},
/* 11-20 */
{0, 0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0},
{0, 0, 2, -2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, -8, 3, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0},
/* 21-30 */
{0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2},
{0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0},
{2, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0},
/* 31-40 */
{0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0},
/* 41-50 */
{0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2},
{1, 0, 0, 0, 0, 0, -18, 16, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2},
/* 51-60 */
{0, 0, 1, -1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, -10, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 0, 0, -5, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2},
{1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1},
{1, 0, -2, 0, -2, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0},
{0, 0, 2, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0},
/* 61-70 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, -2},
{0, 0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -11, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 8, -16, 4, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0},
/* 71-80 */
{0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 8, -15, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2},
{0, 0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0},
/* 81-90 */
{2, 0, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -1},
{2, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 8, -13, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 5, 0, 0, 0},
{1, 0, 0, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2},
{1, 0, 0, 0, -1, 0, -18, 16, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -5, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0},
/* 91-100 */
{1, 0, 0, -2, 0, 0, 19, -21, 3, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2},
{1, 0, 0, 0, 1, 0, -18, 16, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 6, -16, 4, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, -2},
/* 101-110 */
{0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1},
{2, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0},
{2, 0, 0, -2, -1, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2},
/* 111-120 */
{0, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2},
{0, 0, 2, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, -6, 8, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0},
/* 121-130 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -10, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -2},
{1, 0, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0},
/* 131-140 */
{0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0},
/* 141-150 */
{1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 9, -11, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 8, -15, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2},
/* 151-160 */
{1, 0, 0, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -2},
{0, 0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0},
/* 161-170 */
{0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0},
{2, 0, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0},
/* 171-180 */
{0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0},
{1, 0, 0, -1, -1, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1},
{1, 0, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0},
/* 181-190 */
{0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1},
{0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, -8, 3, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 6, -10, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2},
{0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, -5, 7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1},
/* 191-200 */
{0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -10, 0, 0, 0, 0, 0, -2},
{1, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0},
/* 201-210 */
{0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2},
{2, 0, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 8, -14, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
/* 211-220 */
{0, 0, 0, 0, 1, 0, 0, 8, -15, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2},
{2, 0, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0},
/* 221-230 */
{2, 0, 0, -2, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -9, 4, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -2},
/* 231-240 */
{0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1},
{0, 0, 0, 0, 0, 0, 7, -11, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2},
{0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0},
{2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 8, -15, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, -1},
/* 241-250 */
{0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2},
{0, 0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0},
/* 251-260 */
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0},
{1, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1},
/* 261-270 */
{0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2},
{2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 5, 0, 0, 0},
{2, 0, 0, -2, -1, 0, -6, 8, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2},
{0, 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0},
/* 271-280 */
{0, 0, 1, -1, 0, 0, 0, -1, 0, -2, 5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 6, -15, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2},
{1, 0, 0, -1, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2},
/* 281-290 */
{0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1},
{0, 0, 2, -2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 6, -11, 0, 0, 0, 0, -2},
/* 291-300 */
{0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 9, -12, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1},
{0, 0, 1, -1, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -1},
/* 301-310 */
{0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, -5, 0, 0, 0, 0, -2},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 3, -1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2},
/* 311-320 */
{0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1},
{0, 0, 1, -1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2},
{0, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0},
/* 321-330 */
{0, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0},
{2, 0, -1, -1, -1, 0, 0, -1, 0, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 5, -10, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 8, -13, 0, 0, 0, 0, 0, 1},
{0, 0, 2, -2, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0},
/* 331-340 */
{0, 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 2, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, -2},
/* 341-350 */
{0, 0, 0, 0, 0, 0, 0, 8, -15, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 7, -13, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2},
{0, 0, 2, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 8, -10, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1},
/* 351-360 */
{0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0},
{2, 0, 0, -2, -1, 0, 0, -5, 6, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, -2},
{2, 0, -1, -1, -1, 0, 0, 3, -7, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0},
/* 361-370 */
{2, 0, 0, -2, 0, 0, 0, -2, 0, 4, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 6, -11, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2},
{1, 0, -2, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{0, 0, 0, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1},
/* 371-380 */
{0, 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2},
{0, 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 7, -13, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2},
/* 381-390 */
{0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0},
{2, 0, 0, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{2, 0, -1, -1, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{1, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{1, 0, -1, 1, -1, 0, -18, 17, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 2, -2, -1, 0, -5, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0},
/* 391-400 */
{0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -16, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2},
{0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0},
{2, 0, -1, -1, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -10, 0, 0, 0, 0, 0, -1},
{0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2},
{2, 0, 0, -2, -1, 0, 0, -2, 0, 4, -5, 0, 0, 0},
/* 401-410 */
{2, 0, 0, -2, -1, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{2, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0},
{1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0},
{1, 0, -1, -1, -1, 0, 20, -20, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0},
/* 411-420 */
{0, 0, 0, 0, 0, 0, 9, -11, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1},
{0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0},
{0, 0, 1, -1, 2, 0, 0, -1, 0, -2, 5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0},
/* 421-430 */
{0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, -2},
{1, 0, 0, -2, 0, 0, 20, -21, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -12, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 8, -12, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 9, -17, 0, 0, 0, 0, 0},
/* 431-440 */
{0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, -7, 0, 0, 0, 0, -2},
{1, 0, 0, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0},
{1, 0, -2, 0, -2, 0, -10, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -2},
{1, 0, -2, -2, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
/* 441-450 */
{0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0},
{0, 0, 1, -1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -10, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, -2},
/* 451-460 */
{0, 0, 0, 0, 0, 0, 0, 1, 0, -5, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1},
{1, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0},
{2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 6, -10, 0, 0, 0, 0, -2},
/* 461-470 */
{1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0},
{0, 0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0},
/* 471-480 */
{0, 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -10, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 3, -8, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2},
/* 481-490 */
{0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1},
{2, 0, 0, -2, -1, 0, 0, -6, 8, 0, 0, 0, 0, 0},
{2, 0, -1, -1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -1},
/* 491-500 */
{0, 0, 1, -1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0},
{2, 0, 0, -2, -1, 0, 0, -2, 0, 3, -1, 0, 0, 0},
{1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{1, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0},
/* 501-510 */
{1, 0, 0, -1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0},
{1, 0, -1, 0, -1, 0, -3, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 7, -13, 0, 0, 0, 0, 0},
/* 511-520 */
{0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 7, -11, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1},
/* 521-530 */
{0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 9, -17, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0},
/* 531-540 */
{2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 17, -16, 0, -2, 0, 0, 0, 0},
{1, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0},
/* 541-550 */
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2},
{0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2},
{2, 0, 0, -2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0},
/* 551-560 */
{1, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0},
{0, 0, 1, -1, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0},
/* 561-570 */
{0, 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0},
{2, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0},
{1, 0, 0, 0, 1, 0, -10, 3, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, -1, 0, -10, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0},
/* 571-580 */
{0, 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0},
{2, 0, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{2, 0, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 5, -5, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 1, 5, 0, 0, 0},
{2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0},
/* 581-590 */
{2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0},
{2, 0, 0, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0},
{2, 0, -2, 0, -2, 0, 0, 5, -9, 0, 0, 0, 0, 0},
{2, 0, -1, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0},
{1, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{1, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0},
{1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0},
{1, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0},
/* 591-600 */
{1, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0},
{1, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0},
{1, 0, -2, -2, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0},
{1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, -1, -1, 0, 0, 0, 8, -15, 0, 0, 0, 0, 0},
{0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0},
{0, 0, 2, -2, 1, 0, 0, -10, 15, 0, 0, 0, 0, 0},
{0, 0, 2, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0},
/* 601-610 */
{0, 0, 1, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0},
{0, 0, 1, -1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0},
{0, 0, 1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -1, -1, 0, -5, 7, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0},
/* 611-620 */
{0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 9, -13, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 8, -14, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 8, -11, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -2},
/* 621-630 */
{0, 0, 0, 0, 0, 0, 5, -6, -4, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 7, -12, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, -2},
/* 631-640 */
{0, 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 6, -10, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -1},
{0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 5, -16, 4, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 5, -13, 0, 0, 0, 0, -2},
/* 641-650 */
{0, 0, 0, 0, 0, 0, 0, 3, 0, -5, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, -9, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 2, -8, 1, 5, 0, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0},
/* 651-NFPL */
{0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 3, 0, -2},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2},
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
}
/* Number of frequencies: planetary */
NFPL := len(mfapl)
/* Pointers into amplitudes array, one pointer per frequency */
nc := []int{
/* 1-100 */
1, 21, 37, 51, 65, 79, 91, 103, 115, 127,
139, 151, 163, 172, 184, 196, 207, 219, 231, 240,
252, 261, 273, 285, 297, 309, 318, 327, 339, 351,
363, 372, 384, 396, 405, 415, 423, 435, 444, 452,
460, 467, 474, 482, 490, 498, 506, 513, 521, 528,
536, 543, 551, 559, 566, 574, 582, 590, 597, 605,
613, 620, 628, 636, 644, 651, 658, 666, 674, 680,
687, 695, 702, 710, 717, 725, 732, 739, 746, 753,
760, 767, 774, 782, 790, 798, 805, 812, 819, 826,
833, 840, 846, 853, 860, 867, 874, 881, 888, 895,
/* 101-200 */
901, 908, 914, 921, 928, 934, 941, 948, 955, 962,
969, 976, 982, 989, 996, 1003, 1010, 1017, 1024, 1031,
1037, 1043, 1050, 1057, 1064, 1071, 1078, 1084, 1091, 1098,
1104, 1112, 1118, 1124, 1131, 1138, 1145, 1151, 1157, 1164,
1171, 1178, 1185, 1192, 1199, 1205, 1212, 1218, 1226, 1232,
1239, 1245, 1252, 1259, 1266, 1272, 1278, 1284, 1292, 1298,
1304, 1310, 1316, 1323, 1329, 1335, 1341, 1347, 1353, 1359,
1365, 1371, 1377, 1383, 1389, 1396, 1402, 1408, 1414, 1420,
1426, 1434, 1440, 1446, 1452, 1459, 1465, 1471, 1477, 1482,
1488, 1493, 1499, 1504, 1509, 1514, 1520, 1527, 1532, 1538,
/* 201-300 */
1543, 1548, 1553, 1558, 1564, 1569, 1574, 1579, 1584, 1589,
1594, 1596, 1598, 1600, 1602, 1605, 1608, 1610, 1612, 1617,
1619, 1623, 1625, 1627, 1629, 1632, 1634, 1640, 1642, 1644,
1646, 1648, 1650, 1652, 1654, 1658, 1660, 1662, 1664, 1668,
1670, 1672, 1673, 1675, 1679, 1681, 1683, 1684, 1686, 1688,
1690, 1693, 1695, 1697, 1701, 1703, 1705, 1707, 1709, 1711,
1712, 1715, 1717, 1721, 1723, 1725, 1727, 1729, 1731, 1733,
1735, 1737, 1739, 1741, 1743, 1745, 1747, 1749, 1751, 1753,
1755, 1757, 1759, 1761, 1762, 1764, 1766, 1768, 1769, 1771,
1773, 1775, 1777, 1779, 1781, 1783, 1785, 1787, 1788, 1790,
/* 301-400 */
1792, 1794, 1796, 1798, 1800, 1802, 1804, 1806, 1807, 1809,
1811, 1815, 1817, 1819, 1821, 1823, 1825, 1827, 1829, 1831,
1833, 1835, 1837, 1839, 1840, 1842, 1844, 1848, 1850, 1852,
1854, 1856, 1858, 1859, 1860, 1862, 1864, 1866, 1868, 1869,
1871, 1873, 1875, 1877, 1879, 1881, 1883, 1885, 1887, 1889,
1891, 1892, 1896, 1898, 1900, 1901, 1903, 1905, 1907, 1909,
1910, 1911, 1913, 1915, 1919, 1921, 1923, 1927, 1929, 1931,
1933, 1935, 1937, 1939, 1943, 1945, 1947, 1948, 1949, 1951,
1953, 1955, 1957, 1958, 1960, 1962, 1964, 1966, 1968, 1970,
1971, 1973, 1974, 1975, 1977, 1979, 1980, 1981, 1982, 1984,
/* 401-500 */
1986, 1988, 1990, 1992, 1994, 1995, 1997, 1999, 2001, 2003,
2005, 2007, 2008, 2009, 2011, 2013, 2015, 2017, 2019, 2021,
2023, 2024, 2025, 2027, 2029, 2031, 2033, 2035, 2037, 2041,
2043, 2045, 2046, 2047, 2049, 2051, 2053, 2055, 2056, 2057,
2059, 2061, 2063, 2065, 2067, 2069, 2070, 2071, 2072, 2074,
2076, 2078, 2080, 2082, 2084, 2086, 2088, 2090, 2092, 2094,
2095, 2096, 2097, 2099, 2101, 2105, 2106, 2107, 2108, 2109,
2110, 2111, 2113, 2115, 2119, 2121, 2123, 2125, 2127, 2129,
2131, 2133, 2135, 2136, 2137, 2139, 2141, 2143, 2145, 2147,
2149, 2151, 2153, 2155, 2157, 2159, 2161, 2163, 2165, 2167,
/* 501-600 */
2169, 2171, 2173, 2175, 2177, 2179, 2181, 2183, 2185, 2186,
2187, 2188, 2192, 2193, 2195, 2197, 2199, 2201, 2203, 2205,
2207, 2209, 2211, 2213, 2217, 2219, 2221, 2223, 2225, 2227,
2229, 2231, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240,
2241, 2244, 2246, 2248, 2250, 2252, 2254, 2256, 2258, 2260,
2262, 2264, 2266, 2268, 2270, 2272, 2274, 2276, 2278, 2280,
2282, 2284, 2286, 2288, 2290, 2292, 2294, 2296, 2298, 2300,
2302, 2303, 2304, 2305, 2306, 2307, 2309, 2311, 2313, 2315,
2317, 2319, 2321, 2323, 2325, 2327, 2329, 2331, 2333, 2335,
2337, 2341, 2343, 2345, 2347, 2349, 2351, 2352, 2355, 2356,
/* 601-700 */
2357, 2358, 2359, 2361, 2363, 2364, 2365, 2366, 2367, 2368,
2369, 2370, 2371, 2372, 2373, 2374, 2376, 2378, 2380, 2382,
2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393,
2394, 2395, 2396, 2397, 2398, 2399, 2400, 2401, 2402, 2403,
2404, 2405, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413,
2414, 2415, 2417, 2418, 2430, 2438, 2445, 2453, 2460, 2468,
2474, 2480, 2488, 2496, 2504, 2512, 2520, 2527, 2535, 2543,
2550, 2558, 2566, 2574, 2580, 2588, 2596, 2604, 2612, 2619,
2627, 2634, 2642, 2648, 2656, 2664, 2671, 2679, 2685, 2693,
2701, 2709, 2717, 2725, 2733, 2739, 2747, 2753, 2761, 2769,
/* 701-800 */
2777, 2785, 2793, 2801, 2809, 2817, 2825, 2833, 2841, 2848,
2856, 2864, 2872, 2878, 2884, 2892, 2898, 2906, 2914, 2922,
2930, 2938, 2944, 2952, 2958, 2966, 2974, 2982, 2988, 2996,
3001, 3009, 3017, 3025, 3032, 3039, 3045, 3052, 3059, 3067,
3069, 3076, 3083, 3090, 3098, 3105, 3109, 3111, 3113, 3120,
3124, 3128, 3132, 3136, 3140, 3144, 3146, 3150, 3158, 3161,
3165, 3166, 3168, 3172, 3176, 3180, 3182, 3185, 3189, 3193,
3194, 3197, 3200, 3204, 3208, 3212, 3216, 3219, 3221, 3222,
3226, 3230, 3234, 3238, 3242, 3243, 3247, 3251, 3254, 3258,
3262, 3266, 3270, 3274, 3275, 3279, 3283, 3287, 3289, 3293,
/* 801-900 */
3296, 3300, 3303, 3307, 3311, 3315, 3319, 3321, 3324, 3327,
3330, 3334, 3338, 3340, 3342, 3346, 3350, 3354, 3358, 3361,
3365, 3369, 3373, 3377, 3381, 3385, 3389, 3393, 3394, 3398,
3402, 3406, 3410, 3413, 3417, 3421, 3425, 3429, 3433, 3435,
3439, 3443, 3446, 3450, 3453, 3457, 3458, 3461, 3464, 3468,
3472, 3476, 3478, 3481, 3485, 3489, 3493, 3497, 3501, 3505,
3507, 3511, 3514, 3517, 3521, 3524, 3525, 3527, 3529, 3533,
3536, 3540, 3541, 3545, 3548, 3551, 3555, 3559, 3563, 3567,
3569, 3570, 3574, 3576, 3578, 3582, 3586, 3590, 3593, 3596,
3600, 3604, 3608, 3612, 3616, 3620, 3623, 3626, 3630, 3632,
/* 901-1000 */
3636, 3640, 3643, 3646, 3648, 3652, 3656, 3660, 3664, 3667,
3669, 3671, 3675, 3679, 3683, 3687, 3689, 3693, 3694, 3695,
3699, 3703, 3705, 3707, 3710, 3713, 3717, 3721, 3725, 3729,
3733, 3736, 3740, 3744, 3748, 3752, 3754, 3757, 3759, 3763,
3767, 3770, 3773, 3777, 3779, 3783, 3786, 3790, 3794, 3798,
3801, 3805, 3809, 3813, 3817, 3821, 3825, 3827, 3831, 3835,
3836, 3837, 3840, 3844, 3848, 3852, 3856, 3859, 3863, 3867,
3869, 3871, 3875, 3879, 3883, 3887, 3890, 3894, 3898, 3901,
3905, 3909, 3913, 3917, 3921, 3922, 3923, 3924, 3926, 3930,
3932, 3936, 3938, 3940, 3944, 3948, 3952, 3956, 3959, 3963,
/* 1001-1100 */
3965, 3969, 3973, 3977, 3979, 3981, 3982, 3986, 3989, 3993,
3997, 4001, 4004, 4006, 4009, 4012, 4016, 4020, 4024, 4026,
4028, 4032, 4036, 4040, 4044, 4046, 4050, 4054, 4058, 4060,
4062, 4063, 4064, 4068, 4071, 4075, 4077, 4081, 4083, 4087,
4089, 4091, 4095, 4099, 4101, 4103, 4105, 4107, 4111, 4115,
4119, 4123, 4127, 4129, 4131, 4135, 4139, 4141, 4143, 4145,
4149, 4153, 4157, 4161, 4165, 4169, 4173, 4177, 4180, 4183,
4187, 4191, 4195, 4198, 4201, 4205, 4209, 4212, 4213, 4216,
4217, 4221, 4223, 4226, 4230, 4234, 4236, 4240, 4244, 4248,
4252, 4256, 4258, 4262, 4264, 4266, 4268, 4270, 4272, 4276,
/* 1101-1200 */
4279, 4283, 4285, 4287, 4289, 4293, 4295, 4299, 4300, 4301,
4305, 4309, 4313, 4317, 4319, 4323, 4325, 4329, 4331, 4333,
4335, 4337, 4341, 4345, 4349, 4351, 4353, 4357, 4361, 4365,
4367, 4369, 4373, 4377, 4381, 4383, 4387, 4389, 4391, 4395,
4399, 4403, 4407, 4411, 4413, 4414, 4415, 4418, 4419, 4421,
4423, 4427, 4429, 4431, 4433, 4435, 4437, 4439, 4443, 4446,
4450, 4452, 4456, 4458, 4460, 4462, 4466, 4469, 4473, 4477,
4481, 4483, 4487, 4489, 4491, 4493, 4497, 4499, 4501, 4504,
4506, 4510, 4513, 4514, 4515, 4518, 4521, 4522, 4525, 4526,
4527, 4530, 4533, 4534, 4537, 4541, 4542, 4543, 4544, 4545,
/* 1201-1300 */
4546, 4547, 4550, 4553, 4554, 4555, 4558, 4561, 4564, 4567,
4568, 4571, 4574, 4575, 4578, 4581, 4582, 4585, 4586, 4588,
4590, 4592, 4596, 4598, 4602, 4604, 4608, 4612, 4613, 4616,
4619, 4622, 4623, 4624, 4625, 4626, 4629, 4632, 4633, 4636,
4639, 4640, 4641, 4642, 4643, 4644, 4645, 4648, 4649, 4650,
4651, 4652, 4653, 4656, 4657, 4660, 4661, 4664, 4667, 4670,
4671, 4674, 4675, 4676, 4677, 4678, 4681, 4682, 4683, 4684,
4687, 4688, 4689, 4692, 4693, 4696, 4697, 4700, 4701, 4702,
4703, 4704, 4707, 4708, 4711, 4712, 4715, 4716, 4717, 4718,
4719, 4720, 4721, 4722, 4723, 4726, 4729, 4730, 4733, 4736,
/* 1301-(NFLS+NFPL) */
4737, 4740, 4741, 4742, 4745, 4746, 4749, 4752, 4753,
}
/* Amplitude coefficients (microarcsec); indexed using the nc array. */
a := []float64{
/* 1-105 */
-6844318.44, 9205236.26, 1328.67, 1538.18, 205833.11,
153041.79, -3309.73, 853.32, 2037.98, -2301.27,
81.46, 120.56, -20.39, -15.22, 1.73, -1.61, -0.10, 0.11,
-0.02, -0.02, -523908.04, 573033.42, -544.75, -458.66,
12814.01, 11714.49, 198.97, -290.91, 155.74, -143.27,
-2.75, -1.03, -1.27, -1.16, 0.00, -0.01, -90552.22,
97846.69, 111.23, 137.41, 2187.91, 2024.68, 41.44, -51.26,
26.92, -24.46, -0.46, -0.28, -0.22, -0.20, 82168.76,
-89618.24, -27.64, -29.05, -2004.36, -1837.32,
-36.07, 48.00, -24.43, 22.41, 0.47, 0.24, 0.20, 0.18,
58707.02, 7387.02, 470.05, -192.40, 164.33, -1312.21,
-179.73, -28.93, -17.36, -1.83, -0.50, 3.57, 0.00, 0.13,
-20557.78, 22438.42, -20.84, -17.40, 501.82, 459.68,
59.20, -67.30, 6.08, -5.61, -1.36, -1.19, 28288.28,
-674.99, -34.69, 35.80, -15.07, -632.54, -11.19, 0.78, -8.41,
0.17, 0.01, 0.07, -15406.85, 20069.50, 15.12,
/* 106-219 */
31.80, 448.76, 344.50, -5.77, 1.41, 4.59, -5.02, 0.17,
0.24, -11991.74, 12902.66, 32.46, 36.70, 288.49,
268.14, 5.70, -7.06, 3.57, -3.23, -0.06, -0.04,
-8584.95, -9592.72, 4.42, -13.20, -214.50, 192.06,
23.87, 29.83, 2.54, 2.40, 0.60, -0.48, 5095.50,
-6918.22, 7.19, 3.92, -154.91, -113.94, 2.86, -1.04,
-1.52, 1.73, -0.07, -0.10, -4910.93, -5331.13,
0.76, 0.40, -119.21, 109.81, 2.16, 3.20, 1.46, 1.33,
0.04, -0.02, -6245.02, -123.48, -6.68, -8.20, -2.76,
139.64, 2.71, 0.15, 1.86, 2511.85, -3323.89, 1.07,
-0.90, -74.33, -56.17, 1.16, -0.01, -0.75, 0.83, -0.02,
-0.04, 2307.58, 3143.98, -7.52, 7.50, 70.31, -51.60, 1.46,
0.16, -0.69, -0.79, 0.02, -0.05, 2372.58, 2554.51, 5.93,
-6.60, 57.12, -53.05, -0.96, -1.24, -0.71, -0.64, -0.01,
-2053.16, 2636.13, 5.13, 7.80, 58.94, 45.91, -0.42,
-0.12, 0.61, -0.66, 0.02, 0.03, -1825.49,
/* 220-339 */
-2423.59, 1.23, -2.00, -54.19, 40.82, -1.07, -1.02,
0.54, 0.61, -0.04, 0.04, 2521.07, -122.28, -5.97, 2.90,
-2.73, -56.37, -0.82, 0.13, -0.75, -1534.09, 1645.01,
6.29, 6.80, 36.78, 34.30, 0.92, -1.25, 0.46, -0.41,
-0.02, -0.01, 1898.27, 47.70, -0.72, 2.50, 1.07, -42.45,
-0.94, 0.02, -0.56, -1292.02, -1387.00, 0.00,
0.00, -31.01, 28.89, 0.68, 0.00, 0.38, 0.35, -0.01,
-0.01, -1234.96, 1323.81, 5.21, 5.90, 29.60, 27.61,
0.74, -1.22, 0.37, -0.33, -0.02, -0.01, 1137.48,
-1233.89, -0.04, -0.30, -27.59, -25.43, -0.61, 1.00,
-0.34, 0.31, 0.01, 0.01, -813.13, -1075.60, 0.40,
0.30, -24.05, 18.18, -0.40, -0.01, 0.24, 0.27, -0.01,
0.01, 1163.22, -60.90, -2.94, 1.30, -1.36, -26.01, -0.58,
0.07, -0.35, 1029.70, -55.55, -2.63, 1.10, -1.25, -23.02,
-0.52, 0.06, -0.31, -556.26, 852.85, 3.16, -4.48, 19.06,
12.44, -0.81, -0.27, 0.17, -0.21, 0.00, 0.02, -603.52,
/* 340-467 */
-800.34, 0.44, 0.10, -17.90, 13.49, -0.08, -0.01, 0.18,
0.20, -0.01, 0.01, -628.24, 684.99, -0.64, -0.50, 15.32,
14.05, 3.18, -4.19, 0.19, -0.17, -0.09, -0.07, -866.48,
-16.26, 0.52, -1.30, -0.36, 19.37, 0.43, -0.01, 0.26,
-512.37, 695.54, -1.47, -1.40, 15.55, 11.46, -0.16, 0.03,
0.15, -0.17, 0.01, 0.01, 506.65, 643.75, 2.54, -2.62,
14.40, -11.33, -0.77, -0.06, -0.15, -0.16, 0.00, 0.01,
664.57, 16.81, -0.40, 1.00, 0.38, -14.86, -3.71, -0.09,
-0.20, 405.91, 522.11, 0.99, -1.50, 11.67, -9.08, -0.25,
-0.02, -0.12, -0.13, -305.78, 326.60, 1.75, 1.90, 7.30,
6.84, 0.20, -0.04, 300.99, -325.03, -0.44, -0.50, -7.27,
-6.73, -1.01, 0.01, 0.00, 0.08, 0.00, 0.02, 438.51,
10.47, -0.56, -0.20, 0.24, -9.81, -0.24, 0.01, -0.13,
-264.02, 335.24, 0.99, 1.40, 7.49, 5.90, -0.27, -0.02,
284.09, 307.03, 0.32, -0.40, 6.87, -6.35, -0.99, -0.01,
-250.54, 327.11, 0.08, 0.40, 7.31, 5.60, -0.30, 230.72,
/* 468-595 */
-304.46, 0.08, -0.10, -6.81, -5.16, 0.27, 229.78, 304.17,
-0.60, 0.50, 6.80, -5.14, 0.33, 0.01, 256.30, -276.81,
-0.28, -0.40, -6.19, -5.73, -0.14, 0.01, -212.82, 269.45,
0.84, 1.20, 6.02, 4.76, 0.14, -0.02, 196.64, 272.05,
-0.84, 0.90, 6.08, -4.40, 0.35, 0.02, 188.95, 272.22,
-0.12, 0.30, 6.09, -4.22, 0.34, -292.37, -5.10, -0.32,
-0.40, -0.11, 6.54, 0.14, 0.01, 161.79, -220.67, 0.24,
0.10, -4.93, -3.62, -0.08, 261.54, -19.94, -0.95, 0.20,
-0.45, -5.85, -0.13, 0.02, 142.16, -190.79, 0.20, 0.10,
-4.27, -3.18, -0.07, 187.95, -4.11, -0.24, 0.30, -0.09,
-4.20, -0.09, 0.01, 0.00, 0.00, -79.08, 167.90, 0.04,
0.00, 3.75, 1.77, 121.98, 131.04, -0.08, 0.10, 2.93,
-2.73, -0.06, -172.95, -8.11, -0.40, -0.20, -0.18, 3.87,
0.09, 0.01, -160.15, -55.30, -14.04, 13.90, -1.23, 3.58,
0.40, 0.31, -115.40, 123.20, 0.60, 0.70, 2.75, 2.58,
0.08, -0.01, -168.26, -2.00, 0.20, -0.20, -0.04, 3.76,
/* 596-723 */
0.08, -114.49, 123.20, 0.32, 0.40, 2.75, 2.56, 0.07,
-0.01, 112.14, 120.70, 0.28, -0.30, 2.70, -2.51, -0.07,
-0.01, 161.34, 4.03, 0.20, 0.20, 0.09, -3.61, -0.08,
91.31, 126.64, -0.40, 0.40, 2.83, -2.04, -0.04, 0.01,
105.29, 112.90, 0.44, -0.50, 2.52, -2.35, -0.07, -0.01,
98.69, -106.20, -0.28, -0.30, -2.37, -2.21, -0.06, 0.01,
86.74, -112.94, -0.08, -0.20, -2.53, -1.94, -0.05, -134.81,
3.51, 0.20, -0.20, 0.08, 3.01, 0.07, 79.03, 107.31,
-0.24, 0.20, 2.40, -1.77, -0.04, 0.01, 132.81, -10.77,
-0.52, 0.10, -0.24, -2.97, -0.07, 0.01, -130.31, -0.90,
0.04, 0.00, 0.00, 2.91, -78.56, 85.32, 0.00, 0.00,
1.91, 1.76, 0.04, 0.00, 0.00, -41.53, 89.10, 0.02,
0.00, 1.99, 0.93, 66.03, -71.00, -0.20, -0.20, -1.59,
-1.48, -0.04, 60.50, 64.70, 0.36, -0.40, 1.45, -1.35,
-0.04, -0.01, -52.27, -70.01, 0.00, 0.00, -1.57, 1.17,
0.03, -52.95, 66.29, 0.32, 0.40, 1.48, 1.18, 0.04,
/* 724-851 */
-0.01, 51.02, 67.25, 0.00, 0.00, 1.50, -1.14, -0.03,
-55.66, -60.92, 0.16, -0.20, -1.36, 1.24, 0.03, -54.81,
-59.20, -0.08, 0.20, -1.32, 1.23, 0.03, 51.32, -55.60,
0.00, 0.00, -1.24, -1.15, -0.03, 48.29, 51.80, 0.20,
-0.20, 1.16, -1.08, -0.03, -45.59, -49.00, -0.12, 0.10,
-1.10, 1.02, 0.03, 40.54, -52.69, -0.04, -0.10, -1.18,
-0.91, -0.02, -40.58, -49.51, -1.00, 1.00, -1.11, 0.91,
0.04, 0.02, -43.76, 46.50, 0.36, 0.40, 1.04, 0.98,
0.03, -0.01, 62.65, -5.00, -0.24, 0.00, -0.11, -1.40,
-0.03, 0.01, -38.57, 49.59, 0.08, 0.10, 1.11, 0.86,
0.02, -33.22, -44.04, 0.08, -0.10, -0.98, 0.74, 0.02,
37.15, -39.90, -0.12, -0.10, -0.89, -0.83, -0.02, 36.68,
-39.50, -0.04, -0.10, -0.88, -0.82, -0.02, -53.22, -3.91,
-0.20, 0.00, -0.09, 1.19, 0.03, 32.43, -42.19, -0.04,
-0.10, -0.94, -0.73, -0.02, -51.00, -2.30, -0.12, -0.10,
0.00, 1.14, -29.53, -39.11, 0.04, 0.00, -0.87, 0.66,
/* 852-979 */
0.02, 28.50, -38.92, -0.08, -0.10, -0.87, -0.64, -0.02,
26.54, 36.95, -0.12, 0.10, 0.83, -0.59, -0.01, 26.54,
34.59, 0.04, -0.10, 0.77, -0.59, -0.02, 28.35, -32.55,
-0.16, 0.20, -0.73, -0.63, -0.01, -28.00, 30.40, 0.00,
0.00, 0.68, 0.63, 0.01, -27.61, 29.40, 0.20, 0.20,
0.66, 0.62, 0.02, 40.33, 0.40, -0.04, 0.10, 0.00,
-0.90, -23.28, 31.61, -0.08, -0.10, 0.71, 0.52, 0.01,
37.75, 0.80, 0.04, 0.10, 0.00, -0.84, 23.66, 25.80,
0.00, 0.00, 0.58, -0.53, -0.01, 21.01, -27.91, 0.00,
0.00, -0.62, -0.47, -0.01, -34.81, 2.89, 0.04, 0.00,
0.00, 0.78, -23.49, -25.31, 0.00, 0.00, -0.57, 0.53,
0.01, -23.47, 25.20, 0.16, 0.20, 0.56, 0.52, 0.02,
19.58, 27.50, -0.12, 0.10, 0.62, -0.44, -0.01, -22.67,
-24.40, -0.08, 0.10, -0.55, 0.51, 0.01, -19.97, 25.00,
0.12, 0.20, 0.56, 0.45, 0.01, 21.28, -22.80, -0.08,
-0.10, -0.51, -0.48, -0.01, -30.47, 0.91, 0.04, 0.00,
/* 980-1107 */
0.00, 0.68, 18.58, 24.00, 0.04, -0.10, 0.54, -0.42,
-0.01, -18.02, 24.40, -0.04, -0.10, 0.55, 0.40, 0.01,
17.74, 22.50, 0.08, -0.10, 0.50, -0.40, -0.01, -19.41,
20.70, 0.08, 0.10, 0.46, 0.43, 0.01, -18.64, 20.11,
0.00, 0.00, 0.45, 0.42, 0.01, -16.75, 21.60, 0.04,
0.10, 0.48, 0.37, 0.01, -18.42, -20.00, 0.00, 0.00,
-0.45, 0.41, 0.01, -26.77, 1.41, 0.08, 0.00, 0.00,
0.60, -26.17, -0.19, 0.00, 0.00, 0.00, 0.59, -15.52,
20.51, 0.00, 0.00, 0.46, 0.35, 0.01, -25.42, -1.91,
-0.08, 0.00, -0.04, 0.57, 0.45, -17.42, 18.10, 0.00,
0.00, 0.40, 0.39, 0.01, 16.39, -17.60, -0.08, -0.10,
-0.39, -0.37, -0.01, -14.37, 18.91, 0.00, 0.00, 0.42,
0.32, 0.01, 23.39, -2.40, -0.12, 0.00, 0.00, -0.52,
14.32, -18.50, -0.04, -0.10, -0.41, -0.32, -0.01, 15.69,
17.08, 0.00, 0.00, 0.38, -0.35, -0.01, -22.99, 0.50,
0.04, 0.00, 0.00, 0.51, 0.00, 0.00, 14.47, -17.60,
/* 1108-1235 */
-0.01, 0.00, -0.39, -0.32, -13.33, 18.40, -0.04, -0.10,
0.41, 0.30, 22.47, -0.60, -0.04, 0.00, 0.00, -0.50,
-12.78, -17.41, 0.04, 0.00, -0.39, 0.29, 0.01, -14.10,
-15.31, 0.04, 0.00, -0.34, 0.32, 0.01, 11.98, 16.21,
-0.04, 0.00, 0.36, -0.27, -0.01, 19.65, -1.90, -0.08,
0.00, 0.00, -0.44, 19.61, -1.50, -0.08, 0.00, 0.00,
-0.44, 13.41, -14.30, -0.04, -0.10, -0.32, -0.30, -0.01,
-13.29, 14.40, 0.00, 0.00, 0.32, 0.30, 0.01, 11.14,
-14.40, -0.04, 0.00, -0.32, -0.25, -0.01, 12.24, -13.38,
0.04, 0.00, -0.30, -0.27, -0.01, 10.07, -13.81, 0.04,
0.00, -0.31, -0.23, -0.01, 10.46, 13.10, 0.08, -0.10,
0.29, -0.23, -0.01, 16.55, -1.71, -0.08, 0.00, 0.00,
-0.37, 9.75, -12.80, 0.00, 0.00, -0.29, -0.22, -0.01,
9.11, 12.80, 0.00, 0.00, 0.29, -0.20, 0.00, 0.00,
-6.44, -13.80, 0.00, 0.00, -0.31, 0.14, -9.19, -12.00,
0.00, 0.00, -0.27, 0.21, -10.30, 10.90, 0.08, 0.10,
/* 1236-1363 */
0.24, 0.23, 0.01, 14.92, -0.80, -0.04, 0.00, 0.00,
-0.33, 10.02, -10.80, 0.00, 0.00, -0.24, -0.22, -0.01,
-9.75, 10.40, 0.04, 0.00, 0.23, 0.22, 0.01, 9.67,
-10.40, -0.04, 0.00, -0.23, -0.22, -0.01, -8.28, -11.20,
0.04, 0.00, -0.25, 0.19, 13.32, -1.41, -0.08, 0.00,
0.00, -0.30, 8.27, 10.50, 0.04, 0.00, 0.23, -0.19,
0.00, 0.00, 13.13, 0.00, 0.00, 0.00, 0.00, -0.29,
-12.93, 0.70, 0.04, 0.00, 0.00, 0.29, 7.91, -10.20,
0.00, 0.00, -0.23, -0.18, -7.84, -10.00, -0.04, 0.00,
-0.22, 0.18, 7.44, 9.60, 0.00, 0.00, 0.21, -0.17,
-7.64, 9.40, 0.08, 0.10, 0.21, 0.17, 0.01, -11.38,
0.60, 0.04, 0.00, 0.00, 0.25, -7.48, 8.30, 0.00,
0.00, 0.19, 0.17, -10.98, -0.20, 0.00, 0.00, 0.00,
0.25, 10.98, 0.20, 0.00, 0.00, 0.00, -0.25, 7.40,
-7.90, -0.04, 0.00, -0.18, -0.17, -6.09, 8.40, -0.04,
0.00, 0.19, 0.14, -6.94, -7.49, 0.00, 0.00, -0.17,
/* 1364-1491 */
0.16, 6.92, 7.50, 0.04, 0.00, 0.17, -0.15, 6.20,
8.09, 0.00, 0.00, 0.18, -0.14, -6.12, 7.80, 0.04,
0.00, 0.17, 0.14, 5.85, -7.50, 0.00, 0.00, -0.17,
-0.13, -6.48, 6.90, 0.08, 0.10, 0.15, 0.14, 0.01,
6.32, 6.90, 0.00, 0.00, 0.15, -0.14, 5.61, -7.20,
0.00, 0.00, -0.16, -0.13, 9.07, 0.00, 0.00, 0.00,
0.00, -0.20, 5.25, 6.90, 0.00, 0.00, 0.15, -0.12,
-8.47, -0.40, 0.00, 0.00, 0.00, 0.19, 6.32, -5.39,
-1.11, 1.10, -0.12, -0.14, 0.02, 0.02, 5.73, -6.10,
-0.04, 0.00, -0.14, -0.13, 4.70, 6.60, -0.04, 0.00,
0.15, -0.11, -4.90, -6.40, 0.00, 0.00, -0.14, 0.11,
-5.33, 5.60, 0.04, 0.10, 0.13, 0.12, 0.01, -4.81,
6.00, 0.04, 0.00, 0.13, 0.11, 5.13, 5.50, 0.04,
0.00, 0.12, -0.11, 4.50, 5.90, 0.00, 0.00, 0.13,
-0.10, -4.22, 6.10, 0.00, 0.00, 0.14, -4.53, 5.70,
0.00, 0.00, 0.13, 0.10, 4.18, 5.70, 0.00, 0.00,
/* 1492-1619 */
0.13, -4.75, -5.19, 0.00, 0.00, -0.12, 0.11, -4.06,
5.60, 0.00, 0.00, 0.13, -3.98, 5.60, -0.04, 0.00,
0.13, 4.02, -5.40, 0.00, 0.00, -0.12, 4.49, -4.90,
-0.04, 0.00, -0.11, -0.10, -3.62, -5.40, -0.16, 0.20,
-0.12, 0.00, 0.01, 4.38, 4.80, 0.00, 0.00, 0.11,
-6.40, -0.10, 0.00, 0.00, 0.00, 0.14, -3.98, 5.00,
0.04, 0.00, 0.11, -3.82, -5.00, 0.00, 0.00, -0.11,
-3.71, 5.07, 0.00, 0.00, 0.11, 4.14, 4.40, 0.00,
0.00, 0.10, -6.01, -0.50, -0.04, 0.00, 0.00, 0.13,
-4.04, 4.39, 0.00, 0.00, 0.10, 3.45, -4.72, 0.00,
0.00, -0.11, 3.31, 4.71, 0.00, 0.00, 0.11, 3.26,
-4.50, 0.00, 0.00, -0.10, -3.26, -4.50, 0.00, 0.00,
-0.10, -3.34, -4.40, 0.00, 0.00, -0.10, -3.74, -4.00,
3.70, 4.00, 3.34, -4.30, 3.30, -4.30, -3.66, 3.90,
0.04, 3.66, 3.90, 0.04, -3.62, -3.90, -3.61, 3.90,
-0.20, 5.30, 0.00, 0.00, 0.12, 3.06, 4.30, 3.30,
/* 1620-1747 */
4.00, 0.40, 0.20, 3.10, 4.10, -3.06, 3.90, -3.30,
-3.60, -3.30, 3.36, 0.01, 3.14, 3.40, -4.57, -0.20,
0.00, 0.00, 0.00, 0.10, -2.70, -3.60, 2.94, -3.20,
-2.90, 3.20, 2.47, -3.40, 2.55, -3.30, 2.80, -3.08,
2.51, 3.30, -4.10, 0.30, -0.12, -0.10, 4.10, 0.20,
-2.74, 3.00, 2.46, 3.23, -3.66, 1.20, -0.20, 0.20,
3.74, -0.40, -2.51, -2.80, -3.74, 2.27, -2.90, 0.00,
0.00, -2.50, 2.70, -2.51, 2.60, -3.50, 0.20, 3.38,
-2.22, -2.50, 3.26, -0.40, 1.95, -2.60, 3.22, -0.40,
-0.04, -1.79, -2.60, 1.91, 2.50, 0.74, 3.05, -0.04,
0.08, 2.11, -2.30, -2.11, 2.20, -1.87, -2.40, 2.03,
-2.20, -2.03, 2.20, 2.98, 0.00, 0.00, 2.98, -1.71,
2.40, 2.94, -0.10, -0.12, 0.10, 1.67, 2.40, -1.79,
2.30, -1.79, 2.20, -1.67, 2.20, 1.79, -2.00, 1.87,
-1.90, 1.63, -2.10, -1.59, 2.10, 1.55, -2.10, -1.55,
2.10, -2.59, -0.20, -1.75, -1.90, -1.75, 1.90, -1.83,
/* 1748-1875 */
-1.80, 1.51, 2.00, -1.51, -2.00, 1.71, 1.80, 1.31,
2.10, -1.43, 2.00, 1.43, 2.00, -2.43, -1.51, 1.90,
-1.47, 1.90, 2.39, 0.20, -2.39, 1.39, 1.90, 1.39,
-1.80, 1.47, -1.60, 1.47, -1.60, 1.43, -1.50, -1.31,
1.60, 1.27, -1.60, -1.27, 1.60, 1.27, -1.60, 2.03,
1.35, 1.50, -1.39, -1.40, 1.95, -0.20, -1.27, 1.49,
1.19, 1.50, 1.27, 1.40, 1.15, 1.50, 1.87, -0.10,
-1.12, -1.50, 1.87, -1.11, -1.50, -1.11, -1.50, 0.00,
0.00, 1.19, 1.40, 1.27, -1.30, -1.27, -1.30, -1.15,
1.40, -1.23, 1.30, -1.23, -1.30, 1.22, -1.29, 1.07,
-1.40, 1.75, -0.20, -1.03, -1.40, -1.07, 1.20, -1.03,
1.15, 1.07, 1.10, 1.51, -1.03, 1.10, 1.03, -1.10,
0.00, 0.00, -1.03, -1.10, 0.91, -1.20, -0.88, -1.20,
-0.88, 1.20, -0.95, 1.10, -0.95, -1.10, 1.43, -1.39,
0.95, -1.00, -0.95, 1.00, -0.80, 1.10, 0.91, -1.00,
-1.35, 0.88, 1.00, -0.83, 1.00, -0.91, 0.90, 0.91,
/* 1876-2003 */
0.90, 0.88, -0.90, -0.76, -1.00, -0.76, 1.00, 0.76,
1.00, -0.72, 1.00, 0.84, -0.90, 0.84, 0.90, 1.23,
0.00, 0.00, -0.52, -1.10, -0.68, 1.00, 1.19, -0.20,
1.19, 0.76, 0.90, 1.15, -0.10, 1.15, -0.10, 0.72,
-0.90, -1.15, -1.15, 0.68, 0.90, -0.68, 0.90, -1.11,
0.00, 0.00, 0.20, 0.79, 0.80, -1.11, -0.10, 0.00,
0.00, -0.48, -1.00, -0.76, -0.80, -0.72, -0.80, -1.07,
-0.10, 0.64, 0.80, -0.64, -0.80, 0.64, 0.80, 0.40,
0.60, 0.52, -0.50, -0.60, -0.80, -0.71, 0.70, -0.99,
0.99, 0.56, 0.80, -0.56, 0.80, 0.68, -0.70, 0.68,
0.70, -0.95, -0.64, 0.70, 0.64, 0.70, -0.60, 0.70,
-0.60, -0.70, -0.91, -0.10, -0.51, 0.76, -0.91, -0.56,
0.70, 0.88, 0.88, -0.63, -0.60, 0.55, -0.60, -0.80,
0.80, -0.80, -0.52, 0.60, 0.52, 0.60, 0.52, -0.60,
-0.48, 0.60, 0.48, 0.60, 0.48, 0.60, -0.76, 0.44,
-0.60, 0.52, -0.50, -0.52, 0.50, 0.40, 0.60, -0.40,
/* 2004-2131 */
-0.60, 0.40, -0.60, 0.72, -0.72, -0.51, -0.50, -0.48,
0.50, 0.48, -0.50, -0.48, 0.50, -0.48, 0.50, 0.48,
-0.50, -0.48, -0.50, -0.68, -0.68, 0.44, 0.50, -0.64,
-0.10, -0.64, -0.10, -0.40, 0.50, 0.40, 0.50, 0.40,
0.50, 0.00, 0.00, -0.40, -0.50, -0.36, -0.50, 0.36,
-0.50, 0.60, -0.60, 0.40, -0.40, 0.40, 0.40, -0.40,
0.40, -0.40, 0.40, -0.56, -0.56, 0.36, -0.40, -0.36,
0.40, 0.36, -0.40, -0.36, -0.40, 0.36, 0.40, 0.36,
0.40, -0.52, 0.52, 0.52, 0.32, 0.40, -0.32, 0.40,
-0.32, 0.40, -0.32, 0.40, 0.32, -0.40, -0.32, -0.40,
0.32, -0.40, 0.28, -0.40, -0.28, 0.40, 0.28, -0.40,
0.28, 0.40, 0.48, -0.48, 0.48, 0.36, -0.30, -0.36,
-0.30, 0.00, 0.00, 0.20, 0.40, -0.44, 0.44, -0.44,
-0.44, -0.44, -0.44, 0.32, -0.30, 0.32, 0.30, 0.24,
0.30, -0.12, -0.10, -0.28, 0.30, 0.28, 0.30, 0.28,
0.30, 0.28, -0.30, 0.28, -0.30, 0.28, -0.30, 0.28,
/* 2132-2259 */
0.30, -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.24,
-0.30, 0.24, -0.30, -0.24, -0.30, 0.24, 0.30, 0.24,
-0.30, -0.24, 0.30, 0.24, -0.30, -0.24, -0.30, 0.24,
-0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, 0.20,
-0.30, 0.20, -0.30, 0.20, -0.30, 0.20, 0.30, 0.20,
-0.30, 0.20, -0.30, 0.20, 0.30, 0.20, 0.30, -0.20,
-0.30, 0.20, -0.30, 0.20, -0.30, -0.36, -0.36, -0.36,
-0.04, 0.30, 0.12, -0.10, -0.32, -0.24, 0.20, 0.24,
0.20, 0.20, -0.20, -0.20, -0.20, -0.20, -0.20, 0.20,
0.20, 0.20, -0.20, 0.20, 0.20, 0.20, 0.20, -0.20,
-0.20, 0.00, 0.00, -0.20, -0.20, -0.20, 0.20, -0.20,
0.20, 0.20, -0.20, -0.20, -0.20, 0.20, 0.20, 0.20,
0.20, 0.20, -0.20, 0.20, -0.20, 0.28, 0.28, 0.28,
0.28, 0.28, 0.28, -0.28, 0.28, 0.12, 0.00, 0.24,
0.16, -0.20, 0.16, -0.20, 0.16, -0.20, 0.16, 0.20,
-0.16, 0.20, 0.16, 0.20, -0.16, 0.20, -0.16, 0.20,
/* 2260-2387 */
-0.16, 0.20, 0.16, -0.20, 0.16, 0.20, 0.16, -0.20,
-0.16, 0.20, -0.16, -0.20, -0.16, 0.20, 0.16, 0.20,
0.16, -0.20, 0.16, -0.20, 0.16, 0.20, 0.16, 0.20,
0.16, 0.20, -0.16, -0.20, 0.16, 0.20, -0.16, 0.20,
0.16, 0.20, -0.16, -0.20, 0.16, -0.20, 0.16, -0.20,
-0.16, -0.20, 0.24, -0.24, -0.24, 0.24, 0.24, 0.12,
0.20, 0.12, 0.20, -0.12, -0.20, 0.12, -0.20, 0.12,
-0.20, -0.12, 0.20, -0.12, 0.20, -0.12, -0.20, 0.12,
0.20, 0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
-0.20, -0.12, 0.20, 0.12, 0.20, 0.00, 0.00, -0.12,
0.20, -0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
0.20, 0.00, -0.21, -0.20, 0.00, 0.00, 0.20, -0.20,
-0.20, -0.20, 0.20, -0.16, -0.10, 0.00, 0.17, 0.16,
0.16, 0.16, 0.16, -0.16, 0.16, 0.16, -0.16, 0.16,
-0.16, 0.16, 0.12, 0.10, 0.12, -0.10, -0.12, 0.10,
-0.12, 0.10, 0.12, -0.10, -0.12, 0.12, -0.12, 0.12,
/* 2388-2515 */
-0.12, 0.12, -0.12, -0.12, -0.12, -0.12, -0.12, -0.12,
-0.12, 0.12, 0.12, 0.12, 0.12, -0.12, -0.12, 0.12,
0.12, 0.12, -0.12, 0.12, -0.12, -0.12, -0.12, 0.12,
-0.12, -0.12, 0.12, 0.00, 0.11, 0.11, -122.67, 164.70,
203.78, 273.50, 3.58, 2.74, 6.18, -4.56, 0.00, -0.04,
0.00, -0.07, 57.44, -77.10, 95.82, 128.60, -1.77, -1.28,
2.85, -2.14, 82.14, 89.50, 0.00, 0.00, 2.00, -1.84,
-0.04, 47.73, -64.10, 23.79, 31.90, -1.45, -1.07, 0.69,
-0.53, -46.38, 50.50, 0.00, 0.00, 1.13, 1.04, 0.02,
-18.38, 0.00, 63.80, 0.00, 0.00, 0.41, 0.00, -1.43,
59.07, 0.00, 0.00, 0.00, 0.00, -1.32, 57.28, 0.00,
0.00, 0.00, 0.00, -1.28, -48.65, 0.00, -1.15, 0.00,
0.00, 1.09, 0.00, 0.03, -18.30, 24.60, -17.30, -23.20,
0.56, 0.41, -0.51, 0.39, -16.91, 26.90, 8.43, 13.30,
0.60, 0.38, 0.31, -0.19, 1.23, -1.70, -19.13, -25.70,
-0.03, -0.03, -0.58, 0.43, -0.72, 0.90, -17.34, -23.30,
/* 2516-2643 */
0.03, 0.02, -0.52, 0.39, -19.49, -21.30, 0.00, 0.00,
-0.48, 0.44, 0.01, 20.57, -20.10, 0.64, 0.70, -0.45,
-0.46, 0.00, -0.01, 4.89, 5.90, -16.55, 19.90, 0.14,
-0.11, 0.44, 0.37, 18.22, 19.80, 0.00, 0.00, 0.44,
-0.41, -0.01, 4.89, -5.30, -16.51, -18.00, -0.11, -0.11,
-0.41, 0.37, -17.86, 0.00, 17.10, 0.00, 0.00, 0.40,
0.00, -0.38, 0.32, 0.00, 24.42, 0.00, 0.00, -0.01,
0.00, -0.55, -23.79, 0.00, 0.00, 0.00, 0.00, 0.53,
14.72, -16.00, -0.32, 0.00, -0.36, -0.33, -0.01, 0.01,
3.34, -4.50, 11.86, 15.90, -0.11, -0.07, 0.35, -0.27,
-3.26, 4.40, 11.62, 15.60, 0.09, 0.07, 0.35, -0.26,
-19.53, 0.00, 5.09, 0.00, 0.00, 0.44, 0.00, -0.11,
-13.48, 14.70, 0.00, 0.00, 0.33, 0.30, 0.01, 10.86,
-14.60, 3.18, 4.30, -0.33, -0.24, 0.09, -0.07, -11.30,
-15.10, 0.00, 0.00, -0.34, 0.25, 0.01, 2.03, -2.70,
10.82, 14.50, -0.07, -0.05, 0.32, -0.24, 17.46, 0.00,
/* 2644-2771 */
0.00, 0.00, 0.00, -0.39, 16.43, 0.00, 0.52, 0.00,
0.00, -0.37, 0.00, -0.01, 9.35, 0.00, 13.29, 0.00,
0.00, -0.21, 0.00, -0.30, -10.42, 11.40, 0.00, 0.00,
0.25, 0.23, 0.01, 0.44, 0.50, -10.38, 11.30, 0.02,
-0.01, 0.25, 0.23, -14.64, 0.00, 0.00, 0.00, 0.00,
0.33, 0.56, 0.80, -8.67, 11.70, 0.02, -0.01, 0.26,
0.19, 13.88, 0.00, -2.47, 0.00, 0.00, -0.31, 0.00,
0.06, -1.99, 2.70, 7.72, 10.30, 0.06, 0.04, 0.23,
-0.17, -0.20, 0.00, 13.05, 0.00, 0.00, 0.00, 0.00,
-0.29, 6.92, -9.30, 3.34, 4.50, -0.21, -0.15, 0.10,
-0.07, -6.60, 0.00, 10.70, 0.00, 0.00, 0.15, 0.00,
-0.24, -8.04, -8.70, 0.00, 0.00, -0.19, 0.18, -10.58,
0.00, -3.10, 0.00, 0.00, 0.24, 0.00, 0.07, -7.32,
8.00, -0.12, -0.10, 0.18, 0.16, 1.63, 1.70, 6.96,
-7.60, 0.03, -0.04, -0.17, -0.16, -3.62, 0.00, 9.86,
0.00, 0.00, 0.08, 0.00, -0.22, 0.20, -0.20, -6.88,
/* 2772-2899 */
-7.50, 0.00, 0.00, -0.17, 0.15, -8.99, 0.00, 4.02,
0.00, 0.00, 0.20, 0.00, -0.09, -1.07, 1.40, -5.69,
-7.70, 0.03, 0.02, -0.17, 0.13, 6.48, -7.20, -0.48,
-0.50, -0.16, -0.14, -0.01, 0.01, 5.57, -7.50, 1.07,
1.40, -0.17, -0.12, 0.03, -0.02, 8.71, 0.00, 3.54,
0.00, 0.00, -0.19, 0.00, -0.08, 0.40, 0.00, 9.27,
0.00, 0.00, -0.01, 0.00, -0.21, -6.13, 6.70, -1.19,
-1.30, 0.15, 0.14, -0.03, 0.03, 5.21, -5.70, -2.51,
-2.60, -0.13, -0.12, -0.06, 0.06, 5.69, -6.20, -0.12,
-0.10, -0.14, -0.13, -0.01, 2.03, -2.70, 4.53, 6.10,
-0.06, -0.05, 0.14, -0.10, 5.01, 5.50, -2.51, 2.70,
0.12, -0.11, 0.06, 0.06, -1.91, 2.60, -4.38, -5.90,
0.06, 0.04, -0.13, 0.10, 4.65, -6.30, 0.00, 0.00,
-0.14, -0.10, -5.29, 5.70, 0.00, 0.00, 0.13, 0.12,
-2.23, -4.00, -4.65, 4.20, -0.09, 0.05, 0.10, 0.10,
-4.53, 6.10, 0.00, 0.00, 0.14, 0.10, 2.47, 2.70,
/* 2900-3027 */
-4.46, 4.90, 0.06, -0.06, 0.11, 0.10, -5.05, 5.50,
0.84, 0.90, 0.12, 0.11, 0.02, -0.02, 4.97, -5.40,
-1.71, 0.00, -0.12, -0.11, 0.00, 0.04, -0.99, -1.30,
4.22, -5.70, -0.03, 0.02, -0.13, -0.09, 0.99, 1.40,
4.22, -5.60, 0.03, -0.02, -0.13, -0.09, -4.69, -5.20,
0.00, 0.00, -0.12, 0.10, -3.42, 0.00, 6.09, 0.00,
0.00, 0.08, 0.00, -0.14, -4.65, -5.10, 0.00, 0.00,
-0.11, 0.10, 0.00, 0.00, -4.53, -5.00, 0.00, 0.00,
-0.11, 0.10, -2.43, -2.70, -3.82, 4.20, -0.06, 0.05,
0.10, 0.09, 0.00, 0.00, -4.53, 4.90, 0.00, 0.00,
0.11, 0.10, -4.49, -4.90, 0.00, 0.00, -0.11, 0.10,
2.67, -2.90, -3.62, -3.90, -0.06, -0.06, -0.09, 0.08,
3.94, -5.30, 0.00, 0.00, -0.12, -3.38, 3.70, -2.78,
-3.10, 0.08, 0.08, -0.07, 0.06, 3.18, -3.50, -2.82,
-3.10, -0.08, -0.07, -0.07, 0.06, -5.77, 0.00, 1.87,
0.00, 0.00, 0.13, 0.00, -0.04, 3.54, -4.80, -0.64,
/* 3028-3155 */
-0.90, -0.11, 0.00, -0.02, -3.50, -4.70, 0.68, -0.90,
-0.11, 0.00, -0.02, 5.49, 0.00, 0.00, 0.00, 0.00,
-0.12, 1.83, -2.50, 2.63, 3.50, -0.06, 0.00, 0.08,
3.02, -4.10, 0.68, 0.90, -0.09, 0.00, 0.02, 0.00,
0.00, 5.21, 0.00, 0.00, 0.00, 0.00, -0.12, -3.54,
3.80, 2.70, 3.60, -1.35, 1.80, 0.08, 0.00, 0.04,
-2.90, 3.90, 0.68, 0.90, 0.09, 0.00, 0.02, 0.80,
-1.10, -2.78, -3.70, -0.02, 0.00, -0.08, 4.10, 0.00,
-2.39, 0.00, 0.00, -0.09, 0.00, 0.05, -1.59, 2.10,
2.27, 3.00, 0.05, 0.00, 0.07, -2.63, 3.50, -0.48,
-0.60, -2.94, -3.20, -2.94, 3.20, 2.27, -3.00, -1.11,
-1.50, -0.07, 0.00, -0.03, -0.56, -0.80, -2.35, 3.10,
0.00, -0.60, -3.42, 1.90, -0.12, -0.10, 2.63, -2.90,
2.51, 2.80, -0.64, 0.70, -0.48, -0.60, 2.19, -2.90,
0.24, -0.30, 2.15, 2.90, 2.15, -2.90, 0.52, 0.70,
2.07, -2.80, -3.10, 0.00, 1.79, 0.00, 0.00, 0.07,
/* 3156-3283 */
0.00, -0.04, 0.88, 0.00, -3.46, 2.11, 2.80, -0.36,
0.50, 3.54, -0.20, -3.50, -1.39, 1.50, -1.91, -2.10,
-1.47, 2.00, 1.39, 1.90, 2.07, -2.30, 0.91, 1.00,
1.99, -2.70, 3.30, 0.00, 0.60, -0.44, -0.70, -1.95,
2.60, 2.15, -2.40, -0.60, -0.70, 3.30, 0.84, 0.00,
-3.10, -3.10, 0.00, -0.72, -0.32, 0.40, -1.87, -2.50,
1.87, -2.50, 0.32, 0.40, -0.24, 0.30, -1.87, -2.50,
-0.24, -0.30, 1.87, -2.50, -2.70, 0.00, 1.55, 2.03,
2.20, -2.98, -1.99, -2.20, 0.12, -0.10, -0.40, 0.50,
1.59, 2.10, 0.00, 0.00, -1.79, 2.00, -1.03, 1.40,
-1.15, -1.60, 0.32, 0.50, 1.39, -1.90, 2.35, -1.27,
1.70, 0.60, 0.80, -0.32, -0.40, 1.35, -1.80, 0.44,
0.00, 2.23, -0.84, 0.90, -1.27, -1.40, -1.47, 1.60,
-0.28, -0.30, -0.28, 0.40, -1.27, -1.70, 0.28, -0.40,
-1.43, -1.50, 0.00, 0.00, -1.27, -1.70, 2.11, -0.32,
-0.40, -1.23, 1.60, 1.19, -1.30, -0.72, -0.80, 0.72,
/* 3284-3411 */
-0.80, -1.15, -1.30, -1.35, -1.50, -1.19, -1.60, -0.12,
0.20, 1.79, 0.00, -0.88, -0.28, 0.40, 1.11, 1.50,
-1.83, 0.00, 0.56, -0.12, 0.10, -1.27, -1.40, 0.00,
0.00, 1.15, 1.50, -0.12, 0.20, 1.11, 1.50, 0.36,
-0.50, -1.07, -1.40, -1.11, 1.50, 1.67, 0.00, 0.80,
-1.11, 0.00, 1.43, 1.23, -1.30, -0.24, -1.19, -1.30,
-0.24, 0.20, -0.44, -0.90, -0.95, 1.10, 1.07, -1.40,
1.15, -1.30, 1.03, -1.10, -0.56, -0.60, -0.68, 0.90,
-0.76, -1.00, -0.24, -0.30, 0.95, -1.30, 0.56, 0.70,
0.84, -1.10, -0.56, 0.00, -1.55, 0.91, -1.30, 0.28,
0.30, 0.16, -0.20, 0.95, 1.30, 0.40, -0.50, -0.88,
-1.20, 0.95, -1.10, -0.48, -0.50, 0.00, 0.00, -1.07,
1.20, 0.44, -0.50, 0.95, 1.10, 0.00, 0.00, 0.92,
-1.30, 0.95, 1.00, -0.52, 0.60, 1.59, 0.24, -0.40,
0.91, 1.20, 0.84, -1.10, -0.44, -0.60, 0.84, 1.10,
-0.44, 0.60, -0.44, 0.60, -0.84, -1.10, -0.80, 0.00,
/* 3412-3539 */
1.35, 0.76, 0.20, -0.91, -1.00, 0.20, -0.30, -0.91,
-1.20, -0.95, 1.00, -0.48, -0.50, 0.88, 1.00, 0.48,
-0.50, -0.95, -1.10, 0.20, -0.20, -0.99, 1.10, -0.84,
1.10, -0.24, -0.30, 0.20, -0.30, 0.84, 1.10, -1.39,
0.00, -0.28, -0.16, 0.20, 0.84, 1.10, 0.00, 0.00,
1.39, 0.00, 0.00, -0.95, 1.00, 1.35, -0.99, 0.00,
0.88, -0.52, 0.00, -1.19, 0.20, 0.20, 0.76, -1.00,
0.00, 0.00, 0.76, 1.00, 0.00, 0.00, 0.76, 1.00,
-0.76, 1.00, 0.00, 0.00, 1.23, 0.76, 0.80, -0.32,
0.40, -0.72, 0.80, -0.40, -0.40, 0.00, 0.00, -0.80,
-0.90, -0.68, 0.90, -0.16, -0.20, -0.16, -0.20, 0.68,
-0.90, -0.36, 0.50, -0.56, -0.80, 0.72, -0.90, 0.44,
-0.60, -0.48, -0.70, -0.16, 0.00, -1.11, 0.32, 0.00,
-1.07, 0.60, -0.80, -0.28, -0.40, -0.64, 0.00, 0.91,
1.11, 0.64, -0.90, 0.76, -0.80, 0.00, 0.00, -0.76,
-0.80, 1.03, 0.00, -0.36, -0.64, -0.70, 0.36, -0.40,
/* 3540-3667 */
1.07, 0.36, -0.50, -0.52, -0.70, 0.60, 0.00, 0.88,
0.95, 0.00, 0.48, 0.16, -0.20, 0.60, 0.80, 0.16,
-0.20, -0.60, -0.80, 0.00, -1.00, 0.12, 0.20, 0.16,
-0.20, 0.68, 0.70, 0.59, -0.80, -0.99, -0.56, -0.60,
0.36, -0.40, -0.68, -0.70, -0.68, -0.70, -0.36, -0.50,
-0.44, 0.60, 0.64, 0.70, -0.12, 0.10, -0.52, 0.60,
0.36, 0.40, 0.00, 0.00, 0.95, -0.84, 0.00, 0.44,
0.56, 0.60, 0.32, -0.30, 0.00, 0.00, 0.60, 0.70,
0.00, 0.00, 0.60, 0.70, -0.12, -0.20, 0.52, -0.70,
0.00, 0.00, 0.56, 0.70, -0.12, 0.10, -0.52, -0.70,
0.00, 0.00, 0.88, -0.76, 0.00, -0.44, 0.00, 0.00,
-0.52, -0.70, 0.52, -0.70, 0.36, -0.40, -0.44, -0.50,
0.00, 0.00, 0.60, 0.60, 0.84, 0.00, 0.12, -0.24,
0.00, 0.80, -0.56, 0.60, -0.32, -0.30, 0.48, -0.50,
0.28, -0.30, -0.48, -0.50, 0.12, 0.20, 0.48, -0.60,
0.48, 0.60, -0.12, 0.20, 0.24, 0.00, 0.76, -0.52,
/* 3668-3795 */
-0.60, -0.52, 0.60, 0.48, -0.50, -0.24, -0.30, 0.12,
-0.10, 0.48, 0.60, 0.52, -0.20, 0.36, 0.40, -0.44,
0.50, -0.24, -0.30, -0.48, -0.60, -0.44, -0.60, -0.12,
0.10, 0.76, 0.76, 0.20, -0.20, 0.48, 0.50, 0.40,
-0.50, -0.24, -0.30, 0.44, -0.60, 0.44, -0.60, 0.36,
0.00, -0.64, 0.72, 0.00, -0.12, 0.00, -0.10, -0.40,
-0.60, -0.20, -0.20, -0.44, 0.50, -0.44, 0.50, 0.20,
0.20, -0.44, -0.50, 0.20, -0.20, -0.20, 0.20, -0.44,
-0.50, 0.64, 0.00, 0.32, -0.36, 0.50, -0.20, -0.30,
0.12, -0.10, 0.48, 0.50, -0.12, 0.30, -0.36, -0.50,
0.00, 0.00, 0.48, 0.50, -0.48, 0.50, 0.68, 0.00,
-0.12, 0.56, -0.40, 0.44, -0.50, -0.12, -0.10, 0.24,
0.30, -0.40, 0.40, 0.64, 0.00, -0.24, 0.64, 0.00,
-0.20, 0.00, 0.00, 0.44, -0.50, 0.44, 0.50, -0.12,
0.20, -0.36, -0.50, 0.12, 0.00, 0.64, -0.40, 0.50,
0.00, 0.10, 0.00, 0.00, -0.40, 0.50, 0.00, 0.00,
/* 3796-3923 */
-0.40, -0.50, 0.56, 0.00, 0.28, 0.00, 0.10, 0.36,
0.50, 0.00, -0.10, 0.36, -0.50, 0.36, 0.50, 0.00,
-0.10, 0.24, -0.20, -0.36, -0.40, 0.16, 0.20, 0.40,
-0.40, 0.00, 0.00, -0.36, -0.50, -0.36, -0.50, -0.32,
-0.50, -0.12, 0.10, 0.20, 0.20, -0.36, 0.40, -0.60,
0.60, 0.28, 0.00, 0.52, 0.12, -0.10, 0.40, 0.40,
0.00, -0.50, 0.20, -0.20, -0.32, 0.40, 0.16, 0.20,
-0.16, 0.20, 0.32, 0.40, 0.56, 0.00, -0.12, 0.32,
-0.40, -0.16, -0.20, 0.00, 0.00, 0.40, 0.40, -0.40,
-0.40, -0.40, 0.40, -0.36, 0.40, 0.12, 0.10, 0.00,
0.10, 0.36, 0.40, 0.00, -0.10, 0.36, 0.40, -0.36,
0.40, 0.00, 0.10, 0.32, 0.00, 0.44, 0.12, 0.20,
0.28, -0.40, 0.00, 0.00, 0.36, 0.40, 0.32, -0.40,
-0.16, 0.12, 0.10, 0.32, -0.40, 0.20, 0.30, -0.24,
0.30, 0.00, 0.10, 0.32, 0.40, 0.00, -0.10, -0.32,
-0.40, -0.32, 0.40, 0.00, 0.10, -0.52, -0.52, 0.52,
/* 3924-4051 */
0.32, -0.40, 0.00, 0.00, 0.32, 0.40, 0.32, -0.40,
0.00, 0.00, -0.32, -0.40, -0.32, 0.40, 0.32, 0.40,
0.00, 0.00, 0.32, 0.40, 0.00, 0.00, -0.32, -0.40,
0.00, 0.00, 0.32, 0.40, 0.16, 0.20, 0.32, -0.30,
-0.16, 0.00, -0.48, -0.20, 0.20, -0.28, -0.30, 0.28,
-0.40, 0.00, 0.00, 0.28, -0.40, 0.00, 0.00, 0.28,
-0.40, 0.00, 0.00, -0.28, -0.40, 0.28, 0.40, -0.28,
-0.40, -0.48, -0.20, 0.20, 0.24, 0.30, 0.44, 0.00,
0.16, 0.24, 0.30, 0.16, -0.20, 0.24, 0.30, -0.12,
0.20, 0.20, 0.30, -0.16, 0.20, 0.00, 0.00, 0.44,
-0.32, 0.30, 0.24, 0.00, -0.36, 0.36, 0.00, 0.24,
0.12, -0.20, 0.20, 0.30, -0.12, 0.00, -0.28, 0.30,
-0.24, 0.30, 0.12, 0.10, -0.28, -0.30, -0.28, 0.30,
0.00, 0.00, -0.28, -0.30, 0.00, 0.00, -0.28, -0.30,
0.00, 0.00, 0.28, 0.30, 0.00, 0.00, -0.28, -0.30,
-0.28, 0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00,
/* 4052-4179 */
0.28, 0.30, 0.00, 0.00, -0.28, 0.30, 0.28, -0.30,
-0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.00, -0.10,
0.16, 0.00, 0.36, -0.20, 0.30, -0.12, -0.10, -0.24,
-0.30, 0.00, 0.00, -0.24, 0.30, -0.24, 0.30, 0.00,
0.00, -0.24, 0.30, -0.24, 0.30, 0.24, -0.30, 0.00,
0.00, 0.24, -0.30, 0.00, 0.00, 0.24, 0.30, 0.24,
-0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, -0.20,
0.20, -0.16, -0.20, 0.00, 0.00, -0.32, 0.20, 0.00,
0.10, 0.20, -0.30, 0.20, -0.20, 0.12, 0.20, -0.16,
0.20, 0.16, 0.20, 0.20, 0.30, 0.20, 0.30, 0.00,
0.00, -0.20, 0.30, 0.00, 0.00, 0.20, 0.30, -0.20,
-0.30, -0.20, -0.30, 0.20, -0.30, 0.00, 0.00, 0.20,
0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
-0.30, 0.00, 0.00, -0.20, -0.30, 0.00, 0.00, -0.20,
0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, 0.36,
/* 4180-4307 */
0.00, 0.00, 0.36, 0.12, 0.10, -0.24, 0.20, 0.12,
-0.20, -0.16, -0.20, -0.13, 0.10, 0.22, 0.21, 0.20,
0.00, -0.28, 0.32, 0.00, -0.12, -0.20, -0.20, 0.12,
-0.10, 0.12, 0.10, -0.20, 0.20, 0.00, 0.00, -0.32,
0.32, 0.00, 0.00, 0.32, 0.32, 0.00, 0.00, -0.24,
-0.20, 0.24, 0.20, 0.20, 0.00, -0.24, 0.00, 0.00,
-0.24, -0.20, 0.00, 0.00, 0.24, 0.20, -0.24, -0.20,
0.00, 0.00, -0.24, 0.20, 0.16, -0.20, 0.12, 0.10,
0.20, 0.20, 0.00, -0.10, -0.12, 0.10, -0.16, -0.20,
-0.12, -0.10, -0.16, 0.20, 0.20, 0.20, 0.00, 0.00,
-0.20, 0.20, -0.20, 0.20, -0.20, 0.20, -0.20, 0.20,
0.20, -0.20, -0.20, -0.20, 0.00, 0.00, -0.20, 0.20,
0.20, 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, -0.20,
0.20, -0.20, -0.20, -0.20, -0.20, 0.00, 0.00, 0.20,
0.20, 0.20, 0.20, 0.12, -0.20, -0.12, -0.10, 0.28,
-0.28, 0.16, -0.20, 0.00, -0.10, 0.00, 0.10, -0.16,
/* 4308-4435 */
0.20, 0.00, -0.10, -0.16, -0.20, 0.00, -0.10, 0.16,
-0.20, 0.16, -0.20, 0.00, 0.00, 0.16, 0.20, -0.16,
0.20, 0.00, 0.00, 0.16, 0.20, 0.16, -0.20, 0.16,
-0.20, -0.16, 0.20, 0.16, -0.20, 0.00, 0.00, 0.16,
0.20, 0.00, 0.00, 0.16, 0.20, 0.00, 0.00, -0.16,
-0.20, 0.16, -0.20, -0.16, -0.20, 0.00, 0.00, -0.16,
-0.20, 0.00, 0.00, -0.16, 0.20, 0.00, 0.00, 0.16,
-0.20, 0.16, 0.20, 0.16, 0.20, 0.00, 0.00, -0.16,
-0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, 0.16,
0.20, 0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.16,
-0.20, 0.16, 0.20, 0.00, 0.00, -0.16, 0.20, 0.00,
0.10, 0.12, -0.20, 0.12, -0.20, 0.00, -0.10, 0.00,
-0.10, 0.12, 0.20, 0.00, -0.10, -0.12, 0.20, -0.15,
0.20, -0.24, 0.24, 0.00, 0.00, 0.24, 0.24, 0.12,
-0.20, -0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
-0.20, 0.12, 0.20, 0.12, 0.20, 0.12, 0.20, 0.12,
/* 4436-4563 */
-0.20, -0.12, 0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
0.00, -0.20, 0.00, 0.00, -0.12, -0.20, 0.12, -0.20,
0.00, 0.00, 0.12, 0.20, -0.12, 0.20, -0.12, 0.20,
0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.20, 0.00,
0.12, 0.00, 0.00, -0.12, 0.20, 0.00, 0.00, -0.12,
-0.20, 0.00, 0.00, -0.12, -0.20, -0.12, -0.20, 0.00,
0.00, 0.12, -0.20, 0.12, -0.20, 0.12, 0.20, -0.12,
-0.20, 0.00, 0.00, 0.12, -0.20, 0.12, -0.20, 0.12,
0.20, 0.12, 0.00, 0.20, -0.12, -0.20, 0.00, 0.00,
0.12, 0.20, -0.16, 0.00, 0.16, -0.20, 0.20, 0.00,
0.00, -0.20, 0.00, 0.00, -0.20, 0.20, 0.00, 0.00,
0.20, 0.20, -0.20, 0.00, 0.00, -0.20, 0.12, 0.00,
-0.16, 0.20, 0.00, 0.00, 0.20, 0.12, -0.10, 0.00,
0.10, 0.16, -0.16, -0.16, -0.16, -0.16, -0.16, 0.00,
0.00, -0.16, 0.00, 0.00, -0.16, -0.16, -0.16, 0.00,
0.00, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00, 0.16,
/* 4564-4691 */
0.00, 0.00, 0.16, 0.16, 0.00, 0.00, -0.16, 0.00,
0.00, -0.16, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00,
-0.16, -0.16, 0.00, 0.00, -0.16, -0.16, 0.12, 0.10,
0.12, -0.10, 0.12, 0.10, 0.00, 0.00, 0.12, 0.10,
-0.12, 0.10, 0.00, 0.00, 0.12, 0.10, 0.12, -0.10,
0.00, 0.00, -0.12, -0.10, 0.00, 0.00, 0.12, 0.10,
0.12, 0.00, 0.00, 0.12, 0.00, 0.00, -0.12, 0.00,
0.00, 0.12, 0.12, 0.12, 0.12, 0.12, 0.00, 0.00,
0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, 0.12,
0.00, 0.00, 0.12, -0.12, -0.12, 0.12, 0.12, -0.12,
-0.12, 0.00, 0.00, 0.12, -0.12, 0.12, 0.12, -0.12,
-0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.00,
0.00, 0.12, -0.12, 0.00, 0.00, -0.12, 0.12, -0.12,
-0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.12, -0.12,
0.00, 0.00, -0.12, -0.12, -0.12, 0.00, 0.00, -0.12,
/* 4692-NA */
-0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, -0.12,
-0.12, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, -0.12,
0.00, 0.00, -0.12, -0.12, 0.00, 0.00, 0.12, -0.12,
-0.12, -0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00,
0.00, -0.12, 0.00, 0.00, -0.12, 0.12, 0.00, 0.00,
0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
-0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00,
0.12, 0.00, 0.00, 0.12, 0.12, 0.08, 0.00, 0.04,
}
/* Number of amplitude coefficients */
NA := len(a)
/* Amplitude usage: X or Y, sin or cos, power of T. */
jaxy := []int{0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1}
jasc := []int{0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0}
japt := []int{0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4}
/* Miscellaneous */
var t, w float64
var pt [MAXPT + 1]float64
var fa [14]float64
var xypr, xypl, xyls, sc [2]float64
var arg float64
var jpt, i, j, jxy, ialast, ifreq, m, ia, jsc int
/* ------------------------------------------------------------------ */
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC
/* Powers of T. */
w = 1.0
for jpt = 0; jpt <= MAXPT; jpt++ {
pt[jpt] = w
w *= t
}
/* Initialize totals in X and Y: polynomial, luni-solar, planetary. */
for jxy = 0; jxy < 2; jxy++ {
xypr[jxy] = 0.0
xyls[jxy] = 0.0
xypl[jxy] = 0.0
}
/* --------------------------------- */
/* Fundamental arguments (IERS 2003) */
/* --------------------------------- */
/* Mean anomaly of the Moon. */
fa[0] = Fal03(t)
/* Mean anomaly of the Sun. */
fa[1] = Falp03(t)
/* Mean argument of the latitude of the Moon. */
fa[2] = Faf03(t)
/* Mean elongation of the Moon from the Sun. */
fa[3] = Fad03(t)
/* Mean longitude of the ascending node of the Moon. */
fa[4] = Faom03(t)
/* Planetary longitudes, Mercury through Neptune. */
fa[5] = Fame03(t)
fa[6] = Fave03(t)
fa[7] = Fae03(t)
fa[8] = Fama03(t)
fa[9] = Faju03(t)
fa[10] = Fasa03(t)
fa[11] = Faur03(t)
fa[12] = Fane03(t)
/* General accumulated precession in longitude. */
fa[13] = Fapa03(t)
/* -------------------------------------- */
/* Polynomial part of precession-nutation */
/* -------------------------------------- */
for jxy = 0; jxy < 2; jxy++ {
for j = MAXPT; j >= 0; j-- {
xypr[jxy] += xyp[jxy][j] * pt[j]
}
}
/* ---------------------------------- */
/* Nutation periodic terms, planetary */
/* ---------------------------------- */
/* Work backwards through the coefficients per frequency list. */
ialast = NA
for ifreq = NFPL - 1; ifreq >= 0; ifreq-- {
/* Obtain the argument functions. */
arg = 0.0
for i = 0; i < 14; i++ {
m = mfapl[ifreq][i]
if m != 0 {
arg += float64(m) * fa[i]
}
}
sc[0] = sin(arg)
sc[1] = cos(arg)
/* Work backwards through the amplitudes at this frequency. */
ia = nc[ifreq+NFLS]
for i = ialast; i >= ia; i-- {
/* Coefficient number (0 = 1st). */
j = i - ia
/* X or Y. */
jxy = jaxy[j]
/* Sin or cos. */
jsc = jasc[j]
/* Power of T. */
jpt = japt[j]
/* Accumulate the component. */
xypl[jxy] += a[i-1] * sc[jsc] * pt[jpt]
}
ialast = ia - 1
}
/* ----------------------------------- */
/* Nutation periodic terms, luni-solar */
/* ----------------------------------- */
/* Continue working backwards through the number of coefficients list. */
for ifreq = NFLS - 1; ifreq >= 0; ifreq-- {
/* Obtain the argument functions. */
arg = 0.0
for i = 0; i < 5; i++ {
m = mfals[ifreq][i]
if m != 0 {
arg += float64(m) * fa[i]
}
}
sc[0] = sin(arg)
sc[1] = cos(arg)
/* Work backwards through the amplitudes at this frequency. */
ia = nc[ifreq]
for i = ialast; i >= ia; i-- {
/* Coefficient number (0 = 1st). */
j = i - ia
/* X or Y. */
jxy = jaxy[j]
/* Sin or cos. */
jsc = jasc[j]
/* Power of T. */
jpt = japt[j]
/* Accumulate the component. */
xyls[jxy] += a[i-1] * sc[jsc] * pt[jpt]
}
ialast = ia - 1
}
/* ------------------------------------ */
/* Results: CIP unit vector components */
/* ------------------------------------ */
*x = DAS2R * (xypr[0] + (xyls[0]+xypl[0])/1e6)
*y = DAS2R * (xypr[1] + (xyls[1]+xypl[1])/1e6)
}
/*
Xys00a CIP and s, IAU 2000A
For a given TT date, compute the X,Y coordinates of the Celestial
Intermediate Pole and the CIO locator s, using the IAU 2000A
precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
x,y float64 Celestial Intermediate Pole (Note 2)
s float64 the CIO locator s (Note 3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The Celestial Intermediate Pole coordinates are the x,y
components of the unit vector in the Geocentric Celestial
Reference System.
3) The CIO locator s (in radians) positions the Celestial
Intermediate Origin on the equator of the CIP.
4) A faster, but slightly less accurate result (about 1 mas for
X,Y), can be obtained by using instead the iauXys00b function.
Called:
Pnm00a classical NPB matrix, IAU 2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S00 the CIO locator s, given X,Y, IAU 2000A
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Xys00a(date1, date2 float64, x, y, s *float64) {
var rbpn [3][3]float64
/* Form the bias-precession-nutation matrix, IAU 2000A. */
Pnm00a(date1, date2, &rbpn)
/* Extract X,Y. */
Bpn2xy(rbpn, x, y)
/* Obtain s. */
*s = S00(date1, date2, *x, *y)
}
/*
Xys00b CIP and s, IAU 2000B
For a given TT date, compute the X,Y coordinates of the Celestial
Intermediate Pole and the CIO locator s, using the IAU 2000B
precession-nutation model.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
x,y float64 Celestial Intermediate Pole (Note 2)
s float64 the CIO locator s (Note 3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The Celestial Intermediate Pole coordinates are the x,y
components of the unit vector in the Geocentric Celestial
Reference System.
3) The CIO locator s (in radians) positions the Celestial
Intermediate Origin on the equator of the CIP.
4) The present function is faster, but slightly less accurate (about
1 mas in X,Y), than the iauXys00a function.
Called:
Pnm00b classical NPB matrix, IAU 2000B
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S00 the CIO locator s, given X,Y, IAU 2000A
Reference:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
*/
func Xys00b(date1, date2 float64, x, y, s *float64) {
var rbpn [3][3]float64
/* Form the bias-precession-nutation matrix, IAU 2000A. */
Pnm00b(date1, date2, &rbpn)
/* Extract X,Y. */
Bpn2xy(rbpn, x, y)
/* Obtain s. */
*s = S00(date1, date2, *x, *y)
}
/*
Xys06a CIP and s, IAU 2006/2000A
For a given TT date, compute the X,Y coordinates of the Celestial
Intermediate Pole and the CIO locator s, using the IAU 2006
precession and IAU 2000A nutation models.
Given:
date1,date2 float64 TT as a 2-part Julian Date (Note 1)
Returned:
x,y float64 Celestial Intermediate Pole (Note 2)
s float64 the CIO locator s (Note 3)
Notes:
1) The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
2) The Celestial Intermediate Pole coordinates are the x,y components
of the unit vector in the Geocentric Celestial Reference System.
3) The CIO locator s (in radians) positions the Celestial
Intermediate Origin on the equator of the CIP.
4) Series-based solutions for generating X and Y are also available:
see Capitaine & Wallace (2006) and iauXy06.
Called:
Pnm06a classical NPB matrix, IAU 2006/2000A
Bpn2xy extract CIP X,Y coordinates from NPB matrix
S06 the CIO locator s, given X,Y, IAU 2006
References:
Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
*/
func Xys06a(date1, date2 float64, x, y, s *float64) {
var rbpn [3][3]float64
/* Form the bias-precession-nutation matrix, IAU 2006/2000A. */
Pnm06a(date1, date2, &rbpn)
/* Extract X,Y. */
Bpn2xy(rbpn, x, y)
/* Obtain s. */
*s = S06(date1, date2, *x, *y)
}
gofa-1.19.1/projection.go 0000664 0000000 0000000 00000041076 14535740236 0015243 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
/*
Tpxes Project celestial to tangent plane, spherical
In the tangent plane projection, given celestial spherical
coordinates for a star and the tangent point, solve for the star's
rectangular coordinates in the tangent plane.
Given:
a,b float64 star's spherical coordinates
a0,b0 float64 tangent point's spherical coordinates
Returned:
xi,eta float64 rectangular coordinates of star image (Note 2)
Returned (function value):
int status: 0 = OK
1 = star too far from axis
2 = antistar on tangent plane
3 = antistar too far from axis
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the spherical coordinates are observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". For right-handed spherical coordinates,
(xi,eta) are also right-handed. The units of (xi,eta) are,
effectively, radians at the tangent point.
3) All angular arguments are in radians.
4) This function is a member of the following set:
spherical vector solve for
> iauTpxes < iauTpxev xi,eta
iauTpsts iauTpstv star
iauTpors iauTporv origin
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tpxes(a, b, a0, b0 float64, xi, eta *float64) int {
const TINY = 1e-6
var j int
var sb0, sb, cb0, cb, da, sda, cda, d float64
/* Functions of the spherical coordinates. */
sb0 = sin(b0)
sb = sin(b)
cb0 = cos(b0)
cb = cos(b)
da = a - a0
sda = sin(da)
cda = cos(da)
/* Reciprocal of star vector length to tangent plane. */
d = sb*sb0 + cb*cb0*cda
/* Check for error cases. */
if d > TINY {
j = 0
} else if d >= 0.0 {
j = 1
d = TINY
} else if d > -TINY {
j = 2
d = -TINY
} else {
j = 3
}
/* Return the tangent plane coordinates (even in dubious cases). */
*xi = cb * sda / d
*eta = (sb*cb0 - cb*sb0*cda) / d
/* Return the status. */
return j
}
/*
Tpxev Project celestial to tangent plane, vector
In the tangent plane projection, given celestial direction cosines
for a star and the tangent point, solve for the star's rectangular
coordinates in the tangent plane.
Given:
v [3]float64 direction cosines of star (Note 4)
v0 [3]float64 direction cosines of tangent point (Note 4)
Returned:
xi,eta float64 tangent plane coordinates of star
Returned (function value):
int status: 0 = OK
1 = star too far from axis
2 = antistar on tangent plane
3 = antistar too far from axis
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the direction cosines represent observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". If the direction cosines are with
respect to a right-handed triad, (xi,eta) are also right-handed.
The units of (xi,eta) are, effectively, radians at the tangent
point.
3) The method used is to extend the star vector to the tangent
plane and then rotate the triad so that (x,y) becomes (xi,eta).
Writing (a,b) for the celestial spherical coordinates of the
star, the sequence of rotations is (a+pi/2) around the z-axis
followed by (pi/2-b) around the x-axis.
4) If vector v0 is not of unit length, or if vector v is of zero
length, the results will be wrong.
5) If v0 points at a pole, the returned (xi,eta) will be based on
the arbitrary assumption that the longitude coordinate of the
tangent point is zero.
6) This function is a member of the following set:
spherical vector solve for
iauTpxes > iauTpxev < xi,eta
iauTpsts iauTpstv star
iauTpors iauTporv origin
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tpxev(v, v0 [3]float64, xi, eta *float64) int {
const TINY = 1e-6
var j int
var x, y, z, x0, y0, z0, r2, r, w, d float64
/* Star and tangent point. */
x = v[0]
y = v[1]
z = v[2]
x0 = v0[0]
y0 = v0[1]
z0 = v0[2]
/* Deal with polar case. */
r2 = x0*x0 + y0*y0
r = sqrt(r2)
if r == 0.0 {
r = 1e-20
x0 = r
}
/* Reciprocal of star vector length to tangent plane. */
w = x*x0 + y*y0
d = w + z*z0
/* Check for error cases. */
if d > TINY {
j = 0
} else if d >= 0.0 {
j = 1
d = TINY
} else if d > -TINY {
j = 2
d = -TINY
} else {
j = 3
}
/* Return the tangent plane coordinates (even in dubious cases). */
d *= r
*xi = (y*x0 - x*y0) / d
*eta = (z*r2 - z0*w) / d
/* Return the status. */
return j
}
/*
Tpsts Project tangent plane to celestial, spherical
In the tangent plane projection, given the star's rectangular
coordinates and the spherical coordinates of the tangent point,
solve for the spherical coordinates of the star.
Given:
xi,eta float64 rectangular coordinates of star image (Note 2)
a0,b0 float64 tangent point's spherical coordinates
Returned:
a,b float64 star's spherical coordinates
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the spherical coordinates are observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". If the spherical coordinates are with
respect to a right-handed triad, (xi,eta) are also right-handed.
The units of (xi,eta) are, effectively, radians at the tangent
point.
3) All angular arguments are in radians.
4) This function is a member of the following set:
spherical vector solve for
iauTpxes iauTpxev xi,eta
> iauTpsts < iauTpstv star
iauTpors iauTporv origin
Called:
Anp normalize angle into range 0 to 2pi
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tpsts(xi, eta, a0, b0 float64, a, b *float64) {
var sb0, cb0, d float64
sb0 = sin(b0)
cb0 = cos(b0)
d = cb0 - eta*sb0
*a = Anp(atan2(xi, d) + a0)
*b = atan2(sb0+eta*cb0, sqrt(xi*xi+d*d))
}
/*
Tpstv Project tangent plane to celestial, vector
In the tangent plane projection, given the star's rectangular
coordinates and the direction cosines of the tangent point, solve
for the direction cosines of the star.
Given:
xi,eta float64 rectangular coordinates of star image (Note 2)
v0 [3]float64 tangent point's direction cosines
Returned:
v [3]float64 star's direction cosines
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the direction cosines represent observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". If the direction cosines are with
respect to a right-handed triad, (xi,eta) are also right-handed.
The units of (xi,eta) are, effectively, radians at the tangent
point.
3) The method used is to complete the star vector in the (xi,eta)
based triad and normalize it, then rotate the triad to put the
tangent point at the pole with the x-axis aligned to zero
longitude. Writing (a0,b0) for the celestial spherical
coordinates of the tangent point, the sequence of rotations is
(b-pi/2) around the x-axis followed by (-a-pi/2) around the
z-axis.
4) If vector v0 is not of unit length, the returned vector v will
be wrong.
5) If vector v0 points at a pole, the returned vector v will be
based on the arbitrary assumption that the longitude coordinate
of the tangent point is zero.
6) This function is a member of the following set:
spherical vector solve for
iauTpxes iauTpxev xi,eta
iauTpsts > iauTpstv < star
iauTpors iauTporv origin
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tpstv(xi, eta float64, v0 [3]float64, v *[3]float64) {
var x, y, z, f, r float64
/* Tangent point. */
x = v0[0]
y = v0[1]
z = v0[2]
/* Deal with polar case. */
r = sqrt(x*x + y*y)
if r == 0.0 {
r = 1e-20
x = r
}
/* Star vector length to tangent plane. */
f = sqrt(1.0 + xi*xi + eta*eta)
/* Apply the transformation and normalize. */
v[0] = (x - (xi*y+eta*x*z)/r) / f
v[1] = (y + (xi*x-eta*y*z)/r) / f
v[2] = (z + eta*r) / f
}
/*
Tpors Solve for tangent point, spherical
In the tangent plane projection, given the rectangular coordinates
of a star and its spherical coordinates, determine the spherical
coordinates of the tangent point.
Given:
xi,eta float64 rectangular coordinates of star image (Note 2)
a,b float64 star's spherical coordinates (Note 3)
Returned:
a01,b01 float64 tangent point's spherical coordinates, Soln. 1
a02,b02 float64 tangent point's spherical coordinates, Soln. 2
Returned (function value):
int number of solutions:
0 = no solutions returned (Note 5)
1 = only the first solution is useful (Note 6)
2 = both solutions are useful (Note 6)
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the spherical coordinates are observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". If the spherical coordinates are with
respect to a right-handed triad, (xi,eta) are also right-handed.
The units of (xi,eta) are, effectively, radians at the tangent
point.
3) All angular arguments are in radians.
4) The angles a01 and a02 are returned in the range 0-2pi. The
angles b01 and b02 are returned in the range +/-pi, but in the
usual, non-pole-crossing, case, the range is +/-pi/2.
5) Cases where there is no solution can arise only near the poles.
For example, it is clearly impossible for a star at the pole
itself to have a non-zero xi value, and hence it is meaningless
to ask where the tangent point would have to be to bring about
this combination of xi and dec.
6) Also near the poles, cases can arise where there are two useful
solutions. The return value indicates whether the second of the
two solutions returned is useful; 1 indicates only one useful
solution, the usual case.
7) The basis of the algorithm is to solve the spherical triangle PSC,
where P is the north celestial pole, S is the star and C is the
tangent point. The spherical coordinates of the tangent point are
[a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c
is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be
found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and
cos(C) = eta/rho. Angle P (to be found) is the longitude
difference between star and tangent point (a-a0).
8) This function is a member of the following set:
spherical vector solve for
iauTpxes iauTpxev xi,eta
iauTpsts iauTpstv star
> iauTpors < iauTporv origin
Called:
Anp normalize angle into range 0 to 2pi
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tpors(xi, eta, a, b float64, a01, b01, a02, b02 *float64) int {
var xi2, r, sb, cb, rsb, rcb, w2, w, s, c float64
xi2 = xi * xi
r = sqrt(1.0 + xi2 + eta*eta)
sb = sin(b)
cb = cos(b)
rsb = r * sb
rcb = r * cb
w2 = rcb*rcb - xi2
if w2 >= 0.0 {
w = sqrt(w2)
s = rsb - eta*w
c = rsb*eta + w
if xi == 0.0 && w == 0.0 {
w = 1.0
}
*a01 = Anp(a - atan2(xi, w))
*b01 = atan2(s, c)
w = -w
s = rsb - eta*w
c = rsb*eta + w
*a02 = Anp(a - atan2(xi, w))
*b02 = atan2(s, c)
if fabs(rsb) < 1.0 {
return 1
} else {
return 2
}
} else {
return 0
}
}
/*
Tporv Solve for tangent point, vector
In the tangent plane projection, given the rectangular coordinates
of a star and its direction cosines, determine the direction
cosines of the tangent point.
Given:
xi,eta float64 rectangular coordinates of star image (Note 2)
v [3]float64 star's direction cosines (Note 3)
Returned:
v01 [3]float64 tangent point's direction cosines, Solution 1
v02 [3]float64 tangent point's direction cosines, Solution 2
Returned (function value):
int number of solutions:
0 = no solutions returned (Note 4)
1 = only the first solution is useful (Note 5)
2 = both solutions are useful (Note 5)
Notes:
1) The tangent plane projection is also called the "gnomonic
projection" and the "central projection".
2) The eta axis points due north in the adopted coordinate system.
If the direction cosines represent observed (RA,Dec), the tangent
plane coordinates (xi,eta) are conventionally called the
"standard coordinates". If the direction cosines are with
respect to a right-handed triad, (xi,eta) are also right-handed.
The units of (xi,eta) are, effectively, radians at the tangent
point.
3) The vector v must be of unit length or the result will be wrong.
4) Cases where there is no solution can arise only near the poles.
For example, it is clearly impossible for a star at the pole
itself to have a non-zero xi value, and hence it is meaningless
to ask where the tangent point would have to be.
5) Also near the poles, cases can arise where there are two useful
solutions. The return value indicates whether the second of the
two solutions returned is useful; 1 indicates only one useful
solution, the usual case.
6) The basis of the algorithm is to solve the spherical triangle
PSC, where P is the north celestial pole, S is the star and C is
the tangent point. Calling the celestial spherical coordinates
of the star and tangent point (a,b) and (a0,b0) respectively, and
writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), and
transforming the vector v into (a,b) in the normal way, side c is
then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be
found) is (pi/2-b0), while angle C is given by sin(C) = xi/rho
and cos(C) = eta/rho; angle P (to be found) is (a-a0). After
solving the spherical triangle, the result (a0,b0) can be
expressed in vector form as v0.
7) This function is a member of the following set:
spherical vector solve for
iauTpxes iauTpxev xi,eta
iauTpsts iauTpstv star
iauTpors > iauTporv < origin
References:
Calabretta M.R. & Greisen, E.W., 2002, "Representations of
celestial coordinates in FITS", Astron.Astrophys. 395, 1077
Green, R.M., "Spherical Astronomy", Cambridge University Press,
1987, Chapter 13.
*/
func Tporv(xi, eta float64, v [3]float64, v01, v02 *[3]float64) int {
var x, y, z, rxy2, xi2, eta2p1, r, rsb, rcb, w2, w, c float64
x = v[0]
y = v[1]
z = v[2]
rxy2 = x*x + y*y
xi2 = xi * xi
eta2p1 = eta*eta + 1.0
r = sqrt(xi2 + eta2p1)
rsb = r * z
rcb = r * sqrt(x*x+y*y)
w2 = rcb*rcb - xi2
if w2 > 0.0 {
w = sqrt(w2)
c = (rsb*eta + w) / (eta2p1 * sqrt(rxy2*(w2+xi2)))
v01[0] = c * (x*w + y*xi)
v01[1] = c * (y*w - x*xi)
v01[2] = (rsb - eta*w) / eta2p1
w = -w
c = (rsb*eta + w) / (eta2p1 * sqrt(rxy2*(w2+xi2)))
v02[0] = c * (x*w + y*xi)
v02[1] = c * (y*w - x*xi)
v02[2] = (rsb - eta*w) / eta2p1
if fabs(rsb) < 1.0 {
return 1
} else {
return 2
}
} else {
return 0
}
}
gofa-1.19.1/sofa_copyr.txt 0000664 0000000 0000000 00000011365 14535740236 0015443 0 ustar 00root root 0000000 0000000 copyr.lis 2021 April 12
COPYRIGHT NOTICE
Text equivalent to that below appears at the end of every SOFA routine
(with one exception). There are small formatting differences between
the Fortran and C versions.
The one exception is the "leap second" routine DAT. This uniquely is
classified as "user replaceable", and has a mitigated license statement
that permits the distribution of local variants under the same name.
This measure allows other SOFA routines to call the local variant, which
may be file or network based, or otherwise equipped to pick up IERS leap
second updates with no need to download new SOFA code.
*+----------------------------------------------------------------------
*
* Copyright (C) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
* =====================
* SOFA Software License
* =====================
*
* NOTICE TO USER:
*
* BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
* CONDITIONS WHICH APPLY TO ITS USE.
*
* 1. The Software is owned by the IAU SOFA Board ("SOFA").
*
* 2. Permission is granted to anyone to use the SOFA software for any
* purpose, including commercial applications, free of charge and
* without payment of royalties, subject to the conditions and
* restrictions listed below.
*
* 3. You (the user) may copy and distribute SOFA source code to others,
* and use and adapt its code and algorithms in your own software,
* on a world-wide, royalty-free basis. That portion of your
* distribution that does not consist of intact and unchanged copies
* of SOFA source code files is a "derived work" that must comply
* with the following requirements:
*
* a) Your work shall be marked or carry a statement that it
* (i) uses routines and computations derived by you from
* software provided by SOFA under license to you; and
* (ii) does not itself constitute software provided by and/or
* endorsed by SOFA.
*
* b) The source code of your derived work must contain descriptions
* of how the derived work is based upon, contains and/or differs
* from the original SOFA software.
*
* c) The names of all routines in your derived work shall not
* include the prefix "iau" or "sofa" or trivial modifications
* thereof such as changes of case.
*
* d) The origin of the SOFA components of your derived work must
* not be misrepresented; you must not claim that you wrote the
* original software, nor file a patent application for SOFA
* software or algorithms embedded in the SOFA software.
*
* e) These requirements must be reproduced intact in any source
* distribution and shall apply to anyone to whom you have
* granted a further right to modify the source code of your
* derived work.
*
* Note that, as originally distributed, the SOFA software is
* intended to be a definitive implementation of the IAU standards,
* and consequently third-party modifications are discouraged. All
* variations, no matter how minor, must be explicitly marked as
* such, as explained above.
*
* 4. You shall not cause the SOFA software to be brought into
* disrepute, either by misuse, or use for inappropriate tasks, or
* by inappropriate modification.
*
* 5. The SOFA software is provided "as is" and SOFA makes no warranty
* as to its use or performance. SOFA does not and cannot warrant
* the performance or results which the user may obtain by using the
* SOFA software. SOFA makes no warranties, express or implied, as
* to non-infringement of third party rights, merchantability, or
* fitness for any particular purpose. In no event will SOFA be
* liable to the user for any consequential, incidental, or special
* damages, including any lost profits or lost savings, even if a
* SOFA representative has been advised of such damages, or for any
* claim by any third party.
*
* 6. The provision of any version of the SOFA software under the terms
* and conditions specified herein does not imply that future
* versions will also be made available under the same terms and
* conditions.
*
* In any published work or commercial product which uses the SOFA
* software directly, acknowledgement (see www.iausofa.org) is
* appreciated.
*
* Correspondence concerning SOFA software should be addressed as
* follows:
*
* By email: sofa@ukho.gov.uk
* By post: IAU SOFA Center
* HM Nautical Almanac Office
* UK Hydrographic Office
* Admiralty Way, Taunton
* Somerset, TA1 2DN
* United Kingdom
*
*-----------------------------------------------------------------------
gofa-1.19.1/test/ 0000775 0000000 0000000 00000000000 14535740236 0013507 5 ustar 00root root 0000000 0000000 gofa-1.19.1/test/angle_test.go 0000664 0000000 0000000 00000004765 14535740236 0016177 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestAnp(t *testing.T) {
vvd(t, gofa.Anp(-0.1), 6.183185307179586477, 1e-12, "Anp", "")
}
func TestAnpm(t *testing.T) {
vvd(t, gofa.Anpm(-4.0), 2.283185307179586477, 1e-12, "Anpm", "")
}
func TestA2af(t *testing.T) {
var idmsf [4]int
var s byte
gofa.A2af(4, 2.345, &s, &idmsf)
vbv(t, s, '+', "A2af", "s")
viv(t, idmsf[0], 134, "A2af", "0")
viv(t, idmsf[1], 21, "A2af", "1")
viv(t, idmsf[2], 30, "A2af", "2")
viv(t, idmsf[3], 9706, "A2af", "3")
}
func TestA2tf(t *testing.T) {
var ihmsf [4]int
var s byte
gofa.A2tf(4, -3.01234, &s, &ihmsf)
vbv(t, s, '-', "A2tf", "s")
viv(t, ihmsf[0], 11, "A2tf", "0")
viv(t, ihmsf[1], 30, "A2tf", "1")
viv(t, ihmsf[2], 22, "A2tf", "2")
viv(t, ihmsf[3], 6484, "A2tf", "3")
}
func TestD2tf(t *testing.T) {
var ihmsf [4]int
var s byte
gofa.D2tf(4, -0.987654321, &s, &ihmsf)
vbv(t, s, '-', "D2tf", "s")
viv(t, ihmsf[0], 23, "D2tf", "ihmsf[0]")
viv(t, ihmsf[1], 42, "D2tf", "ihmsf[1]")
viv(t, ihmsf[2], 13, "D2tf", "ihmsf[2]")
viv(t, ihmsf[3], 3333, "D2tf", "ihmsf[3]")
}
func TestAf2a(t *testing.T) {
var a float64
var j int
j = gofa.Af2a('-', 45, 13, 27.2, &a)
vvd(t, a, -0.7893115794313644842, 1e-12, "Af2a", "a")
viv(t, j, 0, "Af2a", "j")
}
func TestTf2a(t *testing.T) {
var a float64
var j int
j = gofa.Tf2a('+', 4, 58, 20.2, &a)
vvd(t, a, 1.301739278189537429, 1e-12, "Tf2a", "a")
viv(t, j, 0, "Tf2a", "j")
}
func TestTf2d(t *testing.T) {
var d float64
var j int
j = gofa.Tf2d(' ', 23, 55, 10.9, &d)
vvd(t, d, 0.9966539351851851852, 1e-12, "Tf2d", "d")
viv(t, j, 0, "Tf2d", "j")
}
func TestSepp(t *testing.T) {
var a, b [3]float64
var s float64
a[0] = 1.0
a[1] = 0.1
a[2] = 0.2
b[0] = -3.0
b[1] = 1e-3
b[2] = 0.2
s = gofa.Sepp(a, b)
vvd(t, s, 2.860391919024660768, 1e-12, "Sepp", "")
}
func TestSeps(t *testing.T) {
var al, ap, bl, bp, s float64
al = 1.0
ap = 0.1
bl = 0.2
bp = -3.0
s = gofa.Seps(al, ap, bl, bp)
vvd(t, s, 2.346722016996998842, 1e-14, "Seps", "")
}
func TestPap(t *testing.T) {
var a, b [3]float64
var theta float64
a[0] = 1.0
a[1] = 0.1
a[2] = 0.2
b[0] = -3.0
b[1] = 1e-3
b[2] = 0.2
theta = gofa.Pap(a, b)
vvd(t, theta, 0.3671514267841113674, 1e-12, "Pap", "")
}
func TestPas(t *testing.T) {
var al, ap, bl, bp, theta float64
al = 1.0
ap = 0.1
bl = 0.2
bp = -1.0
theta = gofa.Pas(al, ap, bl, bp)
vvd(t, theta, -2.724544922932270424, 1e-12, "Pas", "")
}
gofa-1.19.1/test/astrometry_test.go 0000664 0000000 0000000 00000111112 14535740236 0017303 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestAb(t *testing.T) {
var pnat, v, ppr [3]float64
var s, bm1 float64
pnat[0] = -0.76321968546737951
pnat[1] = -0.60869453983060384
pnat[2] = -0.21676408580639883
v[0] = 2.1044018893653786e-5
v[1] = -8.9108923304429319e-5
v[2] = -3.8633714797716569e-5
s = 0.99980921395708788
bm1 = 0.99999999506209258
gofa.Ab(pnat, v, s, bm1, &ppr)
vvd(t, ppr[0], -0.7631631094219556269, 1e-12, "Ab", "1")
vvd(t, ppr[1], -0.6087553082505590832, 1e-12, "Ab", "2")
vvd(t, ppr[2], -0.2167926269368471279, 1e-12, "Ab", "3")
}
func TestApcg(t *testing.T) {
var date1, date2 float64
var ebpv [2][3]float64
var ehp [3]float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
ebpv[0][0] = 0.901310875
ebpv[0][1] = -0.417402664
ebpv[0][2] = -0.180982288
ebpv[1][0] = 0.00742727954
ebpv[1][1] = 0.0140507459
ebpv[1][2] = 0.00609045792
ehp[0] = 0.903358544
ehp[1] = -0.415395237
ehp[2] = -0.180084014
gofa.Apcg(date1, date2, ebpv, ehp, &astrom)
vvd(t, astrom.Pmt, 12.65133794027378508, 1e-11, "Apcg", "pmt")
vvd(t, astrom.Eb[0], 0.901310875, 1e-12, "Apcg", "eb(1)")
vvd(t, astrom.Eb[1], -0.417402664, 1e-12, "Apcg", "eb(2)")
vvd(t, astrom.Eb[2], -0.180982288, 1e-12, "Apcg", "eb(3)")
vvd(t, astrom.Eh[0], 0.8940025429324143045, 1e-12, "Apcg", "eh(1)")
vvd(t, astrom.Eh[1], -0.4110930268679817955, 1e-12, "Apcg", "eh(2)")
vvd(t, astrom.Eh[2], -0.1782189004872870264, 1e-12, "Apcg", "eh(3)")
vvd(t, astrom.Em, 1.010465295811013146, 1e-12, "Apcg", "em")
vvd(t, astrom.V[0], 0.4289638913597693554e-4, 1e-16, "Apcg", "v(1)")
vvd(t, astrom.V[1], 0.8115034051581320575e-4, 1e-16, "Apcg", "v(2)")
vvd(t, astrom.V[2], 0.3517555136380563427e-4, 1e-16, "Apcg", "v(3)")
vvd(t, astrom.Bm1, 0.9999999951686012981, 1e-12, "Apcg", "bm1")
vvd(t, astrom.Bpn[0][0], 1.0, 0.0, "Apcg", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.0, 0.0, "Apcg", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.0, 0.0, "Apcg", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], 0.0, 0.0, "Apcg", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 1.0, 0.0, "Apcg", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], 0.0, 0.0, "Apcg", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], 0.0, 0.0, "Apcg", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.0, 0.0, "Apcg", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 1.0, 0.0, "Apcg", "bpn(3,3)")
}
func TestApcg13(t *testing.T) {
var date1, date2 float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apcg13(date1, date2, &astrom)
vvd(t, astrom.Pmt, 12.65133794027378508, 1e-11, "Apcg13", "pmt")
vvd(t, astrom.Eb[0], 0.9013108747340644755, 1e-12, "Apcg13", "eb(1)")
vvd(t, astrom.Eb[1], -0.4174026640406119957, 1e-12, "Apcg13", "eb(2)")
vvd(t, astrom.Eb[2], -0.1809822877867817771, 1e-12, "Apcg13", "eb(3)")
vvd(t, astrom.Eh[0], 0.8940025429255499549, 1e-12, "Apcg13", "eh(1)")
vvd(t, astrom.Eh[1], -0.4110930268331896318, 1e-12, "Apcg13", "eh(2)")
vvd(t, astrom.Eh[2], -0.1782189006019749850, 1e-12, "Apcg13", "eh(3)")
vvd(t, astrom.Em, 1.010465295964664178, 1e-12, "Apcg13", "em")
vvd(t, astrom.V[0], 0.4289638912941341125e-4, 1e-16, "Apcg13", "v(1)")
vvd(t, astrom.V[1], 0.8115034032405042132e-4, 1e-16, "Apcg13", "v(2)")
vvd(t, astrom.V[2], 0.3517555135536470279e-4, 1e-16, "Apcg13", "v(3)")
vvd(t, astrom.Bm1, 0.9999999951686013142, 1e-12, "Apcg13", "bm1")
vvd(t, astrom.Bpn[0][0], 1.0, 0.0, "Apcg13", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.0, 0.0, "Apcg13", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.0, 0.0, "Apcg13", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], 0.0, 0.0, "Apcg13", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 1.0, 0.0, "Apcg13", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], 0.0, 0.0, "Apcg13", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], 0.0, 0.0, "Apcg13", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.0, 0.0, "Apcg13", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 1.0, 0.0, "Apcg13", "bpn(3,3)")
}
func TestApci(t *testing.T) {
var date1, date2 float64
var ebpv [2][3]float64
var ehp [3]float64
var x, y, s float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
ebpv[0][0] = 0.901310875
ebpv[0][1] = -0.417402664
ebpv[0][2] = -0.180982288
ebpv[1][0] = 0.00742727954
ebpv[1][1] = 0.0140507459
ebpv[1][2] = 0.00609045792
ehp[0] = 0.903358544
ehp[1] = -0.415395237
ehp[2] = -0.180084014
x = 0.0013122272
y = -2.92808623e-5
s = 3.05749468e-8
gofa.Apci(date1, date2, ebpv, ehp, x, y, s, &astrom)
vvd(t, astrom.Pmt, 12.65133794027378508, 1e-11, "Apci", "pmt")
vvd(t, astrom.Eb[0], 0.901310875, 1e-12, "Apci", "eb(1)")
vvd(t, astrom.Eb[1], -0.417402664, 1e-12, "Apci", "eb(2)")
vvd(t, astrom.Eb[2], -0.180982288, 1e-12, "Apci", "eb(3)")
vvd(t, astrom.Eh[0], 0.8940025429324143045, 1e-12, "Apci", "eh(1)")
vvd(t, astrom.Eh[1], -0.4110930268679817955, 1e-12, "Apci", "eh(2)")
vvd(t, astrom.Eh[2], -0.1782189004872870264, 1e-12, "Apci", "eh(3)")
vvd(t, astrom.Em, 1.010465295811013146, 1e-12, "Apci", "em")
vvd(t, astrom.V[0], 0.4289638913597693554e-4, 1e-16, "Apci", "v(1)")
vvd(t, astrom.V[1], 0.8115034051581320575e-4, 1e-16, "Apci", "v(2)")
vvd(t, astrom.V[2], 0.3517555136380563427e-4, 1e-16, "Apci", "v(3)")
vvd(t, astrom.Bm1, 0.9999999951686012981, 1e-12, "Apci", "bm1")
vvd(t, astrom.Bpn[0][0], 0.9999991390295159156, 1e-12, "Apci", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.4978650072505016932e-7, 1e-12, "Apci", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.1312227200000000000e-2, 1e-12, "Apci", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], -0.1136336653771609630e-7, 1e-12, "Apci", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 0.9999999995713154868, 1e-12, "Apci", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], -0.2928086230000000000e-4, 1e-12, "Apci", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], -0.1312227200895260194e-2, 1e-12, "Apci", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.2928082217872315680e-4, 1e-12, "Apci", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 0.9999991386008323373, 1e-12, "Apci", "bpn(3,3)")
}
func TestApci13(t *testing.T) {
var date1, date2 float64
var eo float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
vvd(t, astrom.Pmt, 12.65133794027378508, 1e-11, "Apci13", "pmt")
vvd(t, astrom.Eb[0], 0.9013108747340644755, 1e-12, "Apci13", "eb(1)")
vvd(t, astrom.Eb[1], -0.4174026640406119957, 1e-12, "Apci13", "eb(2)")
vvd(t, astrom.Eb[2], -0.1809822877867817771, 1e-12, "Apci13", "eb(3)")
vvd(t, astrom.Eh[0], 0.8940025429255499549, 1e-12, "Apci13", "eh(1)")
vvd(t, astrom.Eh[1], -0.4110930268331896318, 1e-12, "Apci13", "eh(2)")
vvd(t, astrom.Eh[2], -0.1782189006019749850, 1e-12, "Apci13", "eh(3)")
vvd(t, astrom.Em, 1.010465295964664178, 1e-12, "Apci13", "em")
vvd(t, astrom.V[0], 0.4289638912941341125e-4, 1e-16, "Apci13", "v(1)")
vvd(t, astrom.V[1], 0.8115034032405042132e-4, 1e-16, "Apci13", "v(2)")
vvd(t, astrom.V[2], 0.3517555135536470279e-4, 1e-16, "Apci13", "v(3)")
vvd(t, astrom.Bm1, 0.9999999951686013142, 1e-12, "Apci13", "bm1")
vvd(t, astrom.Bpn[0][0], 0.9999992060376761710, 1e-12, "Apci13", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.4124244860106037157e-7, 1e-12, "Apci13", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.1260128571051709670e-2, 1e-12, "Apci13", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], -0.1282291987222130690e-7, 1e-12, "Apci13", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 0.9999999997456835325, 1e-12, "Apci13", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], -0.2255288829420524935e-4, 1e-12, "Apci13", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], -0.1260128571661374559e-2, 1e-12, "Apci13", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.2255285422953395494e-4, 1e-12, "Apci13", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 0.9999992057833604343, 1e-12, "Apci13", "bpn(3,3)")
vvd(t, eo, -0.2900618712657375647e-2, 1e-12, "Apci13", "eo")
}
func TestApco(t *testing.T) {
var date1, date2 float64
var ebpv [2][3]float64
var ehp [3]float64
var x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb float64
var astrom gofa.ASTROM
date1 = 2456384.5
date2 = 0.970031644
ebpv[0][0] = -0.974170438
ebpv[0][1] = -0.211520082
ebpv[0][2] = -0.0917583024
ebpv[1][0] = 0.00364365824
ebpv[1][1] = -0.0154287319
ebpv[1][2] = -0.00668922024
ehp[0] = -0.973458265
ehp[1] = -0.209215307
ehp[2] = -0.0906996477
x = 0.0013122272
y = -2.92808623e-5
s = 3.05749468e-8
theta = 3.14540971
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
sp = -3.01974337e-11
refa = 0.000201418779
refb = -2.36140831e-7
gofa.Apco(date1, date2, ebpv, ehp, x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb, &astrom)
vvd(t, astrom.Pmt, 13.25248468622587269, 1e-11, "Apco", "pmt")
vvd(t, astrom.Eb[0], -0.9741827110630322720, 1e-12, "Apco", "eb(1)")
vvd(t, astrom.Eb[1], -0.2115130190135344832, 1e-12, "Apco", "eb(2)")
vvd(t, astrom.Eb[2], -0.09179840186949532298, 1e-12, "Apco", "eb(3)")
vvd(t, astrom.Eh[0], -0.9736425571689739035, 1e-12, "Apco", "eh(1)")
vvd(t, astrom.Eh[1], -0.2092452125849330936, 1e-12, "Apco", "eh(2)")
vvd(t, astrom.Eh[2], -0.09075578152243272599, 1e-12, "Apco", "eh(3)")
vvd(t, astrom.Em, 0.9998233241709957653, 1e-12, "Apco", "em")
vvd(t, astrom.V[0], 0.2078704992916728762e-4, 1e-16, "Apco", "v(1)")
vvd(t, astrom.V[1], -0.8955360107151952319e-4, 1e-16, "Apco", "v(2)")
vvd(t, astrom.V[2], -0.3863338994288951082e-4, 1e-16, "Apco", "v(3)")
vvd(t, astrom.Bm1, 0.9999999950277561236, 1e-12, "Apco", "bm1")
vvd(t, astrom.Bpn[0][0], 0.9999991390295159156, 1e-12, "Apco", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.4978650072505016932e-7, 1e-12, "Apco", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.1312227200000000000e-2, 1e-12, "Apco", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], -0.1136336653771609630e-7, 1e-12, "Apco", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 0.9999999995713154868, 1e-12, "Apco", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], -0.2928086230000000000e-4, 1e-12, "Apco", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], -0.1312227200895260194e-2, 1e-12, "Apco", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.2928082217872315680e-4, 1e-12, "Apco", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 0.9999991386008323373, 1e-12, "Apco", "bpn(3,3)")
vvd(t, astrom.Along, -0.5278008060295995734, 1e-12, "Apco", "along")
vvd(t, astrom.Xpl, 0.1133427418130752958e-5, 1e-17, "Apco", "xpl")
vvd(t, astrom.Ypl, 0.1453347595780646207e-5, 1e-17, "Apco", "ypl")
vvd(t, astrom.Sphi, -0.9440115679003211329, 1e-12, "Apco", "sphi")
vvd(t, astrom.Cphi, 0.3299123514971474711, 1e-12, "Apco", "cphi")
vvd(t, astrom.Diurab, 0, 0, "Apco", "diurab")
vvd(t, astrom.Eral, 2.617608903970400427, 1e-12, "Apco", "eral")
vvd(t, astrom.Refa, 0.2014187790000000000e-3, 1e-15, "Apco", "refa")
vvd(t, astrom.Refb, -0.2361408310000000000e-6, 1e-18, "Apco", "refb")
}
func TestApco13(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, eo float64
var astrom gofa.ASTROM
var j int
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
j = gofa.Apco13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, &eo)
vvd(t, astrom.Pmt, 13.25248468622475727, 1e-11, "Apco13", "pmt")
vvd(t, astrom.Eb[0], -0.9741827107320875162, 1e-12, "Apco13", "eb(1)")
vvd(t, astrom.Eb[1], -0.2115130190489716682, 1e-12, "Apco13", "eb(2)")
vvd(t, astrom.Eb[2], -0.09179840189496755339, 1e-12, "Apco13", "eb(3)")
vvd(t, astrom.Eh[0], -0.9736425572586935247, 1e-12, "Apco13", "eh(1)")
vvd(t, astrom.Eh[1], -0.2092452121603336166, 1e-12, "Apco13", "eh(2)")
vvd(t, astrom.Eh[2], -0.09075578153885665295, 1e-12, "Apco13", "eh(3)")
vvd(t, astrom.Em, 0.9998233240913898141, 1e-12, "Apco13", "em")
vvd(t, astrom.V[0], 0.2078704994520489246e-4, 1e-16, "Apco13", "v(1)")
vvd(t, astrom.V[1], -0.8955360133238868938e-4, 1e-16, "Apco13", "v(2)")
vvd(t, astrom.V[2], -0.3863338993055887398e-4, 1e-16, "Apco13", "v(3)")
vvd(t, astrom.Bm1, 0.9999999950277561004, 1e-12, "Apco13", "bm1")
vvd(t, astrom.Bpn[0][0], 0.9999991390295147999, 1e-12, "Apco13", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0.4978650075315529277e-7, 1e-12, "Apco13", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0.001312227200850293372, 1e-12, "Apco13", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], -0.1136336652812486604e-7, 1e-12, "Apco13", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 0.9999999995713154865, 1e-12, "Apco13", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], -0.2928086230975367296e-4, 1e-12, "Apco13", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], -0.001312227201745553566, 1e-12, "Apco13", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0.2928082218847679162e-4, 1e-12, "Apco13", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 0.9999991386008312212, 1e-12, "Apco13", "bpn(3,3)")
vvd(t, astrom.Along, -0.5278008060295995733, 1e-12, "Apco13", "along")
vvd(t, astrom.Xpl, 0.1133427418130752958e-5, 1e-17, "Apco13", "xpl")
vvd(t, astrom.Ypl, 0.1453347595780646207e-5, 1e-17, "Apco13", "ypl")
vvd(t, astrom.Sphi, -0.9440115679003211329, 1e-12, "Apco13", "sphi")
vvd(t, astrom.Cphi, 0.3299123514971474711, 1e-12, "Apco13", "cphi")
vvd(t, astrom.Diurab, 0, 0, "Apco13", "diurab")
vvd(t, astrom.Eral, 2.617608909189664000, 1e-12, "Apco13", "eral")
vvd(t, astrom.Refa, 0.2014187785940396921e-3, 1e-15, "Apco13", "refa")
vvd(t, astrom.Refb, -0.2361408314943696227e-6, 1e-18, "Apco13", "refb")
vvd(t, eo, -0.003020548354802412839, 1e-14, "Apco13", "eo")
viv(t, j, 0, "Apco13", "j")
}
func TestApcs(t *testing.T) {
var date1, date2 float64
var pv, ebpv [2][3]float64
var ehp [3]float64
var astrom gofa.ASTROM
date1 = 2456384.5
date2 = 0.970031644
pv[0][0] = -1836024.09
pv[0][1] = 1056607.72
pv[0][2] = -5998795.26
pv[1][0] = -77.0361767
pv[1][1] = -133.310856
pv[1][2] = 0.0971855934
ebpv[0][0] = -0.974170438
ebpv[0][1] = -0.211520082
ebpv[0][2] = -0.0917583024
ebpv[1][0] = 0.00364365824
ebpv[1][1] = -0.0154287319
ebpv[1][2] = -0.00668922024
ehp[0] = -0.973458265
ehp[1] = -0.209215307
ehp[2] = -0.0906996477
gofa.Apcs(date1, date2, pv, ebpv, ehp, &astrom)
vvd(t, astrom.Pmt, 13.25248468622587269, 1e-11, "Apcs", "pmt")
vvd(t, astrom.Eb[0], -0.9741827110629881886, 1e-12, "Apcs", "eb(1)")
vvd(t, astrom.Eb[1], -0.2115130190136415986, 1e-12, "Apcs", "eb(2)")
vvd(t, astrom.Eb[2], -0.09179840186954412099, 1e-12, "Apcs", "eb(3)")
vvd(t, astrom.Eh[0], -0.9736425571689454706, 1e-12, "Apcs", "eh(1)")
vvd(t, astrom.Eh[1], -0.2092452125850435930, 1e-12, "Apcs", "eh(2)")
vvd(t, astrom.Eh[2], -0.09075578152248299218, 1e-12, "Apcs", "eh(3)")
vvd(t, astrom.Em, 0.9998233241709796859, 1e-12, "Apcs", "em")
vvd(t, astrom.V[0], 0.2078704993282685510e-4, 1e-16, "Apcs", "v(1)")
vvd(t, astrom.V[1], -0.8955360106989405683e-4, 1e-16, "Apcs", "v(2)")
vvd(t, astrom.V[2], -0.3863338994289409097e-4, 1e-16, "Apcs", "v(3)")
vvd(t, astrom.Bm1, 0.9999999950277561237, 1e-12, "Apcs", "bm1")
vvd(t, astrom.Bpn[0][0], 1, 0, "Apcs", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0, 0, "Apcs", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0, 0, "Apcs", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], 0, 0, "Apcs", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 1, 0, "Apcs", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], 0, 0, "Apcs", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], 0, 0, "Apcs", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0, 0, "Apcs", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 1, 0, "Apcs", "bpn(3,3)")
}
func TestApcs13(t *testing.T) {
var date1, date2 float64
var pv [2][3]float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
pv[0][0] = -6241497.16
pv[0][1] = 401346.896
pv[0][2] = -1251136.04
pv[1][0] = -29.264597
pv[1][1] = -455.021831
pv[1][2] = 0.0266151194
gofa.Apcs13(date1, date2, pv, &astrom)
vvd(t, astrom.Pmt, 12.65133794027378508, 1e-11, "Apcs13", "pmt")
vvd(t, astrom.Eb[0], 0.9012691529025250644, 1e-12, "Apcs13", "eb(1)")
vvd(t, astrom.Eb[1], -0.4173999812023194317, 1e-12, "Apcs13", "eb(2)")
vvd(t, astrom.Eb[2], -0.1809906511146429670, 1e-12, "Apcs13", "eb(3)")
vvd(t, astrom.Eh[0], 0.8939939101760130792, 1e-12, "Apcs13", "eh(1)")
vvd(t, astrom.Eh[1], -0.4111053891734021478, 1e-12, "Apcs13", "eh(2)")
vvd(t, astrom.Eh[2], -0.1782336880636997374, 1e-12, "Apcs13", "eh(3)")
vvd(t, astrom.Em, 1.010428384373491095, 1e-12, "Apcs13", "em")
vvd(t, astrom.V[0], 0.4279877294121697570e-4, 1e-16, "Apcs13", "v(1)")
vvd(t, astrom.V[1], 0.7963255087052120678e-4, 1e-16, "Apcs13", "v(2)")
vvd(t, astrom.V[2], 0.3517564013384691531e-4, 1e-16, "Apcs13", "v(3)")
vvd(t, astrom.Bm1, 0.9999999952947980978, 1e-12, "Apcs13", "bm1")
vvd(t, astrom.Bpn[0][0], 1, 0, "Apcs13", "bpn(1,1)")
vvd(t, astrom.Bpn[1][0], 0, 0, "Apcs13", "bpn(2,1)")
vvd(t, astrom.Bpn[2][0], 0, 0, "Apcs13", "bpn(3,1)")
vvd(t, astrom.Bpn[0][1], 0, 0, "Apcs13", "bpn(1,2)")
vvd(t, astrom.Bpn[1][1], 1, 0, "Apcs13", "bpn(2,2)")
vvd(t, astrom.Bpn[2][1], 0, 0, "Apcs13", "bpn(3,2)")
vvd(t, astrom.Bpn[0][2], 0, 0, "Apcs13", "bpn(1,3)")
vvd(t, astrom.Bpn[1][2], 0, 0, "Apcs13", "bpn(2,3)")
vvd(t, astrom.Bpn[2][2], 1, 0, "Apcs13", "bpn(3,3)")
}
func TestAper(t *testing.T) {
var theta float64
var astrom gofa.ASTROM
astrom.Along = 1.234
theta = 5.678
gofa.Aper(theta, &astrom)
vvd(t, astrom.Eral, 6.912000000000000000, 1e-12, "Aper", "pmt")
}
func TestAper13(t *testing.T) {
var ut11, ut12 float64
var astrom gofa.ASTROM
astrom.Along = 1.234
ut11 = 2456165.5
ut12 = 0.401182685
gofa.Aper13(ut11, ut12, &astrom)
vvd(t, astrom.Eral, 3.316236661789694933, 1e-12, "Aper13", "pmt")
}
func TestApio(t *testing.T) {
var sp, theta, elong, phi, hm, xp, yp, refa, refb float64
var astrom gofa.ASTROM
sp = -3.01974337e-11
theta = 3.14540971
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
refa = 0.000201418779
refb = -2.36140831e-7
gofa.Apio(sp, theta, elong, phi, hm, xp, yp, refa, refb, &astrom)
vvd(t, astrom.Along, -0.5278008060295995734, 1e-12, "Apio", "along")
vvd(t, astrom.Xpl, 0.1133427418130752958e-5, 1e-17, "Apio", "xpl")
vvd(t, astrom.Ypl, 0.1453347595780646207e-5, 1e-17, "Apio", "ypl")
vvd(t, astrom.Sphi, -0.9440115679003211329, 1e-12, "Apio", "sphi")
vvd(t, astrom.Cphi, 0.3299123514971474711, 1e-12, "Apio", "cphi")
vvd(t, astrom.Diurab, 0.5135843661699913529e-6, 1e-12, "Apio", "diurab")
vvd(t, astrom.Eral, 2.617608903970400427, 1e-12, "Apio", "eral")
vvd(t, astrom.Refa, 0.2014187790000000000e-3, 1e-15, "Apio", "refa")
vvd(t, astrom.Refb, -0.2361408310000000000e-6, 1e-18, "Apio", "refb")
}
func TestApio13(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl float64
var j int
var astrom gofa.ASTROM
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
j = gofa.Apio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom)
vvd(t, astrom.Along, -0.5278008060295995733, 1e-12, "Apio13", "along")
vvd(t, astrom.Xpl, 0.1133427418130752958e-5, 1e-17, "Apio13", "xpl")
vvd(t, astrom.Ypl, 0.1453347595780646207e-5, 1e-17, "Apio13", "ypl")
vvd(t, astrom.Sphi, -0.9440115679003211329, 1e-12, "Apio13", "sphi")
vvd(t, astrom.Cphi, 0.3299123514971474711, 1e-12, "Apio13", "cphi")
vvd(t, astrom.Diurab, 0.5135843661699913529e-6, 1e-12, "Apio13", "diurab")
vvd(t, astrom.Eral, 2.617608909189664000, 1e-12, "Apio13", "eral")
vvd(t, astrom.Refa, 0.2014187785940396921e-3, 1e-15, "Apio13", "refa")
vvd(t, astrom.Refb, -0.2361408314943696227e-6, 1e-18, "Apio13", "refb")
viv(t, j, 0, "Apio13", "j")
}
func TestAtcc13(t *testing.T) {
var rc, dc, pr, pd, px, rv, date1, date2, ra, da float64
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
date1 = 2456165.5
date2 = 0.401182685
gofa.Atcc13(rc, dc, pr, pd, px, rv, date1, date2, &ra, &da)
vvd(t, ra, 2.710126504531372384, 1e-12, "Atcc13", "ra")
vvd(t, da, 0.1740632537628350152, 1e-12, "Atcc13", "da")
}
func TestAtccq(t *testing.T) {
var date1, date2 float64
var eo, rc, dc, pr, pd, px, rv, ra, da float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
gofa.Atccq(rc, dc, pr, pd, px, rv, &astrom, &ra, &da)
vvd(t, ra, 2.710126504531372384, 1e-12, "Atccq", "ra")
vvd(t, da, 0.1740632537628350152, 1e-12, "Atccq", "da")
}
func TestAtci13(t *testing.T) {
var rc, dc, pr, pd, px, rv, date1, date2, ri, di, eo float64
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
date1 = 2456165.5
date2 = 0.401182685
gofa.Atci13(rc, dc, pr, pd, px, rv, date1, date2, &ri, &di, &eo)
vvd(t, ri, 2.710121572968696744, 1e-12, "Atci13", "ri")
vvd(t, di, 0.1729371367219539137, 1e-12, "Atci13", "di")
vvd(t, eo, -0.002900618712657375647, 1e-14, "Atci13", "eo")
}
func TestAtciq(t *testing.T) {
var date1, date2 float64
var eo, rc, dc, pr, pd, px, rv, ri, di float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
gofa.Atciq(rc, dc, pr, pd, px, rv, &astrom, &ri, &di)
vvd(t, ri, 2.710121572968696744, 1e-12, "Atciq", "ri")
vvd(t, di, 0.1729371367219539137, 1e-12, "Atciq", "di")
}
func TestAtciqn(t *testing.T) {
// var b [3]gofa.LDBODY
b := make([]gofa.LDBODY, 3)
var date1, date2 float64
var eo, rc, dc, pr, pd, px, rv, ri, di float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
b[0].Bm = 0.00028574
b[0].Dl = 3e-10
b[0].Pv[0][0] = -7.81014427
b[0].Pv[0][1] = -5.60956681
b[0].Pv[0][2] = -1.98079819
b[0].Pv[1][0] = 0.0030723249
b[0].Pv[1][1] = -0.00406995477
b[0].Pv[1][2] = -0.00181335842
b[1].Bm = 0.00095435
b[1].Dl = 3e-9
b[1].Pv[0][0] = 0.738098796
b[1].Pv[0][1] = 4.63658692
b[1].Pv[0][2] = 1.9693136
b[1].Pv[1][0] = -0.00755816922
b[1].Pv[1][1] = 0.00126913722
b[1].Pv[1][2] = 0.000727999001
b[2].Bm = 1.0
b[2].Dl = 6e-6
b[2].Pv[0][0] = -0.000712174377
b[2].Pv[0][1] = -0.00230478303
b[2].Pv[0][2] = -0.00105865966
b[2].Pv[1][0] = 6.29235213e-6
b[2].Pv[1][1] = -3.30888387e-7
b[2].Pv[1][2] = -2.96486623e-7
gofa.Atciqn(rc, dc, pr, pd, px, rv, &astrom, 3, b, &ri, &di)
vvd(t, ri, 2.710122008104983335, 1e-12, "Atciqn", "ri")
vvd(t, di, 0.1729371916492767821, 1e-12, "Atciqn", "di")
}
func TestAtciqz(t *testing.T) {
var date1, date2 float64
var eo, rc, dc, ri, di float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
rc = 2.71
dc = 0.174
gofa.Atciqz(rc, dc, &astrom, &ri, &di)
vvd(t, ri, 2.709994899247256984, 1e-12, "Atciqz", "ri")
vvd(t, di, 0.1728740720984931891, 1e-12, "Atciqz", "di")
}
func TestAtco13(t *testing.T) {
var rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob, eo float64
var j int
rc = 2.71
dc = 0.174
pr = 1e-5
pd = 5e-6
px = 0.1
rv = 55.0
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
j = gofa.Atco13(rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &aob, &zob, &hob, &dob, &rob, &eo)
vvd(t, aob, 0.9251774485485515207e-1, 1e-12, "Atco13", "aob")
vvd(t, zob, 1.407661405256499357, 1e-12, "Atco13", "zob")
vvd(t, hob, -0.9265154431529724692e-1, 1e-12, "Atco13", "hob")
vvd(t, dob, 0.1716626560072526200, 1e-12, "Atco13", "dob")
vvd(t, rob, 2.710260453504961012, 1e-12, "Atco13", "rob")
vvd(t, eo, -0.003020548354802412839, 1e-14, "Atco13", "eo")
viv(t, j, 0, "Atco13", "j")
}
func TestAtic13(t *testing.T) {
var ri, di, date1, date2, rc, dc, eo float64
ri = 2.710121572969038991
di = 0.1729371367218230438
date1 = 2456165.5
date2 = 0.401182685
gofa.Atic13(ri, di, date1, date2, &rc, &dc, &eo)
vvd(t, rc, 2.710126504531716819, 1e-12, "Atic13", "rc")
vvd(t, dc, 0.1740632537627034482, 1e-12, "Atic13", "dc")
vvd(t, eo, -0.002900618712657375647, 1e-14, "Atic13", "eo")
}
func TestAticq(t *testing.T) {
var date1, date2 float64
var eo, ri, di, rc, dc float64
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
ri = 2.710121572969038991
di = 0.1729371367218230438
gofa.Aticq(ri, di, &astrom, &rc, &dc)
vvd(t, rc, 2.710126504531716819, 1e-12, "Aticq", "rc")
vvd(t, dc, 0.1740632537627034482, 1e-12, "Aticq", "dc")
}
func TestAticqn(t *testing.T) {
var date1, date2 float64
var eo, ri, di, rc, dc float64
b := make([]gofa.LDBODY, 3)
var astrom gofa.ASTROM
date1 = 2456165.5
date2 = 0.401182685
gofa.Apci13(date1, date2, &astrom, &eo)
ri = 2.709994899247599271
di = 0.1728740720983623469
b[0].Bm = 0.00028574
b[0].Dl = 3e-10
b[0].Pv[0][0] = -7.81014427
b[0].Pv[0][1] = -5.60956681
b[0].Pv[0][2] = -1.98079819
b[0].Pv[1][0] = 0.0030723249
b[0].Pv[1][1] = -0.00406995477
b[0].Pv[1][2] = -0.00181335842
b[1].Bm = 0.00095435
b[1].Dl = 3e-9
b[1].Pv[0][0] = 0.738098796
b[1].Pv[0][1] = 4.63658692
b[1].Pv[0][2] = 1.9693136
b[1].Pv[1][0] = -0.00755816922
b[1].Pv[1][1] = 0.00126913722
b[1].Pv[1][2] = 0.000727999001
b[2].Bm = 1.0
b[2].Dl = 6e-6
b[2].Pv[0][0] = -0.000712174377
b[2].Pv[0][1] = -0.00230478303
b[2].Pv[0][2] = -0.00105865966
b[2].Pv[1][0] = 6.29235213e-6
b[2].Pv[1][1] = -3.30888387e-7
b[2].Pv[1][2] = -2.96486623e-7
gofa.Aticqn(ri, di, &astrom, 3, b, &rc, &dc)
vvd(t, rc, 2.709999575033027333, 1e-12, "Atciqn", "rc")
vvd(t, dc, 0.1739999656316469990, 1e-12, "Atciqn", "dc")
}
func TestAtio13(t *testing.T) {
var ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob float64
var j int
ri = 2.710121572969038991
di = 0.1729371367218230438
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
j = gofa.Atio13(ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &aob, &zob, &hob, &dob, &rob)
vvd(t, aob, 0.9233952224895122499e-1, 1e-12, "Atio13", "aob")
vvd(t, zob, 1.407758704513549991, 1e-12, "Atio13", "zob")
vvd(t, hob, -0.9247619879881698140e-1, 1e-12, "Atio13", "hob")
vvd(t, dob, 0.1717653435756234676, 1e-12, "Atio13", "dob")
vvd(t, rob, 2.710085107988480746, 1e-12, "Atio13", "rob")
viv(t, j, 0, "Atio13", "j")
}
func TestAtioq(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ri, di, aob, zob, hob, dob, rob float64
var astrom gofa.ASTROM
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
gofa.Apio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom)
ri = 2.710121572969038991
di = 0.1729371367218230438
gofa.Atioq(ri, di, &astrom, &aob, &zob, &hob, &dob, &rob)
vvd(t, aob, 0.9233952224895122499e-1, 1e-12, "Atioq", "aob")
vvd(t, zob, 1.407758704513549991, 1e-12, "Atioq", "zob")
vvd(t, hob, -0.9247619879881698140e-1, 1e-12, "Atioq", "hob")
vvd(t, dob, 0.1717653435756234676, 1e-12, "Atioq", "dob")
vvd(t, rob, 2.710085107988480746, 1e-12, "Atioq", "rob")
}
func TestAtoc13(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, rc, dc float64
var j int
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
ob1 = 2.710085107986886201
ob2 = 0.1717653435758265198
j = gofa.Atoc13("R", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc)
vvd(t, rc, 2.709956744659136129, 1e-12, "Atoc13", "R/rc")
vvd(t, dc, 0.1741696500898471362, 1e-12, "Atoc13", "R/dc")
viv(t, j, 0, "Atoc13", "R/j")
ob1 = -0.09247619879782006106
ob2 = 0.1717653435758265198
j = gofa.Atoc13("H", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc)
vvd(t, rc, 2.709956744659734086, 1e-12, "Atoc13", "H/rc")
vvd(t, dc, 0.1741696500898471362, 1e-12, "Atoc13", "H/dc")
viv(t, j, 0, "Atoc13", "H/j")
ob1 = 0.09233952224794989993
ob2 = 1.407758704513722461
j = gofa.Atoc13("A", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc)
vvd(t, rc, 2.709956744659734086, 1e-12, "Atoc13", "A/rc")
vvd(t, dc, 0.1741696500898471366, 1e-12, "Atoc13", "A/dc")
viv(t, j, 0, "Atoc13", "A/j")
}
func TestAtoi13(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, ri, di float64
var j int
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
ob1 = 2.710085107986886201
ob2 = 0.1717653435758265198
j = gofa.Atoi13("R", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di)
vvd(t, ri, 2.710121574447540810, 1e-12, "Atoi13", "R/ri")
vvd(t, di, 0.1729371839116608778, 1e-12, "Atoi13", "R/di")
viv(t, j, 0, "Atoi13", "R/J")
ob1 = -0.09247619879782006106
ob2 = 0.1717653435758265198
j = gofa.Atoi13("H", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di)
vvd(t, ri, 2.710121574448138676, 1e-12, "Atoi13", "H/ri")
vvd(t, di, 0.1729371839116608778, 1e-12, "Atoi13", "H/di")
viv(t, j, 0, "Atoi13", "H/J")
ob1 = 0.09233952224794989993
ob2 = 1.407758704513722461
j = gofa.Atoi13("A", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di)
vvd(t, ri, 2.710121574448138676, 1e-12, "Atoi13", "A/ri")
vvd(t, di, 0.1729371839116608781, 1e-12, "Atoi13", "A/di")
viv(t, j, 0, "Atoi13", "A/J")
}
func TestAtoiq(t *testing.T) {
var utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, ri, di float64
var astrom gofa.ASTROM
utc1 = 2456384.5
utc2 = 0.969254051
dut1 = 0.1550675
elong = -0.527800806
phi = -1.2345856
hm = 2738.0
xp = 2.47230737e-7
yp = 1.82640464e-6
phpa = 731.0
tc = 12.8
rh = 0.59
wl = 0.55
gofa.Apio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom)
ob1 = 2.710085107986886201
ob2 = 0.1717653435758265198
gofa.Atoiq("R", ob1, ob2, &astrom, &ri, &di)
vvd(t, ri, 2.710121574447540810, 1e-12, "Atoiq", "R/ri")
vvd(t, di, 0.17293718391166087785, 1e-12, "Atoiq", "R/di")
ob1 = -0.09247619879782006106
ob2 = 0.1717653435758265198
gofa.Atoiq("H", ob1, ob2, &astrom, &ri, &di)
vvd(t, ri, 2.710121574448138676, 1e-12, "Atoiq", "H/ri")
vvd(t, di, 0.1729371839116608778, 1e-12, "Atoiq", "H/di")
ob1 = 0.09233952224794989993
ob2 = 1.407758704513722461
gofa.Atoiq("A", ob1, ob2, &astrom, &ri, &di)
vvd(t, ri, 2.710121574448138676, 1e-12, "Atoiq", "A/ri")
vvd(t, di, 0.1729371839116608781, 1e-12, "Atoiq", "A/di")
}
func TestLd(t *testing.T) {
var bm, em, dlim float64
var p, q, e, p1 [3]float64
bm = 0.00028574
p[0] = -0.763276255
p[1] = -0.608633767
p[2] = -0.216735543
q[0] = -0.763276255
q[1] = -0.608633767
q[2] = -0.216735543
e[0] = 0.76700421
e[1] = 0.605629598
e[2] = 0.211937094
em = 8.91276983
dlim = 3e-10
gofa.Ld(bm, p, q, e, em, dlim, &p1)
vvd(t, p1[0], -0.7632762548968159627, 1e-12, "Ld", "1")
vvd(t, p1[1], -0.6086337670823762701, 1e-12, "Ld", "2")
vvd(t, p1[2], -0.2167355431320546947, 1e-12, "Ld", "3")
}
func TestLdn(t *testing.T) {
var n int
b := make([]gofa.LDBODY, 3)
var ob, sc, sn [3]float64
n = 3
b[0].Bm = 0.00028574
b[0].Dl = 3e-10
b[0].Pv[0][0] = -7.81014427
b[0].Pv[0][1] = -5.60956681
b[0].Pv[0][2] = -1.98079819
b[0].Pv[1][0] = 0.0030723249
b[0].Pv[1][1] = -0.00406995477
b[0].Pv[1][2] = -0.00181335842
b[1].Bm = 0.00095435
b[1].Dl = 3e-9
b[1].Pv[0][0] = 0.738098796
b[1].Pv[0][1] = 4.63658692
b[1].Pv[0][2] = 1.9693136
b[1].Pv[1][0] = -0.00755816922
b[1].Pv[1][1] = 0.00126913722
b[1].Pv[1][2] = 0.000727999001
b[2].Bm = 1.0
b[2].Dl = 6e-6
b[2].Pv[0][0] = -0.000712174377
b[2].Pv[0][1] = -0.00230478303
b[2].Pv[0][2] = -0.00105865966
b[2].Pv[1][0] = 6.29235213e-6
b[2].Pv[1][1] = -3.30888387e-7
b[2].Pv[1][2] = -2.96486623e-7
ob[0] = -0.974170437
ob[1] = -0.2115201
ob[2] = -0.0917583114
sc[0] = -0.763276255
sc[1] = -0.608633767
sc[2] = -0.216735543
gofa.Ldn(n, b, ob, sc, &sn)
vvd(t, sn[0], -0.7632762579693333866, 1e-12, "Ldn", "1")
vvd(t, sn[1], -0.6086337636093002660, 1e-12, "Ldn", "2")
vvd(t, sn[2], -0.2167355420646328159, 1e-12, "Ldn", "3")
}
func TestLdsun(t *testing.T) {
var p, e, p1 [3]float64
var em float64
p[0] = -0.763276255
p[1] = -0.608633767
p[2] = -0.216735543
e[0] = -0.973644023
e[1] = -0.20925523
e[2] = -0.0907169552
em = 0.999809214
gofa.Ldsun(p, e, em, &p1)
vvd(t, p1[0], -0.7632762580731413169, 1e-12, "Ldsun", "1")
vvd(t, p1[1], -0.6086337635262647900, 1e-12, "Ldsun", "2")
vvd(t, p1[2], -0.2167355419322321302, 1e-12, "Ldsun", "3")
}
func TestPmpx(t *testing.T) {
var rc, dc, pr, pd, px, rv, pmt float64
var pob, pco [3]float64
rc = 1.234
dc = 0.789
pr = 1e-5
pd = -2e-5
px = 1e-2
rv = 10.0
pmt = 8.75
pob[0] = 0.9
pob[1] = 0.4
pob[2] = 0.1
gofa.Pmpx(rc, dc, pr, pd, px, rv, pmt, pob, &pco)
vvd(t, pco[0], 0.2328137623960308438, 1e-12, "Pmpx", "1")
vvd(t, pco[1], 0.6651097085397855328, 1e-12, "Pmpx", "2")
vvd(t, pco[2], 0.7095257765896359837, 1e-12, "Pmpx", "3")
}
func TestPmsafe(t *testing.T) {
var j int
var ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, ra2, dec2, pmr2, pmd2, px2, rv2 float64
ra1 = 1.234
dec1 = 0.789
pmr1 = 1e-5
pmd1 = -2e-5
px1 = 1e-2
rv1 = 10.0
ep1a = 2400000.5
ep1b = 48348.5625
ep2a = 2400000.5
ep2b = 51544.5
j = gofa.Pmsafe(ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2)
vvd(t, ra2, 1.234087484501017061, 1e-12, "Pmsafe", "ra2")
vvd(t, dec2, 0.7888249982450468567, 1e-12, "Pmsafe", "dec2")
vvd(t, pmr2, 0.9996457663586073988e-5, 1e-12, "Pmsafe", "pmr2")
vvd(t, pmd2, -0.2000040085106754565e-4, 1e-16, "Pmsafe", "pmd2")
vvd(t, px2, 0.9999997295356830666e-2, 1e-12, "Pmsafe", "px2")
vvd(t, rv2, 10.38468380293920069, 1e-10, "Pmsafe", "rv2")
viv(t, j, 0, "Pmsafe", "j")
}
func TestPvstar(t *testing.T) {
var pv [2][3]float64
var ra, dec, pmr, pmd, px, rv float64
var j int
pv[0][0] = 126668.5912743160601
pv[0][1] = 2136.792716839935195
pv[0][2] = -245251.2339876830091
pv[1][0] = -0.4051854035740712739e-2
pv[1][1] = -0.6253919754866173866e-2
pv[1][2] = 0.1189353719774107189e-1
j = gofa.Pvstar(pv, &ra, &dec, &pmr, &pmd, &px, &rv)
vvd(t, ra, 0.1686756e-1, 1e-12, "Pvstar", "ra")
vvd(t, dec, -1.093989828, 1e-12, "Pvstar", "dec")
vvd(t, pmr, -0.1783235160000472788e-4, 1e-16, "Pvstar", "pmr")
vvd(t, pmd, 0.2336024047000619347e-5, 1e-16, "Pvstar", "pmd")
vvd(t, px, 0.74723, 1e-12, "Pvstar", "px")
vvd(t, rv, -21.60000010107306010, 1e-11, "Pvstar", "rv")
viv(t, j, 0, "Pvstar", "j")
}
func TestPvtob(t *testing.T) {
var elong, phi, hm, xp, yp, sp, theta float64
var pv [2][3]float64
elong = 2.0
phi = 0.5
hm = 3000.0
xp = 1e-6
yp = -0.5e-6
sp = 1e-8
theta = 5.0
gofa.Pvtob(elong, phi, hm, xp, yp, sp, theta, &pv)
vvd(t, pv[0][0], 4225081.367071159207, 1e-5, "Pvtob", "p(1)")
vvd(t, pv[0][1], 3681943.215856198144, 1e-5, "Pvtob", "p(2)")
vvd(t, pv[0][2], 3041149.399241260785, 1e-5, "Pvtob", "p(3)")
vvd(t, pv[1][0], -268.4915389365998787, 1e-9, "Pvtob", "v(1)")
vvd(t, pv[1][1], 308.0977983288903123, 1e-9, "Pvtob", "v(2)")
vvd(t, pv[1][2], 0, 0, "Pvtob", "v(3)")
}
func TestRefco(t *testing.T) {
var phpa, tc, rh, wl, refa, refb float64
phpa = 800.0
tc = 10.0
rh = 0.9
wl = 0.4
gofa.Refco(phpa, tc, rh, wl, &refa, &refb)
vvd(t, refa, 0.2264949956241415009e-3, 1e-15, "Refco", "refa")
vvd(t, refb, -0.2598658261729343970e-6, 1e-18, "Refco", "refb")
}
func TestStarpm(t *testing.T) {
var ra1, dec1, pmr1, pmd1, px1, rv1 float64
var ra2, dec2, pmr2, pmd2, px2, rv2 float64
var j int
ra1 = 0.01686756
dec1 = -1.093989828
pmr1 = -1.78323516e-5
pmd1 = 2.336024047e-6
px1 = 0.74723
rv1 = -21.6
j = gofa.Starpm(ra1, dec1, pmr1, pmd1, px1, rv1, 2400000.5, 50083.0, 2400000.5, 53736.0, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2)
vvd(t, ra2, 0.01668919069414256149, 1e-13, "Starpm", "ra")
vvd(t, dec2, -1.093966454217127897, 1e-13, "Starpm", "dec")
vvd(t, pmr2, -0.1783662682153176524e-4, 1e-17, "Starpm", "pmr")
vvd(t, pmd2, 0.2338092915983989595e-5, 1e-17, "Starpm", "pmd")
vvd(t, px2, 0.7473533835317719243, 1e-13, "Starpm", "px")
vvd(t, rv2, -21.59905170476417175, 1e-11, "Starpm", "rv")
viv(t, j, 0, "Starpm", "j")
}
func TestStarpv(t *testing.T) {
var ra, dec, pmr, pmd, px, rv float64
var pv [2][3]float64
var j int
ra = 0.01686756
dec = -1.093989828
pmr = -1.78323516e-5
pmd = 2.336024047e-6
px = 0.74723
rv = -21.6
j = gofa.Starpv(ra, dec, pmr, pmd, px, rv, &pv)
vvd(t, pv[0][0], 126668.5912743160601, 1e-10, "Starpv", "11")
vvd(t, pv[0][1], 2136.792716839935195, 1e-12, "Starpv", "12")
vvd(t, pv[0][2], -245251.2339876830091, 1e-10, "Starpv", "13")
vvd(t, pv[1][0], -0.4051854008955659551e-2, 1e-13, "Starpv", "21")
vvd(t, pv[1][1], -0.6253919754414777970e-2, 1e-15, "Starpv", "22")
vvd(t, pv[1][2], 0.1189353714588109341e-1, 1e-13, "Starpv", "23")
viv(t, j, 0, "Starpv", "j")
}
gofa-1.19.1/test/catalog_test.go 0000664 0000000 0000000 00000012473 14535740236 0016516 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestFk425(t *testing.T) {
var r1950, d1950, dr1950, dd1950, p1950, v1950, r2000, d2000, dr2000, dd2000, p2000, v2000 float64
r1950 = 0.07626899753879587532
d1950 = -1.137405378399605780
dr1950 = 0.1973749217849087460e-4
dd1950 = 0.5659714913272723189e-5
p1950 = 0.134
v1950 = 8.7
gofa.Fk425(r1950, d1950, dr1950, dd1950, p1950, v1950, &r2000, &d2000, &dr2000, &dd2000, &p2000, &v2000)
vvd(t, r2000, 0.08757989933556446040, 1e-14, "Fk425", "r2000")
vvd(t, d2000, -1.132279113042091895, 1e-12, "Fk425", "d2000")
vvd(t, dr2000, 0.1953670614474396139e-4, 1e-17, "Fk425", "dr2000")
vvd(t, dd2000, 0.5637686678659640164e-5, 1e-18, "Fk425", "dd2000")
vvd(t, p2000, 0.1339919950582767871, 1e-13, "Fk425", "p2000")
vvd(t, v2000, 8.736999669183529069, 1e-12, "Fk425", "v2000")
}
func TestFk45z(t *testing.T) {
var r1950, d1950, bepoch, r2000, d2000 float64
r1950 = 0.01602284975382960982
d1950 = -0.1164347929099906024
bepoch = 1954.677617625256806
gofa.Fk45z(r1950, d1950, bepoch, &r2000, &d2000)
vvd(t, r2000, 0.02719295911606862303, 1e-15, "Fk45z", "r2000")
vvd(t, d2000, -0.1115766001565926892, 1e-13, "Fk45z", "d2000")
}
func TestFk524(t *testing.T) {
var r2000, d2000, dr2000, dd2000, p2000, v2000, r1950, d1950, dr1950, dd1950, p1950, v1950 float64
r2000 = 0.8723503576487275595
d2000 = -0.7517076365138887672
dr2000 = 0.2019447755430472323e-4
dd2000 = 0.3541563940505160433e-5
p2000 = 0.1559
v2000 = 86.87
gofa.Fk524(r2000, d2000, dr2000, dd2000, p2000, v2000, &r1950, &d1950, &dr1950, &dd1950, &p1950, &v1950)
vvd(t, r1950, 0.8636359659799603487, 1e-13, "Fk524", "r1950")
vvd(t, d1950, -0.7550281733160843059, 1e-13, "Fk524", "d1950")
vvd(t, dr1950, 0.2023628192747172486e-4, 1e-17, "Fk524", "dr1950")
vvd(t, dd1950, 0.3624459754935334718e-5, 1e-18, "Fk524", "dd1950")
vvd(t, p1950, 0.1560079963299390241, 1e-13, "Fk524", "p1950")
vvd(t, v1950, 86.79606353469163751, 1e-11, "Fk524", "v1950")
}
func TestFk52h(t *testing.T) {
var r5, d5, dr5, dd5, px5, rv5, rh, dh, drh, ddh, pxh, rvh float64
r5 = 1.76779433
d5 = -0.2917517103
dr5 = -1.91851572e-7
dd5 = -5.8468475e-6
px5 = 0.379210
rv5 = -7.6
gofa.Fk52h(r5, d5, dr5, dd5, px5, rv5, &rh, &dh, &drh, &ddh, &pxh, &rvh)
vvd(t, rh, 1.767794226299947632, 1e-14, "Fk52h", "ra")
vvd(t, dh, -0.2917516070530391757, 1e-14, "Fk52h", "dec")
vvd(t, drh, -0.1961874125605721270e-6, 1e-19, "Fk52h", "dr5")
vvd(t, ddh, -0.58459905176693911e-5, 1e-19, "Fk52h", "dd5")
vvd(t, pxh, 0.37921, 1e-14, "Fk52h", "px")
vvd(t, rvh, -7.6000000940000254, 1e-11, "Fk52h", "rv")
}
func TestFk54z(t *testing.T) {
var r2000, d2000, bepoch, r1950, d1950, dr1950, dd1950 float64
r2000 = 0.02719026625066316119
d2000 = -0.1115815170738754813
bepoch = 1954.677308160316374
gofa.Fk54z(r2000, d2000, bepoch, &r1950, &d1950, &dr1950, &dd1950)
vvd(t, r1950, 0.01602015588390065476, 1e-14, "Fk54z", "r1950")
vvd(t, d1950, -0.1164397101110765346, 1e-13, "Fk54z", "d1950")
vvd(t, dr1950, -0.1175712648471090704e-7, 1e-20, "Fk54z", "dr1950")
vvd(t, dd1950, 0.2108109051316431056e-7, 1e-20, "Fk54z", "dd1950")
}
func TestFk5hip(t *testing.T) {
var r5h [3][3]float64
var s5h [3]float64
gofa.Fk5hip(&r5h, &s5h)
vvd(t, r5h[0][0], 0.9999999999999928638, 1e-14, "Fk5hip", "11")
vvd(t, r5h[0][1], 0.1110223351022919694e-6, 1e-17, "Fk5hip", "12")
vvd(t, r5h[0][2], 0.4411803962536558154e-7, 1e-17, "Fk5hip", "13")
vvd(t, r5h[1][0], -0.1110223308458746430e-6, 1e-17, "Fk5hip", "21")
vvd(t, r5h[1][1], 0.9999999999999891830, 1e-14, "Fk5hip", "22")
vvd(t, r5h[1][2], -0.9647792498984142358e-7, 1e-17, "Fk5hip", "23")
vvd(t, r5h[2][0], -0.4411805033656962252e-7, 1e-17, "Fk5hip", "31")
vvd(t, r5h[2][1], 0.9647792009175314354e-7, 1e-17, "Fk5hip", "32")
vvd(t, r5h[2][2], 0.9999999999999943728, 1e-14, "Fk5hip", "33")
vvd(t, s5h[0], -0.1454441043328607981e-8, 1e-17, "Fk5hip", "s1")
vvd(t, s5h[1], 0.2908882086657215962e-8, 1e-17, "Fk5hip", "s2")
vvd(t, s5h[2], 0.3393695767766751955e-8, 1e-17, "Fk5hip", "s3")
}
func TestFk5hz(t *testing.T) {
var r5, d5, rh, dh float64
r5 = 1.76779433
d5 = -0.2917517103
gofa.Fk5hz(r5, d5, 2400000.5, 54479.0, &rh, &dh)
vvd(t, rh, 1.767794191464423978, 1e-12, "Fk5hz", "ra")
vvd(t, dh, -0.2917516001679884419, 1e-12, "Fk5hz", "dec")
}
func TestH2fk5(t *testing.T) {
var rh, dh, drh, ddh, pxh, rvh, r5, d5, dr5, dd5, px5, rv5 float64
rh = 1.767794352
dh = -0.2917512594
drh = -2.76413026e-6
ddh = -5.92994449e-6
pxh = 0.379210
rvh = -7.6
gofa.H2fk5(rh, dh, drh, ddh, pxh, rvh, &r5, &d5, &dr5, &dd5, &px5, &rv5)
vvd(t, r5, 1.767794455700065506, 1e-13, "H2fk5", "ra")
vvd(t, d5, -0.2917513626469638890, 1e-13, "H2fk5", "dec")
vvd(t, dr5, -0.27597945024511204e-5, 1e-18, "H2fk5", "dr5")
vvd(t, dd5, -0.59308014093262838e-5, 1e-18, "H2fk5", "dd5")
vvd(t, px5, 0.37921, 1e-13, "H2fk5", "px")
vvd(t, rv5, -7.6000001309071126, 1e-11, "H2fk5", "rv")
}
func TestHfk5z(t *testing.T) {
var rh, dh, r5, d5, dr5, dd5 float64
rh = 1.767794352
dh = -0.2917512594
gofa.Hfk5z(rh, dh, 2400000.5, 54479.0, &r5, &d5, &dr5, &dd5)
vvd(t, r5, 1.767794490535581026, 1e-13, "Hfk5z", "ra")
vvd(t, d5, -0.2917513695320114258, 1e-14, "Hfk5z", "dec")
vvd(t, dr5, 0.4335890983539243029e-8, 1e-22, "Hfk5z", "dr5")
vvd(t, dd5, -0.8569648841237745902e-9, 1e-23, "Hfk5z", "dd5")
}
gofa-1.19.1/test/coord_test.go 0000664 0000000 0000000 00000016136 14535740236 0016212 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestIcrs2g(t *testing.T) {
var dr, dd, dl, db float64
dr = 5.9338074302227188048671087
dd = -1.1784870613579944551540570
gofa.Icrs2g(dr, dd, &dl, &db)
vvd(t, dl, 5.5850536063818546461558, 1e-14, "Icrs2g", "L")
vvd(t, db, -0.7853981633974483096157, 1e-14, "Icrs2g", "B")
}
func TestG2icrs(t *testing.T) {
var dl, db, dr, dd float64
dl = 5.5850536063818546461558105
db = -0.7853981633974483096156608
gofa.G2icrs(dl, db, &dr, &dd)
vvd(t, dr, 5.9338074302227188048671, 1e-14, "G2icrs", "R")
vvd(t, dd, -1.1784870613579944551541, 1e-14, "G2icrs", "D")
}
func TestAe2hd(t *testing.T) {
var a, e, p, h, d float64
a = 5.5
e = 1.1
p = 0.7
gofa.Ae2hd(a, e, p, &h, &d)
vvd(t, h, 0.5933291115507309663, 1e-14, "Ae2hd", "h")
vvd(t, d, 0.9613934761647817620, 1e-14, "Ae2hd", "d")
}
func TestHd2ae(t *testing.T) {
var h, d, p, a, e float64
h = 1.1
d = 1.2
p = 0.3
gofa.Hd2ae(h, d, p, &a, &e)
vvd(t, a, 5.916889243730066194, 1e-13, "Hd2ae", "a")
vvd(t, e, 0.4472186304990486228, 1e-14, "Hd2ae", "e")
}
func TestHd2pa(t *testing.T) {
var h, d, p, q float64
h = 1.1
d = 1.2
p = 0.3
q = gofa.Hd2pa(h, d, p)
vvd(t, q, 1.906227428001995580, 1e-13, "Hd2pa", "q")
}
func TestEcm06(t *testing.T) {
var date1, date2 float64
var rm [3][3]float64
date1 = 2456165.5
date2 = 0.401182685
gofa.Ecm06(date1, date2, &rm)
vvd(t, rm[0][0], 0.9999952427708701137, 1e-14, "Ecm06", "rm11")
vvd(t, rm[0][1], -0.2829062057663042347e-2, 1e-14, "Ecm06", "rm12")
vvd(t, rm[0][2], -0.1229163741100017629e-2, 1e-14, "Ecm06", "rm13")
vvd(t, rm[1][0], 0.3084546876908653562e-2, 1e-14, "Ecm06", "rm21")
vvd(t, rm[1][1], 0.9174891871550392514, 1e-14, "Ecm06", "rm22")
vvd(t, rm[1][2], 0.3977487611849338124, 1e-14, "Ecm06", "rm23")
vvd(t, rm[2][0], 0.2488512951527405928e-5, 1e-14, "Ecm06", "rm31")
vvd(t, rm[2][1], -0.3977506604161195467, 1e-14, "Ecm06", "rm32")
vvd(t, rm[2][2], 0.9174935488232863071, 1e-14, "Ecm06", "rm33")
}
func TestEqec06(t *testing.T) {
var date1, date2, dr, dd, dl, db float64
date1 = 1234.5
date2 = 2440000.5
dr = 1.234
dd = 0.987
gofa.Eqec06(date1, date2, dr, dd, &dl, &db)
vvd(t, dl, 1.342509918994654619, 1e-14, "Eqec06", "dl")
vvd(t, db, 0.5926215259704608132, 1e-14, "Eqec06", "db")
}
func TestEceq06(t *testing.T) {
var date1, date2, dl, db, dr, dd float64
date1 = 2456165.5
date2 = 0.401182685
dl = 5.1
db = -0.9
gofa.Eceq06(date1, date2, dl, db, &dr, &dd)
vvd(t, dr, 5.533459733613627767, 1e-14, "Eceq06", "dr")
vvd(t, dd, -1.246542932554480576, 1e-14, "Eceq06", "dd")
}
func TestLtecm(t *testing.T) {
var epj float64
var rm [3][3]float64
epj = -3000.0
gofa.Ltecm(epj, &rm)
vvd(t, rm[0][0], 0.3564105644859788825, 1e-14, "Ltecm", "rm11")
vvd(t, rm[0][1], 0.8530575738617682284, 1e-14, "Ltecm", "rm12")
vvd(t, rm[0][2], 0.3811355207795060435, 1e-14, "Ltecm", "rm13")
vvd(t, rm[1][0], -0.9343283469640709942, 1e-14, "Ltecm", "rm21")
vvd(t, rm[1][1], 0.3247830597681745976, 1e-14, "Ltecm", "rm22")
vvd(t, rm[1][2], 0.1467872751535940865, 1e-14, "Ltecm", "rm23")
vvd(t, rm[2][0], 0.1431636191201167793e-2, 1e-14, "Ltecm", "rm31")
vvd(t, rm[2][1], -0.4084222566960599342, 1e-14, "Ltecm", "rm32")
vvd(t, rm[2][2], 0.9127919865189030899, 1e-14, "Ltecm", "rm33")
}
func TestLteqec(t *testing.T) {
var epj, dr, dd, dl, db float64
epj = -1500.0
dr = 1.234
dd = 0.987
gofa.Lteqec(epj, dr, dd, &dl, &db)
vvd(t, dl, 0.5039483649047114859, 1e-14, "Lteqec", "dl")
vvd(t, db, 0.5848534459726224882, 1e-14, "Lteqec", "db")
}
func TestLteceq(t *testing.T) {
var epj, dl, db, dr, dd float64
epj = 2500.0
dl = 1.5
db = 0.6
gofa.Lteceq(epj, dl, db, &dr, &dd)
vvd(t, dr, 1.275156021861921167, 1e-14, "Lteceq", "dr")
vvd(t, dd, 0.9966573543519204791, 1e-14, "Lteceq", "dd")
}
func TestEform(t *testing.T) {
var j int
var a, f float64
j = gofa.Eform(0, &a, &f)
viv(t, j, -1, "Eform", "j0")
j = gofa.Eform(gofa.WGS84, &a, &f)
viv(t, j, 0, "Eform", "j1")
vvd(t, a, 6378137.0, 1e-10, "Eform", "a1")
vvd(t, f, 0.3352810664747480720e-2, 1e-18, "Eform", "f1")
j = gofa.Eform(gofa.GRS80, &a, &f)
viv(t, j, 0, "Eform", "j2")
vvd(t, a, 6378137.0, 1e-10, "Eform", "a2")
vvd(t, f, 0.3352810681182318935e-2, 1e-18, "Eform", "f2")
j = gofa.Eform(gofa.WGS72, &a, &f)
viv(t, j, 0, "Eform", "j2")
vvd(t, a, 6378135.0, 1e-10, "Eform", "a3")
vvd(t, f, 0.3352779454167504862e-2, 1e-18, "Eform", "f3")
j = gofa.Eform(4, &a, &f)
viv(t, j, -1, "Eform", "j3")
}
func TestGc2gd(t *testing.T) {
var j int
xyz := [3]float64{2e6, 3e6, 5.244e6}
var e, p, h float64
j = gofa.Gc2gd(0, xyz, &e, &p, &h)
viv(t, j, -1, "Gc2gd", "j0")
j = gofa.Gc2gd(gofa.WGS84, xyz, &e, &p, &h)
viv(t, j, 0, "Gc2gd", "j1")
vvd(t, e, 0.9827937232473290680, 1e-14, "Gc2gd", "e1")
vvd(t, p, 0.97160184819075459, 1e-14, "Gc2gd", "p1")
vvd(t, h, 331.4172461426059892, 1e-8, "Gc2gd", "h1")
j = gofa.Gc2gd(gofa.GRS80, xyz, &e, &p, &h)
viv(t, j, 0, "Gc2gd", "j2")
vvd(t, e, 0.9827937232473290680, 1e-14, "Gc2gd", "e2")
vvd(t, p, 0.97160184820607853, 1e-14, "Gc2gd", "p2")
vvd(t, h, 331.41731754844348, 1e-8, "Gc2gd", "h2")
j = gofa.Gc2gd(gofa.WGS72, xyz, &e, &p, &h)
viv(t, j, 0, "Gc2gd", "j3")
vvd(t, e, 0.9827937232473290680, 1e-14, "Gc2gd", "e3")
vvd(t, p, 0.9716018181101511937, 1e-14, "Gc2gd", "p3")
vvd(t, h, 333.2770726130318123, 1e-8, "Gc2gd", "h3")
j = gofa.Gc2gd(4, xyz, &e, &p, &h)
viv(t, j, -1, "Gc2gd", "j4")
}
func TestGc2gde(t *testing.T) {
var j int
a := 6378136.0
f := 0.0033528
xyz := [3]float64{2e6, 3e6, 5.244e6}
var e, p, h float64
j = gofa.Gc2gde(a, f, xyz, &e, &p, &h)
viv(t, j, 0, "Gc2gde", "j")
vvd(t, e, 0.9827937232473290680, 1e-14, "Gc2gde", "e")
vvd(t, p, 0.9716018377570411532, 1e-14, "Gc2gde", "p")
vvd(t, h, 332.36862495764397, 1e-8, "Gc2gde", "h")
}
func TestGd2gc(t *testing.T) {
var j int
e := 3.1
p := -0.5
h := 2500.0
var xyz [3]float64
j = gofa.Gd2gc(0, e, p, h, &xyz)
viv(t, j, -1, "Gd2gc", "j0")
j = gofa.Gd2gc(gofa.WGS84, e, p, h, &xyz)
viv(t, j, 0, "Gd2gc", "j1")
vvd(t, xyz[0], -5599000.5577049947, 1e-7, "Gd2gc", "1/1")
vvd(t, xyz[1], 233011.67223479203, 1e-7, "Gd2gc", "2/1")
vvd(t, xyz[2], -3040909.4706983363, 1e-7, "Gd2gc", "3/1")
j = gofa.Gd2gc(gofa.GRS80, e, p, h, &xyz)
viv(t, j, 0, "Gd2gc", "j2")
vvd(t, xyz[0], -5599000.5577260984, 1e-7, "Gd2gc", "1/2")
vvd(t, xyz[1], 233011.6722356702949, 1e-7, "Gd2gc", "2/2")
vvd(t, xyz[2], -3040909.4706095476, 1e-7, "Gd2gc", "3/2")
j = gofa.Gd2gc(gofa.WGS72, e, p, h, &xyz)
viv(t, j, 0, "Gd2gc", "j3")
vvd(t, xyz[0], -5598998.7626301490, 1e-7, "Gd2gc", "1/3")
vvd(t, xyz[1], 233011.5975297822211, 1e-7, "Gd2gc", "2/3")
vvd(t, xyz[2], -3040908.6861467111, 1e-7, "Gd2gc", "3/3")
j = gofa.Gd2gc(4, e, p, h, &xyz)
viv(t, j, -1, "Gd2gc", "j4")
}
func TestGd2gce(t *testing.T) {
var j int
a := 6378136.0
f := 0.0033528
e := 3.1
p := -0.5
h := 2500.0
var xyz [3]float64
j = gofa.Gd2gce(a, f, e, p, h, &xyz)
viv(t, j, 0, "Gd2gce", "j")
vvd(t, xyz[0], -5598999.6665116328, 1e-7, "Gd2gce", "1")
vvd(t, xyz[1], 233011.6351463057189, 1e-7, "Gd2gce", "2")
vvd(t, xyz[2], -3040909.0517314132, 1e-7, "Gd2gce", "3")
}
gofa-1.19.1/test/ephem_test.go 0000664 0000000 0000000 00000005512 14535740236 0016176 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestEpv00(t *testing.T) {
var pvh, pvb [2][3]float64
var j int
j = gofa.Epv00(2400000.5, 53411.52501161, &pvh, &pvb)
vvd(t, pvh[0][0], -0.7757238809297706813, 1e-14, "Epv00", "ph(x)")
vvd(t, pvh[0][1], 0.5598052241363340596, 1e-14, "Epv00", "ph(y)")
vvd(t, pvh[0][2], 0.2426998466481686993, 1e-14, "Epv00", "ph(z)")
vvd(t, pvh[1][0], -0.1091891824147313846e-1, 1e-15, "Epv00", "vh(x)")
vvd(t, pvh[1][1], -0.1247187268440845008e-1, 1e-15, "Epv00", "vh(y)")
vvd(t, pvh[1][2], -0.5407569418065039061e-2, 1e-15, "Epv00", "vh(z)")
vvd(t, pvb[0][0], -0.7714104440491111971, 1e-14, "Epv00", "pb(x)")
vvd(t, pvb[0][1], 0.5598412061824171323, 1e-14, "Epv00", "pb(y)")
vvd(t, pvb[0][2], 0.2425996277722452400, 1e-14, "Epv00", "pb(z)")
vvd(t, pvb[1][0], -0.1091874268116823295e-1, 1e-15, "Epv00", "vb(x)")
vvd(t, pvb[1][1], -0.1246525461732861538e-1, 1e-15, "Epv00", "vb(y)")
vvd(t, pvb[1][2], -0.5404773180966231279e-2, 1e-15, "Epv00", "vb(z)")
viv(t, j, 0, "Epv00", "j")
}
func TestMoon98(t *testing.T) {
var pv [2][3]float64
gofa.Moon98(2400000.5, 43999.9, &pv)
wpv := [2][3]float64{{-0.2601295959971044180e-2, 0.6139750944302742189e-3, 0.2640794528229828909e-3}, {-0.1244321506649895021e-3, -0.5219076942678119398e-3, -0.1716132214378462047e-3}}
vpv(t, pv, wpv, 1e-11, "Moon98")
}
func TestPlan94(t *testing.T) {
var pv [2][3]float64
var j int
j = gofa.Plan94(2400000.5, 1e6, 0, &pv)
vvd(t, pv[0][0], 0.0, 0.0, "Plan94", "x 1")
vvd(t, pv[0][1], 0.0, 0.0, "Plan94", "y 1")
vvd(t, pv[0][2], 0.0, 0.0, "Plan94", "z 1")
vvd(t, pv[1][0], 0.0, 0.0, "Plan94", "xd 1")
vvd(t, pv[1][1], 0.0, 0.0, "Plan94", "yd 1")
vvd(t, pv[1][2], 0.0, 0.0, "Plan94", "zd 1")
viv(t, j, -1, "Plan94", "j 1")
j = gofa.Plan94(2400000.5, 1e6, 10, &pv)
viv(t, j, -1, "Plan94", "j 2")
j = gofa.Plan94(2400000.5, -320000, 3, &pv)
vvd(t, pv[0][0], 0.9308038666832975759, 1e-11, "Plan94", "x 3")
vvd(t, pv[0][1], 0.3258319040261346000, 1e-11, "Plan94", "y 3")
vvd(t, pv[0][2], 0.1422794544481140560, 1e-11, "Plan94", "z 3")
vvd(t, pv[1][0], -0.6429458958255170006e-2, 1e-11, "Plan94", "xd 3")
vvd(t, pv[1][1], 0.1468570657704237764e-1, 1e-11, "Plan94", "yd 3")
vvd(t, pv[1][2], 0.6406996426270981189e-2, 1e-11, "Plan94", "zd 3")
viv(t, j, 1, "Plan94", "j 3")
j = gofa.Plan94(2400000.5, 43999.9, 1, &pv)
vvd(t, pv[0][0], 0.2945293959257430832, 1e-11, "Plan94", "x 4")
vvd(t, pv[0][1], -0.2452204176601049596, 1e-11, "Plan94", "y 4")
vvd(t, pv[0][2], -0.1615427700571978153, 1e-11, "Plan94", "z 4")
vvd(t, pv[1][0], 0.1413867871404614441e-1, 1e-11, "Plan94", "xd 4")
vvd(t, pv[1][1], 0.1946548301104706582e-1, 1e-11, "Plan94", "yd 4")
vvd(t, pv[1][2], 0.8929809783898904786e-2, 1e-11, "Plan94", "zd 4")
viv(t, j, 0, "Plan94", "j 4")
}
gofa-1.19.1/test/erast_test.go 0000664 0000000 0000000 00000005240 14535740236 0016214 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestEe00(t *testing.T) {
var epsa, dpsi, ee float64
epsa = 0.4090789763356509900
dpsi = -0.9630909107115582393e-5
ee = gofa.Ee00(2400000.5, 53736.0, epsa, dpsi)
vvd(t, ee, -0.8834193235367965479e-5, 1e-18, "Ee00", "")
}
func TestEe00a(t *testing.T) {
ee := gofa.Ee00a(2400000.5, 53736.0)
vvd(t, ee, -0.8834192459222588227e-5, 1e-18, "Ee00a", "")
}
func TestEe00b(t *testing.T) {
ee := gofa.Ee00b(2400000.5, 53736.0)
vvd(t, ee, -0.8835700060003032831e-5, 1e-18, "Ee00b", "")
}
func TestEe06a(t *testing.T) {
ee := gofa.Ee06a(2400000.5, 53736.0)
vvd(t, ee, -0.8834195072043790156e-5, 1e-15, "Ee06a", "")
}
func TestEect00(t *testing.T) {
eect := gofa.Eect00(2400000.5, 53736.0)
vvd(t, eect, 0.2046085004885125264e-8, 1e-20, "Eect00", "")
}
func TestEqeq94(t *testing.T) {
eqeq := gofa.Eqeq94(2400000.5, 41234.0)
vvd(t, eqeq, 0.5357758254609256894e-4, 1e-17, "Eqeq94", "")
}
func TestEra00(t *testing.T) {
era00 := gofa.Era00(2400000.5, 54388.0)
vvd(t, era00, 0.4022837240028158102, 1e-12, "Era00", "")
}
func TestGmst00(t *testing.T) {
theta := gofa.Gmst00(2400000.5, 53736.0, 2400000.5, 53736.0)
vvd(t, theta, 1.754174972210740592, 1e-12, "Gmst00", "")
}
func TestGmst06(t *testing.T) {
theta := gofa.Gmst06(2400000.5, 53736.0, 2400000.5, 53736.0)
vvd(t, theta, 1.754174971870091203, 1e-12, "Gmst06", "")
}
func TestGmst82(t *testing.T) {
theta := gofa.Gmst82(2400000.5, 53736.0)
vvd(t, theta, 1.754174981860675096, 1e-12, "Gmst82", "")
}
func TestGst00a(t *testing.T) {
theta := gofa.Gst00a(2400000.5, 53736.0, 2400000.5, 53736.0)
vvd(t, theta, 1.754166138018281369, 1e-12, "Gst00a", "")
}
func TestGst00b(t *testing.T) {
theta := gofa.Gst00b(2400000.5, 53736.0)
vvd(t, theta, 1.754166136510680589, 1e-12, "Gst00b", "")
}
func TestGst06(t *testing.T) {
var rnpb [3][3]float64
rnpb[0][0] = 0.9999989440476103608
rnpb[0][1] = -0.1332881761240011518e-2
rnpb[0][2] = -0.5790767434730085097e-3
rnpb[1][0] = 0.1332858254308954453e-2
rnpb[1][1] = 0.9999991109044505944
rnpb[1][2] = -0.4097782710401555759e-4
rnpb[2][0] = 0.5791308472168153320e-3
rnpb[2][1] = 0.4020595661593994396e-4
rnpb[2][2] = 0.9999998314954572365
theta := gofa.Gst06(2400000.5, 53736.0, 2400000.5, 53736.0, rnpb)
vvd(t, theta, 1.754166138018167568, 1e-12, "Gst06", "")
}
func TestGst06a(t *testing.T) {
theta := gofa.Gst06a(2400000.5, 53736.0, 2400000.5, 53736.0)
vvd(t, theta, 1.754166137675019159, 1e-12, "Gst06a", "")
}
func TestGst94(t *testing.T) {
theta := gofa.Gst94(2400000.5, 53736.0)
vvd(t, theta, 1.754166136020645203, 1e-12, "Gst94", "")
}
gofa-1.19.1/test/fundargs_test.go 0000664 0000000 0000000 00000003044 14535740236 0016707 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestFad03(t *testing.T) {
vvd(t, gofa.Fad03(0.80), 1.946709205396925672, 1e-12, "Fad03", "")
}
func TestFae03(t *testing.T) {
vvd(t, gofa.Fae03(0.80), 1.744713738913081846, 1e-12, "Fae03", "")
}
func TestFaf03(t *testing.T) {
vvd(t, gofa.Faf03(0.80), 0.2597711366745499518, 1e-12, "Faf03", "")
}
func TestFaju03(t *testing.T) {
vvd(t, gofa.Faju03(0.80), 5.275711665202481138, 1e-12, "Faju03", "")
}
func TestFal03(t *testing.T) {
vvd(t, gofa.Fal03(0.80), 5.132369751108684150, 1e-12, "Fal03", "")
}
func TestFalp03(t *testing.T) {
vvd(t, gofa.Falp03(0.80), 6.226797973505507345, 1e-12, "Falp03", "")
}
func TestFama03(t *testing.T) {
vvd(t, gofa.Fama03(0.80), 3.275506840277781492, 1e-12, "Fama03", "")
}
func TestFame03(t *testing.T) {
vvd(t, gofa.Fame03(0.80), 5.417338184297289661, 1e-12, "Fame03", "")
}
func TestFane03(t *testing.T) {
vvd(t, gofa.Fane03(0.80), 2.079343830860413523, 1e-12, "Fane03", "")
}
func TestFaom03(t *testing.T) {
vvd(t, gofa.Faom03(0.80), -5.973618440951302183, 1e-12, "Faom03", "")
}
func TestFapa03(t *testing.T) {
vvd(t, gofa.Fapa03(0.80), 0.1950884762240000000e-1, 1e-12, "Fapa03", "")
}
func TestFasa03(t *testing.T) {
vvd(t, gofa.Fasa03(0.80), 5.371574539440827046, 1e-12, "Fasa03", "")
}
func TestFaur03(t *testing.T) {
vvd(t, gofa.Faur03(0.80), 5.180636450180413523, 1e-12, "Faur03", "")
}
func TestFave03(t *testing.T) {
vvd(t, gofa.Fave03(0.80), 3.424900460533758000, 1e-12, "Fave03", "")
}
gofa-1.19.1/test/gofa_test.go 0000664 0000000 0000000 00000002711 14535740236 0016012 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"fmt"
"math"
"testing"
)
// Test from t_sofa.c
const (
EPS7 = 1e-7
EPS12 = 1e-12
)
func vvd(t *testing.T, val, want, eps float64, fun, param string) {
var a, f float64
a = val - want
if a != 0.0 && math.Abs(a) > math.Abs(eps) {
t.Fail()
f = math.Abs(want / a)
t.Errorf("%s failed: %s want %v got %v ((1/%.3f)) \n", fun, param, want, val, f)
} else {
f = math.Abs(want / a)
t.Logf("%s passed: %s want %v got %v ((1/%.3f)) \n", fun, param, want, val, f)
}
}
func viv(t *testing.T, val, want int, fun, param string) {
if val != want {
t.Errorf("%s failed: %s want %v got %v\n", fun, param, want, val)
} else {
t.Logf("%s passed: %s want %v got %v\n", fun, param, want, val)
}
}
func vbv(t *testing.T, val, want byte, fun, param string) {
if val != want {
t.Errorf("%s failed: %s want %s got %s\n", fun, param, string(want), string(val))
} else {
t.Logf("%s passed: %s want %s got %s\n", fun, param, string(want), string(val))
}
}
func vrv(t *testing.T, val, want [3][3]float64, eps float64, fun string) {
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
vvd(t, val[i][j], want[i][j], eps, fun, fmt.Sprintf("[%d][%d]", i+1, j+1))
}
}
}
func vpv(t *testing.T, val, want [2][3]float64, eps float64, fun string) {
for i := 0; i < 2; i++ {
for j := 0; j < 3; j++ {
vvd(t, val[i][j], want[i][j], eps, fun, fmt.Sprintf("[%d][%d]", i+1, j+1))
}
}
}
gofa-1.19.1/test/jd_test.go 0000664 0000000 0000000 00000003362 14535740236 0015476 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestCal2jd(t *testing.T) {
var j int
var djm0, djm float64
j = gofa.Cal2jd(2003, 06, 01, &djm0, &djm)
vvd(t, djm0, 2400000.5, EPS7, "Cal2jd", "djm0")
vvd(t, djm, 52791.0, EPS7, "Cal2jd", "djm")
viv(t, 0, j, "Cal2jd", "status")
}
func TestJd2cal(t *testing.T) {
var dj1, dj2, fd float64
var iy, im, id, j int
dj1 = 2400000.5
dj2 = 50123.9999
j = gofa.Jd2cal(dj1, dj2, &iy, &im, &id, &fd)
viv(t, iy, 1996, "Jd2cal", "y")
viv(t, im, 2, "Jd2cal", "m")
viv(t, id, 10, "Jd2cal", "d")
vvd(t, fd, 0.9999, EPS7, "Jd2cal", "fd")
viv(t, 0, j, "Cal2jd", "")
}
func TestJdcalf(t *testing.T) {
var dj1, dj2 float64
var iydmf [4]int
var j int
dj1 = 2400000.5
dj2 = 50123.9999
j = gofa.Jdcalf(4, dj1, dj2, &iydmf)
viv(t, iydmf[0], 1996, "iauJdcalf", "y")
viv(t, iydmf[1], 2, "iauJdcalf", "m")
viv(t, iydmf[2], 10, "iauJdcalf", "d")
viv(t, iydmf[3], 9999, "iauJdcalf", "f")
viv(t, j, 0, "iauJdcalf", "j")
}
func TestEpb(t *testing.T) {
var epb float64
epb = gofa.Epb(2415019.8135, 30103.18648)
vvd(t, epb, 1982.418424159278580, 1e-12, "iauEpb", "")
}
func TestEpj(t *testing.T) {
var epj float64
epj = gofa.Epj(2451545, -7392.5)
vvd(t, epj, 1979.760438056125941, 1e-12, "iauEpj", "")
}
func TestEpb2jd(t *testing.T) {
var epb, djm0, djm float64
epb = 1957.3
gofa.Epb2jd(epb, &djm0, &djm)
vvd(t, djm0, 2400000.5, 1e-9, "iauEpb2jd", "djm0")
vvd(t, djm, 35948.1915101513, 1e-9, "iauEpb2jd", "mjd")
}
func TestEpj2jd(t *testing.T) {
var epj, djm0, djm float64
epj = 1996.8
gofa.Epj2jd(epj, &djm0, &djm)
vvd(t, djm0, 2400000.5, 1e-9, "iauEpj2jd", "djm0")
vvd(t, djm, 50375.7, 1e-9, "iauEpj2jd", "mjd")
}
gofa-1.19.1/test/pn_test.go 0000664 0000000 0000000 00000147731 14535740236 0015527 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestBi00(t *testing.T) {
var dpsibi, depsbi, dra float64
gofa.Bi00(&dpsibi, &depsbi, &dra)
vvd(t, dpsibi, -0.2025309152835086613e-6, 1e-12, "Bi00", "dpsibi")
vvd(t, depsbi, -0.3306041454222147847e-7, 1e-12, "Bi00", "depsbi")
vvd(t, dra, -0.7078279744199225506e-7, 1e-12, "Bi00", "dra")
}
func TestBp00(t *testing.T) {
var rb, rp, rbp [3][3]float64
gofa.Bp00(2400000.5, 50123.9999, &rb, &rp, &rbp)
vvd(t, rb[0][0], 0.9999999999999942498, 1e-12, "Bp00", "rb11")
vvd(t, rb[0][1], -0.7078279744199196626e-7, 1e-16, "Bp00", "rb12")
vvd(t, rb[0][2], 0.8056217146976134152e-7, 1e-16, "Bp00", "rb13")
vvd(t, rb[1][0], 0.7078279477857337206e-7, 1e-16, "Bp00", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Bp00", "rb22")
vvd(t, rb[1][2], 0.3306041454222136517e-7, 1e-16, "Bp00", "rb23")
vvd(t, rb[2][0], -0.8056217380986972157e-7, 1e-16, "Bp00", "rb31")
vvd(t, rb[2][1], -0.3306040883980552500e-7, 1e-16, "Bp00", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Bp00", "rb33")
vvd(t, rp[0][0], 0.9999995504864048241, 1e-12, "Bp00", "rp11")
vvd(t, rp[0][1], 0.8696113836207084411e-3, 1e-14, "Bp00", "rp12")
vvd(t, rp[0][2], 0.3778928813389333402e-3, 1e-14, "Bp00", "rp13")
vvd(t, rp[1][0], -0.8696113818227265968e-3, 1e-14, "Bp00", "rp21")
vvd(t, rp[1][1], 0.9999996218879365258, 1e-12, "Bp00", "rp22")
vvd(t, rp[1][2], -0.1690679263009242066e-6, 1e-14, "Bp00", "rp23")
vvd(t, rp[2][0], -0.3778928854764695214e-3, 1e-14, "Bp00", "rp31")
vvd(t, rp[2][1], -0.1595521004195286491e-6, 1e-14, "Bp00", "rp32")
vvd(t, rp[2][2], 0.9999999285984682756, 1e-12, "Bp00", "rp33")
vvd(t, rbp[0][0], 0.9999995505175087260, 1e-12, "Bp00", "rbp11")
vvd(t, rbp[0][1], 0.8695405883617884705e-3, 1e-14, "Bp00", "rbp12")
vvd(t, rbp[0][2], 0.3779734722239007105e-3, 1e-14, "Bp00", "rbp13")
vvd(t, rbp[1][0], -0.8695405990410863719e-3, 1e-14, "Bp00", "rbp21")
vvd(t, rbp[1][1], 0.9999996219494925900, 1e-12, "Bp00", "rbp22")
vvd(t, rbp[1][2], -0.1360775820404982209e-6, 1e-14, "Bp00", "rbp23")
vvd(t, rbp[2][0], -0.3779734476558184991e-3, 1e-14, "Bp00", "rbp31")
vvd(t, rbp[2][1], -0.1925857585832024058e-6, 1e-14, "Bp00", "rbp32")
vvd(t, rbp[2][2], 0.9999999285680153377, 1e-12, "Bp00", "rbp33")
}
func TestBp06(t *testing.T) {
var rb, rp, rbp [3][3]float64
gofa.Bp06(2400000.5, 50123.9999, &rb, &rp, &rbp)
vvd(t, rb[0][0], 0.9999999999999942497, 1e-12, "Bp06", "rb11")
vvd(t, rb[0][1], -0.7078368960971557145e-7, 1e-14, "Bp06", "rb12")
vvd(t, rb[0][2], 0.8056213977613185606e-7, 1e-14, "Bp06", "rb13")
vvd(t, rb[1][0], 0.7078368694637674333e-7, 1e-14, "Bp06", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Bp06", "rb22")
vvd(t, rb[1][2], 0.3305943742989134124e-7, 1e-14, "Bp06", "rb23")
vvd(t, rb[2][0], -0.8056214211620056792e-7, 1e-14, "Bp06", "rb31")
vvd(t, rb[2][1], -0.3305943172740586950e-7, 1e-14, "Bp06", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Bp06", "rb33")
vvd(t, rp[0][0], 0.9999995504864960278, 1e-12, "Bp06", "rp11")
vvd(t, rp[0][1], 0.8696112578855404832e-3, 1e-14, "Bp06", "rp12")
vvd(t, rp[0][2], 0.3778929293341390127e-3, 1e-14, "Bp06", "rp13")
vvd(t, rp[1][0], -0.8696112560510186244e-3, 1e-14, "Bp06", "rp21")
vvd(t, rp[1][1], 0.9999996218880458820, 1e-12, "Bp06", "rp22")
vvd(t, rp[1][2], -0.1691646168941896285e-6, 1e-14, "Bp06", "rp23")
vvd(t, rp[2][0], -0.3778929335557603418e-3, 1e-14, "Bp06", "rp31")
vvd(t, rp[2][1], -0.1594554040786495076e-6, 1e-14, "Bp06", "rp32")
vvd(t, rp[2][2], 0.9999999285984501222, 1e-12, "Bp06", "rp33")
vvd(t, rbp[0][0], 0.9999995505176007047, 1e-12, "Bp06", "rbp11")
vvd(t, rbp[0][1], 0.8695404617348208406e-3, 1e-14, "Bp06", "rbp12")
vvd(t, rbp[0][2], 0.3779735201865589104e-3, 1e-14, "Bp06", "rbp13")
vvd(t, rbp[1][0], -0.8695404723772031414e-3, 1e-14, "Bp06", "rbp21")
vvd(t, rbp[1][1], 0.9999996219496027161, 1e-12, "Bp06", "rbp22")
vvd(t, rbp[1][2], -0.1361752497080270143e-6, 1e-14, "Bp06", "rbp23")
vvd(t, rbp[2][0], -0.3779734957034089490e-3, 1e-14, "Bp06", "rbp31")
vvd(t, rbp[2][1], -0.1924880847894457113e-6, 1e-14, "Bp06", "rbp32")
vvd(t, rbp[2][2], 0.9999999285679971958, 1e-12, "Bp06", "rbp33")
}
func TestBpn2xy(t *testing.T) {
var rbpn [3][3]float64
var x, y float64
rbpn[0][0] = 9.999962358680738e-1
rbpn[0][1] = -2.516417057665452e-3
rbpn[0][2] = -1.093569785342370e-3
rbpn[1][0] = 2.516462370370876e-3
rbpn[1][1] = 9.999968329010883e-1
rbpn[1][2] = 4.006159587358310e-5
rbpn[2][0] = 1.093465510215479e-3
rbpn[2][1] = -4.281337229063151e-5
rbpn[2][2] = 9.999994012499173e-1
gofa.Bpn2xy(rbpn, &x, &y)
vvd(t, x, 1.093465510215479e-3, 1e-12, "Bpn2xy", "x")
vvd(t, y, -4.281337229063151e-5, 1e-12, "Bpn2xy", "y")
}
func TestC2i00a(t *testing.T) {
var rc2i [3][3]float64
gofa.C2i00a(2400000.5, 53736.0, &rc2i)
vvd(t, rc2i[0][0], 0.9999998323037165557, 1e-12, "C2i00a", "11")
vvd(t, rc2i[0][1], 0.5581526348992140183e-9, 1e-12, "C2i00a", "12")
vvd(t, rc2i[0][2], -0.5791308477073443415e-3, 1e-12, "C2i00a", "13")
vvd(t, rc2i[1][0], -0.2384266227870752452e-7, 1e-12, "C2i00a", "21")
vvd(t, rc2i[1][1], 0.9999999991917405258, 1e-12, "C2i00a", "22")
vvd(t, rc2i[1][2], -0.4020594955028209745e-4, 1e-12, "C2i00a", "23")
vvd(t, rc2i[2][0], 0.5791308472168152904e-3, 1e-12, "C2i00a", "31")
vvd(t, rc2i[2][1], 0.4020595661591500259e-4, 1e-12, "C2i00a", "32")
vvd(t, rc2i[2][2], 0.9999998314954572304, 1e-12, "C2i00a", "33")
}
func TestC2i00b(t *testing.T) {
var rc2i [3][3]float64
gofa.C2i00b(2400000.5, 53736.0, &rc2i)
vvd(t, rc2i[0][0], 0.9999998323040954356, 1e-12, "C2i00b", "11")
vvd(t, rc2i[0][1], 0.5581526349131823372e-9, 1e-12, "C2i00b", "12")
vvd(t, rc2i[0][2], -0.5791301934855394005e-3, 1e-12, "C2i00b", "13")
vvd(t, rc2i[1][0], -0.2384239285499175543e-7, 1e-12, "C2i00b", "21")
vvd(t, rc2i[1][1], 0.9999999991917574043, 1e-12, "C2i00b", "22")
vvd(t, rc2i[1][2], -0.4020552974819030066e-4, 1e-12, "C2i00b", "23")
vvd(t, rc2i[2][0], 0.5791301929950208873e-3, 1e-12, "C2i00b", "31")
vvd(t, rc2i[2][1], 0.4020553681373720832e-4, 1e-12, "C2i00b", "32")
vvd(t, rc2i[2][2], 0.9999998314958529887, 1e-12, "C2i00b", "33")
}
func TestC2i06a(t *testing.T) {
var rc2i [3][3]float64
gofa.C2i06a(2400000.5, 53736.0, &rc2i)
vvd(t, rc2i[0][0], 0.9999998323037159379, 1e-12, "C2i06a", "11")
vvd(t, rc2i[0][1], 0.5581121329587613787e-9, 1e-12, "C2i06a", "12")
vvd(t, rc2i[0][2], -0.5791308487740529749e-3, 1e-12, "C2i06a", "13")
vvd(t, rc2i[1][0], -0.2384253169452306581e-7, 1e-12, "C2i06a", "21")
vvd(t, rc2i[1][1], 0.9999999991917467827, 1e-12, "C2i06a", "22")
vvd(t, rc2i[1][2], -0.4020579392895682558e-4, 1e-12, "C2i06a", "23")
vvd(t, rc2i[2][0], 0.5791308482835292617e-3, 1e-12, "C2i06a", "31")
vvd(t, rc2i[2][1], 0.4020580099454020310e-4, 1e-12, "C2i06a", "32")
vvd(t, rc2i[2][2], 0.9999998314954628695, 1e-12, "C2i06a", "33")
}
func TestC2ibpn(t *testing.T) {
var rbpn, rc2i [3][3]float64
rbpn[0][0] = 9.999962358680738e-1
rbpn[0][1] = -2.516417057665452e-3
rbpn[0][2] = -1.093569785342370e-3
rbpn[1][0] = 2.516462370370876e-3
rbpn[1][1] = 9.999968329010883e-1
rbpn[1][2] = 4.006159587358310e-5
rbpn[2][0] = 1.093465510215479e-3
rbpn[2][1] = -4.281337229063151e-5
rbpn[2][2] = 9.999994012499173e-1
gofa.C2ibpn(2400000.5, 50123.9999, rbpn, &rc2i)
vvd(t, rc2i[0][0], 0.9999994021664089977, 1e-12, "C2ibpn", "11")
vvd(t, rc2i[0][1], -0.3869195948017503664e-8, 1e-12, "C2ibpn", "12")
vvd(t, rc2i[0][2], -0.1093465511383285076e-2, 1e-12, "C2ibpn", "13")
vvd(t, rc2i[1][0], 0.5068413965715446111e-7, 1e-12, "C2ibpn", "21")
vvd(t, rc2i[1][1], 0.9999999990835075686, 1e-12, "C2ibpn", "22")
vvd(t, rc2i[1][2], 0.4281334246452708915e-4, 1e-12, "C2ibpn", "23")
vvd(t, rc2i[2][0], 0.1093465510215479000e-2, 1e-12, "C2ibpn", "31")
vvd(t, rc2i[2][1], -0.4281337229063151000e-4, 1e-12, "C2ibpn", "32")
vvd(t, rc2i[2][2], 0.9999994012499173103, 1e-12, "C2ibpn", "33")
}
func TestC2ixy(t *testing.T) {
var rc2i [3][3]float64
var x, y float64
x = 0.5791308486706011000e-3
y = 0.4020579816732961219e-4
gofa.C2ixy(2400000.5, 53736, x, y, &rc2i)
vvd(t, rc2i[0][0], 0.9999998323037157138, 1e-12, "C2ixy", "11")
vvd(t, rc2i[0][1], 0.5581526349032241205e-9, 1e-12, "C2ixy", "12")
vvd(t, rc2i[0][2], -0.5791308491611263745e-3, 1e-12, "C2ixy", "13")
vvd(t, rc2i[1][0], -0.2384257057469842953e-7, 1e-12, "C2ixy", "21")
vvd(t, rc2i[1][1], 0.9999999991917468964, 1e-12, "C2ixy", "22")
vvd(t, rc2i[1][2], -0.4020579110172324363e-4, 1e-12, "C2ixy", "23")
vvd(t, rc2i[2][0], 0.5791308486706011000e-3, 1e-12, "C2ixy", "31")
vvd(t, rc2i[2][1], 0.4020579816732961219e-4, 1e-12, "C2ixy", "32")
vvd(t, rc2i[2][2], 0.9999998314954627590, 1e-12, "C2ixy", "33")
}
func TestC2ixys(t *testing.T) {
var rc2i [3][3]float64
var x, y, s float64
x = 0.5791308486706011000e-3
y = 0.4020579816732961219e-4
s = -0.1220040848472271978e-7
gofa.C2ixys(x, y, s, &rc2i)
vvd(t, rc2i[0][0], 0.9999998323037157138, 1e-12, "C2ixys", "11")
vvd(t, rc2i[0][1], 0.5581984869168499149e-9, 1e-12, "C2ixys", "12")
vvd(t, rc2i[0][2], -0.5791308491611282180e-3, 1e-12, "C2ixys", "13")
vvd(t, rc2i[1][0], -0.2384261642670440317e-7, 1e-12, "C2ixys", "21")
vvd(t, rc2i[1][1], 0.9999999991917468964, 1e-12, "C2ixys", "22")
vvd(t, rc2i[1][2], -0.4020579110169668931e-4, 1e-12, "C2ixys", "23")
vvd(t, rc2i[2][0], 0.5791308486706011000e-3, 1e-12, "C2ixys", "31")
vvd(t, rc2i[2][1], 0.4020579816732961219e-4, 1e-12, "C2ixys", "32")
vvd(t, rc2i[2][2], 0.9999998314954627590, 1e-12, "C2ixys", "33")
}
func TestC2t00a(t *testing.T) {
var tta, ttb, uta, utb, xp, yp float64
var rc2t [3][3]float64
tta = 2400000.5
uta = 2400000.5
ttb = 53736.0
utb = 53736.0
xp = 2.55060238e-7
yp = 1.860359247e-6
gofa.C2t00a(tta, ttb, uta, utb, xp, yp, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128307182668, 1e-12, "C2t00a", "11")
vvd(t, rc2t[0][1], 0.9834769806938457836, 1e-12, "C2t00a", "12")
vvd(t, rc2t[0][2], 0.6555535638688341725e-4, 1e-12, "C2t00a", "13")
vvd(t, rc2t[1][0], -0.9834768134135984552, 1e-12, "C2t00a", "21")
vvd(t, rc2t[1][1], -0.1810332203649520727, 1e-12, "C2t00a", "22")
vvd(t, rc2t[1][2], 0.5749801116141056317e-3, 1e-12, "C2t00a", "23")
vvd(t, rc2t[2][0], 0.5773474014081406921e-3, 1e-12, "C2t00a", "31")
vvd(t, rc2t[2][1], 0.3961832391770163647e-4, 1e-12, "C2t00a", "32")
vvd(t, rc2t[2][2], 0.9999998325501692289, 1e-12, "C2t00a", "33")
}
func TestC2t00b(t *testing.T) {
var tta, ttb, uta, utb, xp, yp float64
var rc2t [3][3]float64
tta = 2400000.5
uta = 2400000.5
ttb = 53736.0
utb = 53736.0
xp = 2.55060238e-7
yp = 1.860359247e-6
gofa.C2t00b(tta, ttb, uta, utb, xp, yp, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128439678965, 1e-12, "C2t00b", "11")
vvd(t, rc2t[0][1], 0.9834769806913872359, 1e-12, "C2t00b", "12")
vvd(t, rc2t[0][2], 0.6555565082458415611e-4, 1e-12, "C2t00b", "13")
vvd(t, rc2t[1][0], -0.9834768134115435923, 1e-12, "C2t00b", "21")
vvd(t, rc2t[1][1], -0.1810332203784001946, 1e-12, "C2t00b", "22")
vvd(t, rc2t[1][2], 0.5749793922030017230e-3, 1e-12, "C2t00b", "23")
vvd(t, rc2t[2][0], 0.5773467471863534901e-3, 1e-12, "C2t00b", "31")
vvd(t, rc2t[2][1], 0.3961790411549945020e-4, 1e-12, "C2t00b", "32")
vvd(t, rc2t[2][2], 0.9999998325505635738, 1e-12, "C2t00b", "33")
}
func TestC2t06a(t *testing.T) {
var tta, ttb, uta, utb, xp, yp float64
var rc2t [3][3]float64
tta = 2400000.5
uta = 2400000.5
ttb = 53736.0
utb = 53736.0
xp = 2.55060238e-7
yp = 1.860359247e-6
gofa.C2t06a(tta, ttb, uta, utb, xp, yp, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128305897282, 1e-12, "C2t06a", "11")
vvd(t, rc2t[0][1], 0.9834769806938592296, 1e-12, "C2t06a", "12")
vvd(t, rc2t[0][2], 0.6555550962998436505e-4, 1e-12, "C2t06a", "13")
vvd(t, rc2t[1][0], -0.9834768134136214897, 1e-12, "C2t06a", "21")
vvd(t, rc2t[1][1], -0.1810332203649130832, 1e-12, "C2t06a", "22")
vvd(t, rc2t[1][2], 0.5749800844905594110e-3, 1e-12, "C2t06a", "23")
vvd(t, rc2t[2][0], 0.5773474024748545878e-3, 1e-12, "C2t06a", "31")
vvd(t, rc2t[2][1], 0.3961816829632690581e-4, 1e-12, "C2t06a", "32")
vvd(t, rc2t[2][2], 0.9999998325501747785, 1e-12, "C2t06a", "33")
}
func TestC2tcio(t *testing.T) {
var era float64
var rc2i, rpom, rc2t [3][3]float64
rc2i[0][0] = 0.9999998323037164738
rc2i[0][1] = 0.5581526271714303683e-9
rc2i[0][2] = -0.5791308477073443903e-3
rc2i[1][0] = -0.2384266227524722273e-7
rc2i[1][1] = 0.9999999991917404296
rc2i[1][2] = -0.4020594955030704125e-4
rc2i[2][0] = 0.5791308472168153320e-3
rc2i[2][1] = 0.4020595661593994396e-4
rc2i[2][2] = 0.9999998314954572365
era = 1.75283325530307
rpom[0][0] = 0.9999999999999674705
rpom[0][1] = -0.1367174580728847031e-10
rpom[0][2] = 0.2550602379999972723e-6
rpom[1][0] = 0.1414624947957029721e-10
rpom[1][1] = 0.9999999999982694954
rpom[1][2] = -0.1860359246998866338e-5
rpom[2][0] = -0.2550602379741215275e-6
rpom[2][1] = 0.1860359247002413923e-5
rpom[2][2] = 0.9999999999982369658
gofa.C2tcio(rc2i, era, rpom, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128307110439, 1e-12, "C2tcio", "11")
vvd(t, rc2t[0][1], 0.9834769806938470149, 1e-12, "C2tcio", "12")
vvd(t, rc2t[0][2], 0.6555535638685466874e-4, 1e-12, "C2tcio", "13")
vvd(t, rc2t[1][0], -0.9834768134135996657, 1e-12, "C2tcio", "21")
vvd(t, rc2t[1][1], -0.1810332203649448367, 1e-12, "C2tcio", "22")
vvd(t, rc2t[1][2], 0.5749801116141106528e-3, 1e-12, "C2tcio", "23")
vvd(t, rc2t[2][0], 0.5773474014081407076e-3, 1e-12, "C2tcio", "31")
vvd(t, rc2t[2][1], 0.3961832391772658944e-4, 1e-12, "C2tcio", "32")
vvd(t, rc2t[2][2], 0.9999998325501691969, 1e-12, "C2tcio", "33")
}
func TestC2teqx(t *testing.T) {
var gst float64
var rbpn, rpom, rc2t [3][3]float64
rbpn[0][0] = 0.9999989440476103608
rbpn[0][1] = -0.1332881761240011518e-2
rbpn[0][2] = -0.5790767434730085097e-3
rbpn[1][0] = 0.1332858254308954453e-2
rbpn[1][1] = 0.9999991109044505944
rbpn[1][2] = -0.4097782710401555759e-4
rbpn[2][0] = 0.5791308472168153320e-3
rbpn[2][1] = 0.4020595661593994396e-4
rbpn[2][2] = 0.9999998314954572365
gst = 1.754166138040730516
rpom[0][0] = 0.9999999999999674705
rpom[0][1] = -0.1367174580728847031e-10
rpom[0][2] = 0.2550602379999972723e-6
rpom[1][0] = 0.1414624947957029721e-10
rpom[1][1] = 0.9999999999982694954
rpom[1][2] = -0.1860359246998866338e-5
rpom[2][0] = -0.2550602379741215275e-6
rpom[2][1] = 0.1860359247002413923e-5
rpom[2][2] = 0.9999999999982369658
gofa.C2teqx(rbpn, gst, rpom, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128528685730, 1e-12, "C2teqx", "11")
vvd(t, rc2t[0][1], 0.9834769806897685071, 1e-12, "C2teqx", "12")
vvd(t, rc2t[0][2], 0.6555535639982634449e-4, 1e-12, "C2teqx", "13")
vvd(t, rc2t[1][0], -0.9834768134095211257, 1e-12, "C2teqx", "21")
vvd(t, rc2t[1][1], -0.1810332203871023800, 1e-12, "C2teqx", "22")
vvd(t, rc2t[1][2], 0.5749801116126438962e-3, 1e-12, "C2teqx", "23")
vvd(t, rc2t[2][0], 0.5773474014081539467e-3, 1e-12, "C2teqx", "31")
vvd(t, rc2t[2][1], 0.3961832391768640871e-4, 1e-12, "C2teqx", "32")
vvd(t, rc2t[2][2], 0.9999998325501691969, 1e-12, "C2teqx", "33")
}
func TestC2tpe(t *testing.T) {
var tta, ttb, uta, utb, dpsi, deps, xp, yp float64
var rc2t [3][3]float64
tta = 2400000.5
uta = 2400000.5
ttb = 53736.0
utb = 53736.0
deps = 0.4090789763356509900
dpsi = -0.9630909107115582393e-5
xp = 2.55060238e-7
yp = 1.860359247e-6
gofa.C2tpe(tta, ttb, uta, utb, dpsi, deps, xp, yp, &rc2t)
vvd(t, rc2t[0][0], -0.1813677995763029394, 1e-12, "C2tpe", "11")
vvd(t, rc2t[0][1], 0.9023482206891683275, 1e-12, "C2tpe", "12")
vvd(t, rc2t[0][2], -0.3909902938641085751, 1e-12, "C2tpe", "13")
vvd(t, rc2t[1][0], -0.9834147641476804807, 1e-12, "C2tpe", "21")
vvd(t, rc2t[1][1], -0.1659883635434995121, 1e-12, "C2tpe", "22")
vvd(t, rc2t[1][2], 0.7309763898042819705e-1, 1e-12, "C2tpe", "23")
vvd(t, rc2t[2][0], 0.1059685430673215247e-2, 1e-12, "C2tpe", "31")
vvd(t, rc2t[2][1], 0.3977631855605078674, 1e-12, "C2tpe", "32")
vvd(t, rc2t[2][2], 0.9174875068792735362, 1e-12, "C2tpe", "33")
}
func TestC2txy(t *testing.T) {
var tta, ttb, uta, utb, x, y, xp, yp float64
var rc2t [3][3]float64
tta = 2400000.5
uta = 2400000.5
ttb = 53736.0
utb = 53736.0
x = 0.5791308486706011000e-3
y = 0.4020579816732961219e-4
xp = 2.55060238e-7
yp = 1.860359247e-6
gofa.C2txy(tta, ttb, uta, utb, x, y, xp, yp, &rc2t)
vvd(t, rc2t[0][0], -0.1810332128306279253, 1e-12, "C2txy", "11")
vvd(t, rc2t[0][1], 0.9834769806938520084, 1e-12, "C2txy", "12")
vvd(t, rc2t[0][2], 0.6555551248057665829e-4, 1e-12, "C2txy", "13")
vvd(t, rc2t[1][0], -0.9834768134136142314, 1e-12, "C2txy", "21")
vvd(t, rc2t[1][1], -0.1810332203649529312, 1e-12, "C2txy", "22")
vvd(t, rc2t[1][2], 0.5749800843594139912e-3, 1e-12, "C2txy", "23")
vvd(t, rc2t[2][0], 0.5773474028619264494e-3, 1e-12, "C2txy", "31")
vvd(t, rc2t[2][1], 0.3961816546911624260e-4, 1e-12, "C2txy", "32")
vvd(t, rc2t[2][2], 0.9999998325501746670, 1e-12, "C2txy", "33")
}
func TestEo06a(t *testing.T) {
eo := gofa.Eo06a(2400000.5, 53736.0)
vvd(t, eo, -0.1332882371941833644e-2, 1e-15, "Eo06a", "")
}
func TestEors(t *testing.T) {
var rnpb [3][3]float64
var s, eo float64
rnpb[0][0] = 0.9999989440476103608
rnpb[0][1] = -0.1332881761240011518e-2
rnpb[0][2] = -0.5790767434730085097e-3
rnpb[1][0] = 0.1332858254308954453e-2
rnpb[1][1] = 0.9999991109044505944
rnpb[1][2] = -0.4097782710401555759e-4
rnpb[2][0] = 0.5791308472168153320e-3
rnpb[2][1] = 0.4020595661593994396e-4
rnpb[2][2] = 0.9999998314954572365
s = -0.1220040848472271978e-7
eo = gofa.Eors(rnpb, s)
vvd(t, eo, -0.1332882715130744606e-2, 1e-14, "Eors", "")
}
func TestFw2m(t *testing.T) {
var gamb, phib, psi, eps float64
var r [3][3]float64
gamb = -0.2243387670997992368e-5
phib = 0.4091014602391312982
psi = -0.9501954178013015092e-3
eps = 0.4091014316587367472
gofa.Fw2m(gamb, phib, psi, eps, &r)
vvd(t, r[0][0], 0.9999995505176007047, 1e-12, "Fw2m", "11")
vvd(t, r[0][1], 0.8695404617348192957e-3, 1e-12, "Fw2m", "12")
vvd(t, r[0][2], 0.3779735201865582571e-3, 1e-12, "Fw2m", "13")
vvd(t, r[1][0], -0.8695404723772016038e-3, 1e-12, "Fw2m", "21")
vvd(t, r[1][1], 0.9999996219496027161, 1e-12, "Fw2m", "22")
vvd(t, r[1][2], -0.1361752496887100026e-6, 1e-12, "Fw2m", "23")
vvd(t, r[2][0], -0.3779734957034082790e-3, 1e-12, "Fw2m", "31")
vvd(t, r[2][1], -0.1924880848087615651e-6, 1e-12, "Fw2m", "32")
vvd(t, r[2][2], 0.9999999285679971958, 1e-12, "Fw2m", "33")
}
func TestFw2xy(t *testing.T) {
var gamb, phib, psi, eps, x, y float64
gamb = -0.2243387670997992368e-5
phib = 0.4091014602391312982
psi = -0.9501954178013015092e-3
eps = 0.4091014316587367472
gofa.Fw2xy(gamb, phib, psi, eps, &x, &y)
vvd(t, x, -0.3779734957034082790e-3, 1e-14, "Fw2xy", "x")
vvd(t, y, -0.1924880848087615651e-6, 1e-14, "Fw2xy", "y")
}
func TestLtp(t *testing.T) {
var epj float64
var rp [3][3]float64
epj = 1666.666
gofa.Ltp(epj, &rp)
vvd(t, rp[0][0], 0.9967044141159213819, 1e-14, "Ltp", "rp11")
vvd(t, rp[0][1], 0.7437801893193210840e-1, 1e-14, "Ltp", "rp12")
vvd(t, rp[0][2], 0.3237624409345603401e-1, 1e-14, "Ltp", "rp13")
vvd(t, rp[1][0], -0.7437802731819618167e-1, 1e-14, "Ltp", "rp21")
vvd(t, rp[1][1], 0.9972293894454533070, 1e-14, "Ltp", "rp22")
vvd(t, rp[1][2], -0.1205768842723593346e-2, 1e-14, "Ltp", "rp23")
vvd(t, rp[2][0], -0.3237622482766575399e-1, 1e-14, "Ltp", "rp31")
vvd(t, rp[2][1], -0.1206286039697609008e-2, 1e-14, "Ltp", "rp32")
vvd(t, rp[2][2], 0.9994750246704010914, 1e-14, "Ltp", "rp33")
}
func TestLtpb(t *testing.T) {
var epj float64
var rpb [3][3]float64
epj = 1666.666
gofa.Ltpb(epj, &rpb)
vvd(t, rpb[0][0], 0.9967044167723271851, 1e-14, "Ltpb", "rpb11")
vvd(t, rpb[0][1], 0.7437794731203340345e-1, 1e-14, "Ltpb", "rpb12")
vvd(t, rpb[0][2], 0.3237632684841625547e-1, 1e-14, "Ltpb", "rpb13")
vvd(t, rpb[1][0], -0.7437795663437177152e-1, 1e-14, "Ltpb", "rpb21")
vvd(t, rpb[1][1], 0.9972293947500013666, 1e-14, "Ltpb", "rpb22")
vvd(t, rpb[1][2], -0.1205741865911243235e-2, 1e-14, "Ltpb", "rpb23")
vvd(t, rpb[2][0], -0.3237630543224664992e-1, 1e-14, "Ltpb", "rpb31")
vvd(t, rpb[2][1], -0.1206316791076485295e-2, 1e-14, "Ltpb", "rpb32")
vvd(t, rpb[2][2], 0.9994750220222438819, 1e-14, "Ltpb", "rpb33")
}
func TestLtpecl(t *testing.T) {
var epj float64
var vec [3]float64
epj = -1500.0
gofa.Ltpecl(epj, &vec)
vvd(t, vec[0], 0.4768625676477096525e-3, 1e-14, "Ltpecl", "vec1")
vvd(t, vec[1], -0.4052259533091875112, 1e-14, "Ltpecl", "vec2")
vvd(t, vec[2], 0.9142164401096448012, 1e-14, "Ltpecl", "vec3")
}
func TestLtpequ(t *testing.T) {
var epj float64
var veq [3]float64
epj = -2500.0
gofa.Ltpequ(epj, &veq)
vvd(t, veq[0], -0.3586652560237326659, 1e-14, "Ltpequ", "veq1")
vvd(t, veq[1], -0.1996978910771128475, 1e-14, "Ltpequ", "veq2")
vvd(t, veq[2], 0.9118552442250819624, 1e-14, "Ltpequ", "veq3")
}
func TestNum00a(t *testing.T) {
var rmatn [3][3]float64
gofa.Num00a(2400000.5, 53736.0, &rmatn)
vvd(t, rmatn[0][0], 0.9999999999536227949, 1e-12, "Num00a", "11")
vvd(t, rmatn[0][1], 0.8836238544090873336e-5, 1e-12, "Num00a", "12")
vvd(t, rmatn[0][2], 0.3830835237722400669e-5, 1e-12, "Num00a", "13")
vvd(t, rmatn[1][0], -0.8836082880798569274e-5, 1e-12, "Num00a", "21")
vvd(t, rmatn[1][1], 0.9999999991354655028, 1e-12, "Num00a", "22")
vvd(t, rmatn[1][2], -0.4063240865362499850e-4, 1e-12, "Num00a", "23")
vvd(t, rmatn[2][0], -0.3831194272065995866e-5, 1e-12, "Num00a", "31")
vvd(t, rmatn[2][1], 0.4063237480216291775e-4, 1e-12, "Num00a", "32")
vvd(t, rmatn[2][2], 0.9999999991671660338, 1e-12, "Num00a", "33")
}
func TestNum00b(t *testing.T) {
var rmatn [3][3]float64
gofa.Num00b(2400000.5, 53736, &rmatn)
vvd(t, rmatn[0][0], 0.9999999999536069682, 1e-12, "Num00b", "11")
vvd(t, rmatn[0][1], 0.8837746144871248011e-5, 1e-12, "Num00b", "12")
vvd(t, rmatn[0][2], 0.3831488838252202945e-5, 1e-12, "Num00b", "13")
vvd(t, rmatn[1][0], -0.8837590456632304720e-5, 1e-12, "Num00b", "21")
vvd(t, rmatn[1][1], 0.9999999991354692733, 1e-12, "Num00b", "22")
vvd(t, rmatn[1][2], -0.4063198798559591654e-4, 1e-12, "Num00b", "23")
vvd(t, rmatn[2][0], -0.3831847930134941271e-5, 1e-12, "Num00b", "31")
vvd(t, rmatn[2][1], 0.4063195412258168380e-4, 1e-12, "Num00b", "32")
vvd(t, rmatn[2][2], 0.9999999991671806225, 1e-12, "Num00b", "33")
}
func TestNum06a(t *testing.T) {
var rmatn [3][3]float64
gofa.Num06a(2400000.5, 53736, &rmatn)
vvd(t, rmatn[0][0], 0.9999999999536227668, 1e-12, "Num06a", "11")
vvd(t, rmatn[0][1], 0.8836241998111535233e-5, 1e-12, "Num06a", "12")
vvd(t, rmatn[0][2], 0.3830834608415287707e-5, 1e-12, "Num06a", "13")
vvd(t, rmatn[1][0], -0.8836086334870740138e-5, 1e-12, "Num06a", "21")
vvd(t, rmatn[1][1], 0.9999999991354657474, 1e-12, "Num06a", "22")
vvd(t, rmatn[1][2], -0.4063240188248455065e-4, 1e-12, "Num06a", "23")
vvd(t, rmatn[2][0], -0.3831193642839398128e-5, 1e-12, "Num06a", "31")
vvd(t, rmatn[2][1], 0.4063236803101479770e-4, 1e-12, "Num06a", "32")
vvd(t, rmatn[2][2], 0.9999999991671663114, 1e-12, "Num06a", "33")
}
func TestNumat(t *testing.T) {
var epsa, dpsi, deps float64
var rmatn [3][3]float64
epsa = 0.4090789763356509900
dpsi = -0.9630909107115582393e-5
deps = 0.4063239174001678826e-4
gofa.Numat(epsa, dpsi, deps, &rmatn)
vvd(t, rmatn[0][0], 0.9999999999536227949, 1e-12, "Numat", "11")
vvd(t, rmatn[0][1], 0.8836239320236250577e-5, 1e-12, "Numat", "12")
vvd(t, rmatn[0][2], 0.3830833447458251908e-5, 1e-12, "Numat", "13")
vvd(t, rmatn[1][0], -0.8836083657016688588e-5, 1e-12, "Numat", "21")
vvd(t, rmatn[1][1], 0.9999999991354654959, 1e-12, "Numat", "22")
vvd(t, rmatn[1][2], -0.4063240865361857698e-4, 1e-12, "Numat", "23")
vvd(t, rmatn[2][0], -0.3831192481833385226e-5, 1e-12, "Numat", "31")
vvd(t, rmatn[2][1], 0.4063237480216934159e-4, 1e-12, "Numat", "32")
vvd(t, rmatn[2][2], 0.9999999991671660407, 1e-12, "Numat", "33")
}
func TestNut00a(t *testing.T) {
var dpsi, deps float64
gofa.Nut00a(2400000.5, 53736.0, &dpsi, &deps)
vvd(t, dpsi, -0.9630909107115518431e-5, EPS12, "Nut00a", "dpsi")
vvd(t, deps, 0.4063239174001678710e-4, EPS12, "Nut00a", "deps")
}
func TestNut00b(t *testing.T) {
var dpsi, deps float64
gofa.Nut00b(2400000.5, 53736.0, &dpsi, &deps)
vvd(t, dpsi, -0.9632552291148362783e-5, 1e-13, "Nut00b", "dpsi")
vvd(t, deps, 0.4063197106621159367e-4, 1e-13, "Nut00b", "deps")
}
func TestNut06a(t *testing.T) {
var dpsi, deps float64
gofa.Nut06a(2400000.5, 53736.0, &dpsi, &deps)
vvd(t, dpsi, -0.9630912025820308797e-5, 1e-13, "Nut06a", "dpsi")
vvd(t, deps, 0.4063238496887249798e-4, 1e-13, "Nut06a", "deps")
}
func TestNut80(t *testing.T) {
var dpsi, deps float64
gofa.Nut80(2400000.5, 53736.0, &dpsi, &deps)
vvd(t, dpsi, -0.9643658353226563966e-5, 1e-13, "Nut80", "dpsi")
vvd(t, deps, 0.4060051006879713322e-4, 1e-13, "Nut80", "deps")
}
func TestNutm80(t *testing.T) {
var rmatn [3][3]float64
gofa.Nutm80(2400000.5, 53736.0, &rmatn)
vvd(t, rmatn[0][0], 0.9999999999534999268, 1e-12, "Nutm80", "11")
vvd(t, rmatn[0][1], 0.8847935789636432161e-5, 1e-12, "Nutm80", "12")
vvd(t, rmatn[0][2], 0.3835906502164019142e-5, 1e-12, "Nutm80", "13")
vvd(t, rmatn[1][0], -0.8847780042583435924e-5, 1e-12, "Nutm80", "21")
vvd(t, rmatn[1][1], 0.9999999991366569963, 1e-12, "Nutm80", "22")
vvd(t, rmatn[1][2], -0.4060052702727130809e-4, 1e-12, "Nutm80", "23")
vvd(t, rmatn[2][0], -0.3836265729708478796e-5, 1e-12, "Nutm80", "31")
vvd(t, rmatn[2][1], 0.4060049308612638555e-4, 1e-12, "Nutm80", "32")
vvd(t, rmatn[2][2], 0.9999999991684415129, 1e-12, "Nutm80", "33")
}
func TestObl06(t *testing.T) {
vvd(t, gofa.Obl06(2400000.5, 54388.0), 0.4090749229387258204, 1e-14, "Obl06", "")
}
func TestObl80(t *testing.T) {
eps0 := gofa.Obl80(2400000.5, 54388.0)
vvd(t, eps0, 0.4090751347643816218, 1e-14, "Obl80", "")
}
func TestPb06(t *testing.T) {
var bzeta, bz, btheta float64
gofa.Pb06(2400000.5, 50123.9999, &bzeta, &bz, &btheta)
vvd(t, bzeta, -0.5092634016326478238e-3, 1e-12, "Pb06", "bzeta")
vvd(t, bz, -0.3602772060566044413e-3, 1e-12, "Pb06", "bz")
vvd(t, btheta, -0.3779735537167811177e-3, 1e-12, "Pb06", "btheta")
}
func TestPfw06(t *testing.T) {
var gamb, phib, psib, epsa float64
gofa.Pfw06(2400000.5, 50123.9999, &gamb, &phib, &psib, &epsa)
vvd(t, gamb, -0.2243387670997995690e-5, 1e-16, "Pfw06", "gamb")
vvd(t, phib, 0.4091014602391312808, 1e-12, "Pfw06", "phib")
vvd(t, psib, -0.9501954178013031895e-3, 1e-14, "Pfw06", "psib")
vvd(t, epsa, 0.4091014316587367491, 1e-12, "Pfw06", "epsa")
}
func TestPmat00(t *testing.T) {
var rbp [3][3]float64
gofa.Pmat00(2400000.5, 50123.9999, &rbp)
vvd(t, rbp[0][0], 0.9999995505175087260, 1e-12, "Pmat00", "11")
vvd(t, rbp[0][1], 0.8695405883617884705e-3, 1e-14, "Pmat00", "12")
vvd(t, rbp[0][2], 0.3779734722239007105e-3, 1e-14, "Pmat00", "13")
vvd(t, rbp[1][0], -0.8695405990410863719e-3, 1e-14, "Pmat00", "21")
vvd(t, rbp[1][1], 0.9999996219494925900, 1e-12, "Pmat00", "22")
vvd(t, rbp[1][2], -0.1360775820404982209e-6, 1e-14, "Pmat00", "23")
vvd(t, rbp[2][0], -0.3779734476558184991e-3, 1e-14, "Pmat00", "31")
vvd(t, rbp[2][1], -0.1925857585832024058e-6, 1e-14, "Pmat00", "32")
vvd(t, rbp[2][2], 0.9999999285680153377, 1e-12, "Pmat00", "33")
}
func TestPmat06(t *testing.T) {
var rbp [3][3]float64
gofa.Pmat06(2400000.5, 50123.9999, &rbp)
vvd(t, rbp[0][0], 0.9999995505176007047, 1e-12, "Pmat06", "11")
vvd(t, rbp[0][1], 0.8695404617348208406e-3, 1e-14, "Pmat06", "12")
vvd(t, rbp[0][2], 0.3779735201865589104e-3, 1e-14, "Pmat06", "13")
vvd(t, rbp[1][0], -0.8695404723772031414e-3, 1e-14, "Pmat06", "21")
vvd(t, rbp[1][1], 0.9999996219496027161, 1e-12, "Pmat06", "22")
vvd(t, rbp[1][2], -0.1361752497080270143e-6, 1e-14, "Pmat06", "23")
vvd(t, rbp[2][0], -0.3779734957034089490e-3, 1e-14, "Pmat06", "31")
vvd(t, rbp[2][1], -0.1924880847894457113e-6, 1e-14, "Pmat06", "32")
vvd(t, rbp[2][2], 0.9999999285679971958, 1e-12, "Pmat06", "33")
}
func TestPmat76(t *testing.T) {
var rmatp [3][3]float64
gofa.Pmat76(2400000.5, 50123.9999, &rmatp)
vvd(t, rmatp[0][0], 0.9999995504328350733, 1e-12, "Pmat76", "11")
vvd(t, rmatp[0][1], 0.8696632209480960785e-3, 1e-14, "Pmat76", "12")
vvd(t, rmatp[0][2], 0.3779153474959888345e-3, 1e-14, "Pmat76", "13")
vvd(t, rmatp[1][0], -0.8696632209485112192e-3, 1e-14, "Pmat76", "21")
vvd(t, rmatp[1][1], 0.9999996218428560614, 1e-12, "Pmat76", "22")
vvd(t, rmatp[1][2], -0.1643284776111886407e-6, 1e-14, "Pmat76", "23")
vvd(t, rmatp[2][0], -0.3779153474950335077e-3, 1e-14, "Pmat76", "31")
vvd(t, rmatp[2][1], -0.1643306746147366896e-6, 1e-14, "Pmat76", "32")
vvd(t, rmatp[2][2], 0.9999999285899790119, 1e-12, "Pmat76", "33")
}
func TestPn00(t *testing.T) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn, rbpn [3][3]float64
dpsi = -0.9632552291149335877e-5
deps = 0.4063197106621141414e-4
gofa.Pn00(2400000.5, 53736.0, dpsi, deps,
&epsa, &rb, &rp, &rbp, &rn, &rbpn)
vvd(t, epsa, 0.4090791789404229916, 1e-12, "Pn00", "epsa")
vvd(t, rb[0][0], 0.9999999999999942498, 1e-12, "Pn00", "rb11")
vvd(t, rb[0][1], -0.7078279744199196626e-7, 1e-18, "Pn00", "rb12")
vvd(t, rb[0][2], 0.8056217146976134152e-7, 1e-18, "Pn00", "rb13")
vvd(t, rb[1][0], 0.7078279477857337206e-7, 1e-18, "Pn00", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Pn00", "rb22")
vvd(t, rb[1][2], 0.3306041454222136517e-7, 1e-18, "Pn00", "rb23")
vvd(t, rb[2][0], -0.8056217380986972157e-7, 1e-18, "Pn00", "rb31")
vvd(t, rb[2][1], -0.3306040883980552500e-7, 1e-18, "Pn00", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Pn00", "rb33")
vvd(t, rp[0][0], 0.9999989300532289018, 1e-12, "Pn00", "rp11")
vvd(t, rp[0][1], -0.1341647226791824349e-2, 1e-14, "Pn00", "rp12")
vvd(t, rp[0][2], -0.5829880927190296547e-3, 1e-14, "Pn00", "rp13")
vvd(t, rp[1][0], 0.1341647231069759008e-2, 1e-14, "Pn00", "rp21")
vvd(t, rp[1][1], 0.9999990999908750433, 1e-12, "Pn00", "rp22")
vvd(t, rp[1][2], -0.3837444441583715468e-6, 1e-14, "Pn00", "rp23")
vvd(t, rp[2][0], 0.5829880828740957684e-3, 1e-14, "Pn00", "rp31")
vvd(t, rp[2][1], -0.3984203267708834759e-6, 1e-14, "Pn00", "rp32")
vvd(t, rp[2][2], 0.9999998300623538046, 1e-12, "Pn00", "rp33")
vvd(t, rbp[0][0], 0.9999989300052243993, 1e-12, "Pn00", "rbp11")
vvd(t, rbp[0][1], -0.1341717990239703727e-2, 1e-14, "Pn00", "rbp12")
vvd(t, rbp[0][2], -0.5829075749891684053e-3, 1e-14, "Pn00", "rbp13")
vvd(t, rbp[1][0], 0.1341718013831739992e-2, 1e-14, "Pn00", "rbp21")
vvd(t, rbp[1][1], 0.9999990998959191343, 1e-12, "Pn00", "rbp22")
vvd(t, rbp[1][2], -0.3505759733565421170e-6, 1e-14, "Pn00", "rbp23")
vvd(t, rbp[2][0], 0.5829075206857717883e-3, 1e-14, "Pn00", "rbp31")
vvd(t, rbp[2][1], -0.4315219955198608970e-6, 1e-14, "Pn00", "rbp32")
vvd(t, rbp[2][2], 0.9999998301093036269, 1e-12, "Pn00", "rbp33")
vvd(t, rn[0][0], 0.9999999999536069682, 1e-12, "Pn00", "rn11")
vvd(t, rn[0][1], 0.8837746144872140812e-5, 1e-16, "Pn00", "rn12")
vvd(t, rn[0][2], 0.3831488838252590008e-5, 1e-16, "Pn00", "rn13")
vvd(t, rn[1][0], -0.8837590456633197506e-5, 1e-16, "Pn00", "rn21")
vvd(t, rn[1][1], 0.9999999991354692733, 1e-12, "Pn00", "rn22")
vvd(t, rn[1][2], -0.4063198798559573702e-4, 1e-16, "Pn00", "rn23")
vvd(t, rn[2][0], -0.3831847930135328368e-5, 1e-16, "Pn00", "rn31")
vvd(t, rn[2][1], 0.4063195412258150427e-4, 1e-16, "Pn00", "rn32")
vvd(t, rn[2][2], 0.9999999991671806225, 1e-12, "Pn00", "rn33")
vvd(t, rbpn[0][0], 0.9999989440499982806, 1e-12, "Pn00", "rbpn11")
vvd(t, rbpn[0][1], -0.1332880253640848301e-2, 1e-14, "Pn00", "rbpn12")
vvd(t, rbpn[0][2], -0.5790760898731087295e-3, 1e-14, "Pn00", "rbpn13")
vvd(t, rbpn[1][0], 0.1332856746979948745e-2, 1e-14, "Pn00", "rbpn21")
vvd(t, rbpn[1][1], 0.9999991109064768883, 1e-12, "Pn00", "rbpn22")
vvd(t, rbpn[1][2], -0.4097740555723063806e-4, 1e-14, "Pn00", "rbpn23")
vvd(t, rbpn[2][0], 0.5791301929950205000e-3, 1e-14, "Pn00", "rbpn31")
vvd(t, rbpn[2][1], 0.4020553681373702931e-4, 1e-14, "Pn00", "rbpn32")
vvd(t, rbpn[2][2], 0.9999998314958529887, 1e-12, "Pn00", "rbpn33")
}
func TestPn00a(t *testing.T) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn, rbpn [3][3]float64
gofa.Pn00a(2400000.5, 53736.0,
&dpsi, &deps, &epsa, &rb, &rp, &rbp, &rn, &rbpn)
vvd(t, dpsi, -0.9630909107115518431e-5, 1e-12, "Pn00a", "dpsi")
vvd(t, deps, 0.4063239174001678710e-4, 1e-12, "Pn00a", "deps")
vvd(t, epsa, 0.4090791789404229916, 1e-12, "Pn00a", "epsa")
vvd(t, rb[0][0], 0.9999999999999942498, 1e-12, "Pn00a", "rb11")
vvd(t, rb[0][1], -0.7078279744199196626e-7, 1e-16, "Pn00a", "rb12")
vvd(t, rb[0][2], 0.8056217146976134152e-7, 1e-16, "Pn00a", "rb13")
vvd(t, rb[1][0], 0.7078279477857337206e-7, 1e-16, "Pn00a", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Pn00a", "rb22")
vvd(t, rb[1][2], 0.3306041454222136517e-7, 1e-16, "Pn00a", "rb23")
vvd(t, rb[2][0], -0.8056217380986972157e-7, 1e-16, "Pn00a", "rb31")
vvd(t, rb[2][1], -0.3306040883980552500e-7, 1e-16, "Pn00a", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Pn00a", "rb33")
vvd(t, rp[0][0], 0.9999989300532289018, 1e-12, "Pn00a", "rp11")
vvd(t, rp[0][1], -0.1341647226791824349e-2, 1e-14, "Pn00a", "rp12")
vvd(t, rp[0][2], -0.5829880927190296547e-3, 1e-14, "Pn00a", "rp13")
vvd(t, rp[1][0], 0.1341647231069759008e-2, 1e-14, "Pn00a", "rp21")
vvd(t, rp[1][1], 0.9999990999908750433, 1e-12, "Pn00a", "rp22")
vvd(t, rp[1][2], -0.3837444441583715468e-6, 1e-14, "Pn00a", "rp23")
vvd(t, rp[2][0], 0.5829880828740957684e-3, 1e-14, "Pn00a", "rp31")
vvd(t, rp[2][1], -0.3984203267708834759e-6, 1e-14, "Pn00a", "rp32")
vvd(t, rp[2][2], 0.9999998300623538046, 1e-12, "Pn00a", "rp33")
vvd(t, rbp[0][0], 0.9999989300052243993, 1e-12, "Pn00a", "rbp11")
vvd(t, rbp[0][1], -0.1341717990239703727e-2, 1e-14, "Pn00a", "rbp12")
vvd(t, rbp[0][2], -0.5829075749891684053e-3, 1e-14, "Pn00a", "rbp13")
vvd(t, rbp[1][0], 0.1341718013831739992e-2, 1e-14, "Pn00a", "rbp21")
vvd(t, rbp[1][1], 0.9999990998959191343, 1e-12, "Pn00a", "rbp22")
vvd(t, rbp[1][2], -0.3505759733565421170e-6, 1e-14, "Pn00a", "rbp23")
vvd(t, rbp[2][0], 0.5829075206857717883e-3, 1e-14, "Pn00a", "rbp31")
vvd(t, rbp[2][1], -0.4315219955198608970e-6, 1e-14, "Pn00a", "rbp32")
vvd(t, rbp[2][2], 0.9999998301093036269, 1e-12, "Pn00a", "rbp33")
vvd(t, rn[0][0], 0.9999999999536227949, 1e-12, "Pn00a", "rn11")
vvd(t, rn[0][1], 0.8836238544090873336e-5, 1e-14, "Pn00a", "rn12")
vvd(t, rn[0][2], 0.3830835237722400669e-5, 1e-14, "Pn00a", "rn13")
vvd(t, rn[1][0], -0.8836082880798569274e-5, 1e-14, "Pn00a", "rn21")
vvd(t, rn[1][1], 0.9999999991354655028, 1e-12, "Pn00a", "rn22")
vvd(t, rn[1][2], -0.4063240865362499850e-4, 1e-14, "Pn00a", "rn23")
vvd(t, rn[2][0], -0.3831194272065995866e-5, 1e-14, "Pn00a", "rn31")
vvd(t, rn[2][1], 0.4063237480216291775e-4, 1e-14, "Pn00a", "rn32")
vvd(t, rn[2][2], 0.9999999991671660338, 1e-12, "Pn00a", "rn33")
vvd(t, rbpn[0][0], 0.9999989440476103435, 1e-12, "Pn00a", "rbpn11")
vvd(t, rbpn[0][1], -0.1332881761240011763e-2, 1e-14, "Pn00a", "rbpn12")
vvd(t, rbpn[0][2], -0.5790767434730085751e-3, 1e-14, "Pn00a", "rbpn13")
vvd(t, rbpn[1][0], 0.1332858254308954658e-2, 1e-14, "Pn00a", "rbpn21")
vvd(t, rbpn[1][1], 0.9999991109044505577, 1e-12, "Pn00a", "rbpn22")
vvd(t, rbpn[1][2], -0.4097782710396580452e-4, 1e-14, "Pn00a", "rbpn23")
vvd(t, rbpn[2][0], 0.5791308472168152904e-3, 1e-14, "Pn00a", "rbpn31")
vvd(t, rbpn[2][1], 0.4020595661591500259e-4, 1e-14, "Pn00a", "rbpn32")
vvd(t, rbpn[2][2], 0.9999998314954572304, 1e-12, "Pn00a", "rbpn33")
}
func TestPn00b(t *testing.T) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn, rbpn [3][3]float64
gofa.Pn00b(2400000.5, 53736.0, &dpsi, &deps, &epsa,
&rb, &rp, &rbp, &rn, &rbpn)
vvd(t, dpsi, -0.9632552291148362783e-5, 1e-12, "Pn00b", "dpsi")
vvd(t, deps, 0.4063197106621159367e-4, 1e-12, "Pn00b", "deps")
vvd(t, epsa, 0.4090791789404229916, 1e-12, "Pn00b", "epsa")
vvd(t, rb[0][0], 0.9999999999999942498, 1e-12, "Pn00b", "rb11")
vvd(t, rb[0][1], -0.7078279744199196626e-7, 1e-16, "Pn00b", "rb12")
vvd(t, rb[0][2], 0.8056217146976134152e-7, 1e-16, "Pn00b", "rb13")
vvd(t, rb[1][0], 0.7078279477857337206e-7, 1e-16, "Pn00b", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Pn00b", "rb22")
vvd(t, rb[1][2], 0.3306041454222136517e-7, 1e-16, "Pn00b", "rb23")
vvd(t, rb[2][0], -0.8056217380986972157e-7, 1e-16, "Pn00b", "rb31")
vvd(t, rb[2][1], -0.3306040883980552500e-7, 1e-16, "Pn00b", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Pn00b", "rb33")
vvd(t, rp[0][0], 0.9999989300532289018, 1e-12, "Pn00b", "rp11")
vvd(t, rp[0][1], -0.1341647226791824349e-2, 1e-14, "Pn00b", "rp12")
vvd(t, rp[0][2], -0.5829880927190296547e-3, 1e-14, "Pn00b", "rp13")
vvd(t, rp[1][0], 0.1341647231069759008e-2, 1e-14, "Pn00b", "rp21")
vvd(t, rp[1][1], 0.9999990999908750433, 1e-12, "Pn00b", "rp22")
vvd(t, rp[1][2], -0.3837444441583715468e-6, 1e-14, "Pn00b", "rp23")
vvd(t, rp[2][0], 0.5829880828740957684e-3, 1e-14, "Pn00b", "rp31")
vvd(t, rp[2][1], -0.3984203267708834759e-6, 1e-14, "Pn00b", "rp32")
vvd(t, rp[2][2], 0.9999998300623538046, 1e-12, "Pn00b", "rp33")
vvd(t, rbp[0][0], 0.9999989300052243993, 1e-12, "Pn00b", "rbp11")
vvd(t, rbp[0][1], -0.1341717990239703727e-2, 1e-14, "Pn00b", "rbp12")
vvd(t, rbp[0][2], -0.5829075749891684053e-3, 1e-14, "Pn00b", "rbp13")
vvd(t, rbp[1][0], 0.1341718013831739992e-2, 1e-14, "Pn00b", "rbp21")
vvd(t, rbp[1][1], 0.9999990998959191343, 1e-12, "Pn00b", "rbp22")
vvd(t, rbp[1][2], -0.3505759733565421170e-6, 1e-14, "Pn00b", "rbp23")
vvd(t, rbp[2][0], 0.5829075206857717883e-3, 1e-14, "Pn00b", "rbp31")
vvd(t, rbp[2][1], -0.4315219955198608970e-6, 1e-14, "Pn00b", "rbp32")
vvd(t, rbp[2][2], 0.9999998301093036269, 1e-12, "Pn00b", "rbp33")
vvd(t, rn[0][0], 0.9999999999536069682, 1e-12, "Pn00b", "rn11")
vvd(t, rn[0][1], 0.8837746144871248011e-5, 1e-14, "Pn00b", "rn12")
vvd(t, rn[0][2], 0.3831488838252202945e-5, 1e-14, "Pn00b", "rn13")
vvd(t, rn[1][0], -0.8837590456632304720e-5, 1e-14, "Pn00b", "rn21")
vvd(t, rn[1][1], 0.9999999991354692733, 1e-12, "Pn00b", "rn22")
vvd(t, rn[1][2], -0.4063198798559591654e-4, 1e-14, "Pn00b", "rn23")
vvd(t, rn[2][0], -0.3831847930134941271e-5, 1e-14, "Pn00b", "rn31")
vvd(t, rn[2][1], 0.4063195412258168380e-4, 1e-14, "Pn00b", "rn32")
vvd(t, rn[2][2], 0.9999999991671806225, 1e-12, "Pn00b", "rn33")
vvd(t, rbpn[0][0], 0.9999989440499982806, 1e-12, "Pn00b", "rbpn11")
vvd(t, rbpn[0][1], -0.1332880253640849194e-2, 1e-14, "Pn00b", "rbpn12")
vvd(t, rbpn[0][2], -0.5790760898731091166e-3, 1e-14, "Pn00b", "rbpn13")
vvd(t, rbpn[1][0], 0.1332856746979949638e-2, 1e-14, "Pn00b", "rbpn21")
vvd(t, rbpn[1][1], 0.9999991109064768883, 1e-12, "Pn00b", "rbpn22")
vvd(t, rbpn[1][2], -0.4097740555723081811e-4, 1e-14, "Pn00b", "rbpn23")
vvd(t, rbpn[2][0], 0.5791301929950208873e-3, 1e-14, "Pn00b", "rbpn31")
vvd(t, rbpn[2][1], 0.4020553681373720832e-4, 1e-14, "Pn00b", "rbpn32")
vvd(t, rbpn[2][2], 0.9999998314958529887, 1e-12, "Pn00b", "rbpn33")
}
func TestPn06(t *testing.T) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn, rbpn [3][3]float64
dpsi = -0.9632552291149335877e-5
deps = 0.4063197106621141414e-4
gofa.Pn06(2400000.5, 53736.0, dpsi, deps,
&epsa, &rb, &rp, &rbp, &rn, &rbpn)
vvd(t, epsa, 0.4090789763356509926, 1e-12, "Pn06", "epsa")
vvd(t, rb[0][0], 0.9999999999999942497, 1e-12, "Pn06", "rb11")
vvd(t, rb[0][1], -0.7078368960971557145e-7, 1e-14, "Pn06", "rb12")
vvd(t, rb[0][2], 0.8056213977613185606e-7, 1e-14, "Pn06", "rb13")
vvd(t, rb[1][0], 0.7078368694637674333e-7, 1e-14, "Pn06", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Pn06", "rb22")
vvd(t, rb[1][2], 0.3305943742989134124e-7, 1e-14, "Pn06", "rb23")
vvd(t, rb[2][0], -0.8056214211620056792e-7, 1e-14, "Pn06", "rb31")
vvd(t, rb[2][1], -0.3305943172740586950e-7, 1e-14, "Pn06", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Pn06", "rb33")
vvd(t, rp[0][0], 0.9999989300536854831, 1e-12, "Pn06", "rp11")
vvd(t, rp[0][1], -0.1341646886204443795e-2, 1e-14, "Pn06", "rp12")
vvd(t, rp[0][2], -0.5829880933488627759e-3, 1e-14, "Pn06", "rp13")
vvd(t, rp[1][0], 0.1341646890569782183e-2, 1e-14, "Pn06", "rp21")
vvd(t, rp[1][1], 0.9999990999913319321, 1e-12, "Pn06", "rp22")
vvd(t, rp[1][2], -0.3835944216374477457e-6, 1e-14, "Pn06", "rp23")
vvd(t, rp[2][0], 0.5829880833027867368e-3, 1e-14, "Pn06", "rp31")
vvd(t, rp[2][1], -0.3985701514686976112e-6, 1e-14, "Pn06", "rp32")
vvd(t, rp[2][2], 0.9999998300623534950, 1e-12, "Pn06", "rp33")
vvd(t, rbp[0][0], 0.9999989300056797893, 1e-12, "Pn06", "rbp11")
vvd(t, rbp[0][1], -0.1341717650545059598e-2, 1e-14, "Pn06", "rbp12")
vvd(t, rbp[0][2], -0.5829075756493728856e-3, 1e-14, "Pn06", "rbp13")
vvd(t, rbp[1][0], 0.1341717674223918101e-2, 1e-14, "Pn06", "rbp21")
vvd(t, rbp[1][1], 0.9999990998963748448, 1e-12, "Pn06", "rbp22")
vvd(t, rbp[1][2], -0.3504269280170069029e-6, 1e-14, "Pn06", "rbp23")
vvd(t, rbp[2][0], 0.5829075211461454599e-3, 1e-14, "Pn06", "rbp31")
vvd(t, rbp[2][1], -0.4316708436255949093e-6, 1e-14, "Pn06", "rbp32")
vvd(t, rbp[2][2], 0.9999998301093032943, 1e-12, "Pn06", "rbp33")
vvd(t, rn[0][0], 0.9999999999536069682, 1e-12, "Pn06", "rn11")
vvd(t, rn[0][1], 0.8837746921149881914e-5, 1e-14, "Pn06", "rn12")
vvd(t, rn[0][2], 0.3831487047682968703e-5, 1e-14, "Pn06", "rn13")
vvd(t, rn[1][0], -0.8837591232983692340e-5, 1e-14, "Pn06", "rn21")
vvd(t, rn[1][1], 0.9999999991354692664, 1e-12, "Pn06", "rn22")
vvd(t, rn[1][2], -0.4063198798558931215e-4, 1e-14, "Pn06", "rn23")
vvd(t, rn[2][0], -0.3831846139597250235e-5, 1e-14, "Pn06", "rn31")
vvd(t, rn[2][1], 0.4063195412258792914e-4, 1e-14, "Pn06", "rn32")
vvd(t, rn[2][2], 0.9999999991671806293, 1e-12, "Pn06", "rn33")
vvd(t, rbpn[0][0], 0.9999989440504506688, 1e-12, "Pn06", "rbpn11")
vvd(t, rbpn[0][1], -0.1332879913170492655e-2, 1e-14, "Pn06", "rbpn12")
vvd(t, rbpn[0][2], -0.5790760923225655753e-3, 1e-14, "Pn06", "rbpn13")
vvd(t, rbpn[1][0], 0.1332856406595754748e-2, 1e-14, "Pn06", "rbpn21")
vvd(t, rbpn[1][1], 0.9999991109069366795, 1e-12, "Pn06", "rbpn22")
vvd(t, rbpn[1][2], -0.4097725651142641812e-4, 1e-14, "Pn06", "rbpn23")
vvd(t, rbpn[2][0], 0.5791301952321296716e-3, 1e-14, "Pn06", "rbpn31")
vvd(t, rbpn[2][1], 0.4020538796195230577e-4, 1e-14, "Pn06", "rbpn32")
vvd(t, rbpn[2][2], 0.9999998314958576778, 1e-12, "Pn06", "rbpn33")
}
func TestPn06a(t *testing.T) {
var dpsi, deps, epsa float64
var rb, rp, rbp, rn, rbpn [3][3]float64
gofa.Pn06a(2400000.5, 53736.0, &dpsi, &deps, &epsa,
&rb, &rp, &rbp, &rn, &rbpn)
vvd(t, dpsi, -0.9630912025820308797e-5, 1e-12, "Pn06a", "dpsi")
vvd(t, deps, 0.4063238496887249798e-4, 1e-12, "Pn06a", "deps")
vvd(t, epsa, 0.4090789763356509926, 1e-12, "Pn06a", "epsa")
vvd(t, rb[0][0], 0.9999999999999942497, 1e-12, "Pn06a", "rb11")
vvd(t, rb[0][1], -0.7078368960971557145e-7, 1e-14, "Pn06a", "rb12")
vvd(t, rb[0][2], 0.8056213977613185606e-7, 1e-14, "Pn06a", "rb13")
vvd(t, rb[1][0], 0.7078368694637674333e-7, 1e-14, "Pn06a", "rb21")
vvd(t, rb[1][1], 0.9999999999999969484, 1e-12, "Pn06a", "rb22")
vvd(t, rb[1][2], 0.3305943742989134124e-7, 1e-14, "Pn06a", "rb23")
vvd(t, rb[2][0], -0.8056214211620056792e-7, 1e-14, "Pn06a", "rb31")
vvd(t, rb[2][1], -0.3305943172740586950e-7, 1e-14, "Pn06a", "rb32")
vvd(t, rb[2][2], 0.9999999999999962084, 1e-12, "Pn06a", "rb33")
vvd(t, rp[0][0], 0.9999989300536854831, 1e-12, "Pn06a", "rp11")
vvd(t, rp[0][1], -0.1341646886204443795e-2, 1e-14, "Pn06a", "rp12")
vvd(t, rp[0][2], -0.5829880933488627759e-3, 1e-14, "Pn06a", "rp13")
vvd(t, rp[1][0], 0.1341646890569782183e-2, 1e-14, "Pn06a", "rp21")
vvd(t, rp[1][1], 0.9999990999913319321, 1e-12, "Pn06a", "rp22")
vvd(t, rp[1][2], -0.3835944216374477457e-6, 1e-14, "Pn06a", "rp23")
vvd(t, rp[2][0], 0.5829880833027867368e-3, 1e-14, "Pn06a", "rp31")
vvd(t, rp[2][1], -0.3985701514686976112e-6, 1e-14, "Pn06a", "rp32")
vvd(t, rp[2][2], 0.9999998300623534950, 1e-12, "Pn06a", "rp33")
vvd(t, rbp[0][0], 0.9999989300056797893, 1e-12, "Pn06a", "rbp11")
vvd(t, rbp[0][1], -0.1341717650545059598e-2, 1e-14, "Pn06a", "rbp12")
vvd(t, rbp[0][2], -0.5829075756493728856e-3, 1e-14, "Pn06a", "rbp13")
vvd(t, rbp[1][0], 0.1341717674223918101e-2, 1e-14, "Pn06a", "rbp21")
vvd(t, rbp[1][1], 0.9999990998963748448, 1e-12, "Pn06a", "rbp22")
vvd(t, rbp[1][2], -0.3504269280170069029e-6, 1e-14, "Pn06a", "rbp23")
vvd(t, rbp[2][0], 0.5829075211461454599e-3, 1e-14, "Pn06a", "rbp31")
vvd(t, rbp[2][1], -0.4316708436255949093e-6, 1e-14, "Pn06a", "rbp32")
vvd(t, rbp[2][2], 0.9999998301093032943, 1e-12, "Pn06a", "rbp33")
vvd(t, rn[0][0], 0.9999999999536227668, 1e-12, "Pn06a", "rn11")
vvd(t, rn[0][1], 0.8836241998111535233e-5, 1e-14, "Pn06a", "rn12")
vvd(t, rn[0][2], 0.3830834608415287707e-5, 1e-14, "Pn06a", "rn13")
vvd(t, rn[1][0], -0.8836086334870740138e-5, 1e-14, "Pn06a", "rn21")
vvd(t, rn[1][1], 0.9999999991354657474, 1e-12, "Pn06a", "rn22")
vvd(t, rn[1][2], -0.4063240188248455065e-4, 1e-14, "Pn06a", "rn23")
vvd(t, rn[2][0], -0.3831193642839398128e-5, 1e-14, "Pn06a", "rn31")
vvd(t, rn[2][1], 0.4063236803101479770e-4, 1e-14, "Pn06a", "rn32")
vvd(t, rn[2][2], 0.9999999991671663114, 1e-12, "Pn06a", "rn33")
vvd(t, rbpn[0][0], 0.9999989440480669738, 1e-12, "Pn06a", "rbpn11")
vvd(t, rbpn[0][1], -0.1332881418091915973e-2, 1e-14, "Pn06a", "rbpn12")
vvd(t, rbpn[0][2], -0.5790767447612042565e-3, 1e-14, "Pn06a", "rbpn13")
vvd(t, rbpn[1][0], 0.1332857911250989133e-2, 1e-14, "Pn06a", "rbpn21")
vvd(t, rbpn[1][1], 0.9999991109049141908, 1e-12, "Pn06a", "rbpn22")
vvd(t, rbpn[1][2], -0.4097767128546784878e-4, 1e-14, "Pn06a", "rbpn23")
vvd(t, rbpn[2][0], 0.5791308482835292617e-3, 1e-14, "Pn06a", "rbpn31")
vvd(t, rbpn[2][1], 0.4020580099454020310e-4, 1e-14, "Pn06a", "rbpn32")
vvd(t, rbpn[2][2], 0.9999998314954628695, 1e-12, "Pn06a", "rbpn33")
}
func TestPnm00a(t *testing.T) {
var rbpn [3][3]float64
gofa.Pnm00a(2400000.5, 50123.9999, &rbpn)
vvd(t, rbpn[0][0], 0.9999995832793134257, 1e-12, "Pnm00a", "11")
vvd(t, rbpn[0][1], 0.8372384254137809439e-3, 1e-14, "Pnm00a", "12")
vvd(t, rbpn[0][2], 0.3639684306407150645e-3, 1e-14, "Pnm00a", "13")
vvd(t, rbpn[1][0], -0.8372535226570394543e-3, 1e-14, "Pnm00a", "21")
vvd(t, rbpn[1][1], 0.9999996486491582471, 1e-12, "Pnm00a", "22")
vvd(t, rbpn[1][2], 0.4132915262664072381e-4, 1e-14, "Pnm00a", "23")
vvd(t, rbpn[2][0], -0.3639337004054317729e-3, 1e-14, "Pnm00a", "31")
vvd(t, rbpn[2][1], -0.4163386925461775873e-4, 1e-14, "Pnm00a", "32")
vvd(t, rbpn[2][2], 0.9999999329094390695, 1e-12, "Pnm00a", "33")
}
func TestPnm00b(t *testing.T) {
var rbpn [3][3]float64
gofa.Pnm00b(2400000.5, 50123.9999, &rbpn)
vvd(t, rbpn[0][0], 0.9999995832776208280, 1e-12, "Pnm00b", "11")
vvd(t, rbpn[0][1], 0.8372401264429654837e-3, 1e-14, "Pnm00b", "12")
vvd(t, rbpn[0][2], 0.3639691681450271771e-3, 1e-14, "Pnm00b", "13")
vvd(t, rbpn[1][0], -0.8372552234147137424e-3, 1e-14, "Pnm00b", "21")
vvd(t, rbpn[1][1], 0.9999996486477686123, 1e-12, "Pnm00b", "22")
vvd(t, rbpn[1][2], 0.4132832190946052890e-4, 1e-14, "Pnm00b", "23")
vvd(t, rbpn[2][0], -0.3639344385341866407e-3, 1e-14, "Pnm00b", "31")
vvd(t, rbpn[2][1], -0.4163303977421522785e-4, 1e-14, "Pnm00b", "32")
vvd(t, rbpn[2][2], 0.9999999329092049734, 1e-12, "Pnm00b", "33")
}
func TestPnm06a(t *testing.T) {
var rbpn [3][3]float64
gofa.Pnm06a(2400000.5, 50123.9999, &rbpn)
r := [3][3]float64{
{0.9999995832794205484, 0.8372382772630962111e-3, 0.3639684771140623099e-3},
{-0.8372533744743683605e-3, 0.9999996486492861646, 0.4132905944611019498e-4},
{-0.3639337469629464969e-3, -0.4163377605910663999e-4, 0.9999999329094260057},
}
vrv(t, rbpn, r, 1e-14, "Pnm06a")
}
func TestPnm80(t *testing.T) {
var rmatpn [3][3]float64
gofa.Pnm80(2400000.5, 50123.9999, &rmatpn)
vvd(t, rmatpn[0][0], 0.9999995831934611169, 1e-12, "Pnm80", "11")
vvd(t, rmatpn[0][1], 0.8373654045728124011e-3, 1e-14, "Pnm80", "12")
vvd(t, rmatpn[0][2], 0.3639121916933106191e-3, 1e-14, "Pnm80", "13")
vvd(t, rmatpn[1][0], -0.8373804896118301316e-3, 1e-14, "Pnm80", "21")
vvd(t, rmatpn[1][1], 0.9999996485439674092, 1e-12, "Pnm80", "22")
vvd(t, rmatpn[1][2], 0.4130202510421549752e-4, 1e-14, "Pnm80", "23")
vvd(t, rmatpn[2][0], -0.3638774789072144473e-3, 1e-14, "Pnm80", "31")
vvd(t, rmatpn[2][1], -0.4160674085851722359e-4, 1e-14, "Pnm80", "32")
vvd(t, rmatpn[2][2], 0.9999999329310274805, 1e-12, "Pnm80", "33")
}
func TestP06e(t *testing.T) {
var eps0, psia, oma, bpa, bqa, pia, bpia,
epsa, chia, za, zetaa, thetaa, pa, gam, phi, psi float64
gofa.P06e(2400000.5, 52541.0, &eps0, &psia, &oma, &bpa,
&bqa, &pia, &bpia, &epsa, &chia, &za,
&zetaa, &thetaa, &pa, &gam, &phi, &psi)
vvd(t, eps0, 0.4090926006005828715, 1e-14, "P06e", "eps0")
vvd(t, psia, 0.6664369630191613431e-3, 1e-14, "P06e", "psia")
vvd(t, oma, 0.4090925973783255982, 1e-14, "P06e", "oma")
vvd(t, bpa, 0.5561149371265209445e-6, 1e-14, "P06e", "bpa")
vvd(t, bqa, -0.6191517193290621270e-5, 1e-14, "P06e", "bqa")
vvd(t, pia, 0.6216441751884382923e-5, 1e-14, "P06e", "pia")
vvd(t, bpia, 3.052014180023779882, 1e-14, "P06e", "bpia")
vvd(t, epsa, 0.4090864054922431688, 1e-14, "P06e", "epsa")
vvd(t, chia, 0.1387703379530915364e-5, 1e-14, "P06e", "chia")
vvd(t, za, 0.2921789846651790546e-3, 1e-14, "P06e", "za")
vvd(t, zetaa, 0.3178773290332009310e-3, 1e-14, "P06e", "zetaa")
vvd(t, thetaa, 0.2650932701657497181e-3, 1e-14, "P06e", "thetaa")
vvd(t, pa, 0.6651637681381016288e-3, 1e-14, "P06e", "pa")
vvd(t, gam, 0.1398077115963754987e-5, 1e-14, "P06e", "gam")
vvd(t, phi, 0.4090864090837462602, 1e-14, "P06e", "phi")
vvd(t, psi, 0.6664464807480920325e-3, 1e-14, "P06e", "psi")
}
func TestPom00(t *testing.T) {
var xp, yp, sp float64
var rpom [3][3]float64
xp = 2.55060238e-7
yp = 1.860359247e-6
sp = -0.1367174580728891460e-10
gofa.Pom00(xp, yp, sp, &rpom)
vvd(t, rpom[0][0], 0.9999999999999674721, 1e-12, "Pom00", "11")
vvd(t, rpom[0][1], -0.1367174580728846989e-10, 1e-16, "Pom00", "12")
vvd(t, rpom[0][2], 0.2550602379999972345e-6, 1e-16, "Pom00", "13")
vvd(t, rpom[1][0], 0.1414624947957029801e-10, 1e-16, "Pom00", "21")
vvd(t, rpom[1][1], 0.9999999999982695317, 1e-12, "Pom00", "22")
vvd(t, rpom[1][2], -0.1860359246998866389e-5, 1e-16, "Pom00", "23")
vvd(t, rpom[2][0], -0.2550602379741215021e-6, 1e-16, "Pom00", "31")
vvd(t, rpom[2][1], 0.1860359247002414021e-5, 1e-16, "Pom00", "32")
vvd(t, rpom[2][2], 0.9999999999982370039, 1e-12, "Pom00", "33")
}
func TestPr00(t *testing.T) {
var dpsipr, depspr float64
gofa.Pr00(2400000.5, 53736, &dpsipr, &depspr)
vvd(t, dpsipr, -0.8716465172668347629e-7, 1e-22,
"Pr00", "dpsipr")
vvd(t, depspr, -0.7342018386722813087e-8, 1e-22,
"Pr00", "depspr")
}
func TestPrec76(t *testing.T) {
var ep01, ep02, ep11, ep12, zeta, z, theta float64
ep01 = 2400000.5
ep02 = 33282.0
ep11 = 2400000.5
ep12 = 51544.0
gofa.Prec76(ep01, ep02, ep11, ep12, &zeta, &z, &theta)
vvd(t, zeta, 0.5588961642000161243e-2, 1e-12, "Prec76", "zeta")
vvd(t, z, 0.5589922365870680624e-2, 1e-12, "Prec76", "z")
vvd(t, theta, 0.4858945471687296760e-2, 1e-12, "Prec76", "theta")
}
func TestS00(t *testing.T) {
var x, y, s float64
x = 0.5791308486706011000e-3
y = 0.4020579816732961219e-4
s = gofa.S00(2400000.5, 53736.0, x, y)
vvd(t, s, -0.1220036263270905693e-7, 1e-18, "S00", "")
}
func TestS00a(t *testing.T) {
s := gofa.S00a(2400000.5, 52541.0)
vvd(t, s, -0.1340684448919163584e-7, 1e-18, "S00a", "")
}
func TestS00b(t *testing.T) {
s := gofa.S00b(2400000.5, 52541.0)
vvd(t, s, -0.1340695782951026584e-7, 1e-18, "S00b", "")
}
func TestS06(t *testing.T) {
var x, y, s float64
x = 0.5791308486706011000e-3
y = 0.4020579816732961219e-4
s = gofa.S06(2400000.5, 53736.0, x, y)
vvd(t, s, -0.1220032213076463117e-7, 1e-18, "S06", "")
}
func TestS06a(t *testing.T) {
s := gofa.S06a(2400000.5, 52541.0)
vvd(t, s, -0.1340680437291812383e-7, 1e-18, "S06a", "")
}
func TestSp00(t *testing.T) {
vvd(t, gofa.Sp00(2400000.5, 52541.0),
-0.6216698469981019309e-11, 1e-12, "Sp00", "")
}
func TestXy06(t *testing.T) {
var x, y float64
gofa.Xy06(2400000.5, 53736.0, &x, &y)
vvd(t, x, 0.5791308486706010975e-3, 1e-15, "Xy06", "x")
vvd(t, y, 0.4020579816732958141e-4, 1e-16, "Xy06", "y")
}
func TestXys00a(t *testing.T) {
var x, y, s float64
gofa.Xys00a(2400000.5, 53736.0, &x, &y, &s)
vvd(t, x, 0.5791308472168152904e-3, 1e-14, "Xys00a", "x")
vvd(t, y, 0.4020595661591500259e-4, 1e-15, "Xys00a", "y")
vvd(t, s, -0.1220040848471549623e-7, 1e-18, "Xys00a", "s")
}
func TestXys00b(t *testing.T) {
var x, y, s float64
gofa.Xys00b(2400000.5, 53736.0, &x, &y, &s)
vvd(t, x, 0.5791301929950208873e-3, 1e-14, "Xys00b", "x")
vvd(t, y, 0.4020553681373720832e-4, 1e-15, "Xys00b", "y")
vvd(t, s, -0.1220027377285083189e-7, 1e-18, "Xys00b", "s")
}
func TestXys06a(t *testing.T) {
var x, y, s float64
gofa.Xys06a(2400000.5, 53736.0, &x, &y, &s)
vvd(t, x, 0.5791308482835292617e-3, 1e-14, "Xys06a", "x")
vvd(t, y, 0.4020580099454020310e-4, 1e-15, "Xys06a", "y")
vvd(t, s, -0.1220032294164579896e-7, 1e-18, "Xys06a", "s")
}
gofa-1.19.1/test/projection_test.go 0000664 0000000 0000000 00000005005 14535740236 0017251 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestTpors(t *testing.T) {
var xi, eta, ra, dec, az1, bz1, az2, bz2 float64
var n int
xi = -0.03
eta = 0.07
ra = 1.3
dec = 1.5
n = gofa.Tpors(xi, eta, ra, dec, &az1, &bz1, &az2, &bz2)
vvd(t, az1, 1.736621577783208748, 1e-13, "Tpors", "az1")
vvd(t, bz1, 1.436736561844090323, 1e-13, "Tpors", "bz1")
vvd(t, az2, 4.004971075806584490, 1e-13, "Tpors", "az2")
vvd(t, bz2, 1.565084088476417917, 1e-13, "Tpors", "bz2")
viv(t, n, 2, "Tpors", "n")
}
func TestTporv(t *testing.T) {
var xi, eta, ra, dec float64
var v, vz1, vz2 [3]float64
var n int
xi = -0.03
eta = 0.07
ra = 1.3
dec = 1.5
gofa.S2c(ra, dec, &v)
n = gofa.Tporv(xi, eta, v, &vz1, &vz2)
vvd(t, vz1[0], -0.02206252822366888610, 1e-15, "Tporv", "x1")
vvd(t, vz1[1], 0.1318251060359645016, 1e-14, "Tporv", "y1")
vvd(t, vz1[2], 0.9910274397144543895, 1e-14, "Tporv", "z1")
vvd(t, vz2[0], -0.003712211763801968173, 1e-16, "Tporv", "x2")
vvd(t, vz2[1], -0.004341519956299836813, 1e-16, "Tporv", "y2")
vvd(t, vz2[2], 0.9999836852110587012, 1e-14, "Tporv", "z2")
viv(t, n, 2, "Tporv", "n")
}
func TestTpsts(t *testing.T) {
var xi, eta, raz, decz, ra, dec float64
xi = -0.03
eta = 0.07
raz = 2.3
decz = 1.5
gofa.Tpsts(xi, eta, raz, decz, &ra, &dec)
vvd(t, ra, 0.7596127167359629775, 1e-14, "Tpsts", "ra")
vvd(t, dec, 1.540864645109263028, 1e-13, "Tpsts", "dec")
}
func TestTpstv(t *testing.T) {
var xi, eta, raz, decz float64
var vz, v [3]float64
xi = -0.03
eta = 0.07
raz = 2.3
decz = 1.5
gofa.S2c(raz, decz, &vz)
gofa.Tpstv(xi, eta, vz, &v)
vvd(t, v[0], 0.02170030454907376677, 1e-15, "Tpstv", "x")
vvd(t, v[1], 0.02060909590535367447, 1e-15, "Tpstv", "y")
vvd(t, v[2], 0.9995520806583523804, 1e-14, "Tpstv", "z")
}
func TestTpxes(t *testing.T) {
var ra, dec, raz, decz, xi, eta float64
var j int
ra = 1.3
dec = 1.55
raz = 2.3
decz = 1.5
j = gofa.Tpxes(ra, dec, raz, decz, &xi, &eta)
vvd(t, xi, -0.01753200983236980595, 1e-15, "Tpxes", "xi")
vvd(t, eta, 0.05962940005778712891, 1e-15, "Tpxes", "eta")
viv(t, j, 0, "Tpxes", "j")
}
func TestTpxev(t *testing.T) {
var ra, dec, raz, decz, xi, eta float64
var v, vz [3]float64
var j int
ra = 1.3
dec = 1.55
raz = 2.3
decz = 1.5
gofa.S2c(ra, dec, &v)
gofa.S2c(raz, decz, &vz)
j = gofa.Tpxev(v, vz, &xi, &eta)
vvd(t, xi, -0.01753200983236980595, 1e-15, "Tpxev", "xi")
vvd(t, eta, 0.05962940005778712891, 1e-15, "Tpxev", "eta")
viv(t, j, 0, "Tpxev", "j")
}
gofa-1.19.1/test/ts_test.go 0000664 0000000 0000000 00000012376 14535740236 0015534 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestD2dtf(t *testing.T) {
var j, iy, im, id int
var ihmsf [4]int
j = gofa.D2dtf("UTC", 5, 2400000.5, 49533.99999, &iy, &im, &id, &ihmsf)
viv(t, iy, 1994, "D2dtf", "iy")
viv(t, im, 6, "D2dtf", "im")
viv(t, id, 30, "D2dtf", "id")
viv(t, ihmsf[0], 23, "D2dtf", "ihmsf[0]")
viv(t, ihmsf[1], 59, "D2dtf", "ihmsf[1]")
viv(t, ihmsf[2], 60, "D2dtf", "ihmsf[2]")
viv(t, ihmsf[3], 13599, "D2dtf", "ihmsf[3]")
viv(t, j, 0, "D2dtf", "")
}
func TestDat(t *testing.T) {
var j int
var deltat float64
j = gofa.Dat(2003, 6, 1, 0.0, &deltat)
vvd(t, deltat, 32.0, EPS12, "Dat", "deltat")
viv(t, j, 0, "Dat", "")
j = gofa.Dat(2008, 1, 17, 0.0, &deltat)
vvd(t, deltat, 33.0, EPS12, "Dat", "deltat")
viv(t, j, 0, "Dat", "")
j = gofa.Dat(2017, 9, 1, 0.0, &deltat)
vvd(t, deltat, 37.0, EPS12, "Dat", "deltat")
viv(t, j, 0, "Dat", "")
}
func TestDtdb(t *testing.T) {
dtdb := gofa.Dtdb(2448939.5, 0.123, 0.76543, 5.0123, 5525.242, 3190.0)
vvd(t, dtdb, -0.1280368005936998991e-2, 1e-15, "Dtdb", "")
}
func TestDtf2d(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Dtf2d("UTC", 1994, 6, 30, 23, 59, 60.13599, &u1, &u2)
vvd(t, u1+u2, 2449534.49999, 1e-6, "Dtf2d", "u")
viv(t, j, 0, "Dtf2d", "j")
}
func TestTaitt(t *testing.T) {
var t1, t2 float64
var j int
j = gofa.Taitt(2453750.5, 0.892482639, &t1, &t2)
vvd(t, t1, 2453750.5, 1e-6, "Taitt", "t1")
vvd(t, t2, 0.892855139, 1e-12, "Taitt", "t2")
viv(t, j, 0, "Taitt", "j")
}
func TestTaiut1(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Taiut1(2453750.5, 0.892482639, -32.6659, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Taiut1", "u1")
vvd(t, u2, 0.8921045614537037037, 1e-12, "Taiut1", "u2")
viv(t, j, 0, "Taiut1", "j")
}
func TestTaiutc(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Taiutc(2453750.5, 0.892482639, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Taiutc", "u1")
vvd(t, u2, 0.8921006945555555556, 1e-12, "Taiutc", "u2")
viv(t, j, 0, "Taiutc", "j")
}
func TestTcbtdb(t *testing.T) {
var b1, b2 float64
var j int
j = gofa.Tcbtdb(2453750.5, 0.893019599, &b1, &b2)
vvd(t, b1, 2453750.5, 1e-6, "Tcbtdb", "b1")
vvd(t, b2, 0.8928551362746343397, 1e-12, "Tcbtdb", "b2")
viv(t, j, 0, "Tcbtdb", "j")
}
func TestTcgtt(t *testing.T) {
var t1, t2 float64
var j int
j = gofa.Tcgtt(2453750.5, 0.892862531, &t1, &t2)
vvd(t, t1, 2453750.5, 1e-6, "Tcgtt", "t1")
vvd(t, t2, 0.8928551387488816828, 1e-12, "Tcgtt", "t2")
viv(t, j, 0, "Tcgtt", "j")
}
func TestTdbtcb(t *testing.T) {
var b1, b2 float64
var j int
j = gofa.Tdbtcb(2453750.5, 0.892855137, &b1, &b2)
vvd(t, b1, 2453750.5, 1e-6, "Tdbtcb", "b1")
vvd(t, b2, 0.8930195997253656716, 1e-12, "Tdbtcb", "b2")
viv(t, j, 0, "Tdbtcb", "j")
}
func TestTdbtt(t *testing.T) {
var t1, t2 float64
var j int
j = gofa.Tdbtt(2453750.5, 0.892855137, -0.000201, &t1, &t2)
vvd(t, t1, 2453750.5, 1e-6, "Tdbtt", "t1")
vvd(t, t2, 0.8928551393263888889, 1e-12, "Tdbtt", "t2")
viv(t, j, 0, "Tdbtt", "j")
}
func TestTttai(t *testing.T) {
var a1, a2 float64
var j int
j = gofa.Tttai(2453750.5, 0.892482639, &a1, &a2)
vvd(t, a1, 2453750.5, 1e-6, "Tttai", "a1")
vvd(t, a2, 0.892110139, 1e-12, "Tttai", "a2")
viv(t, j, 0, "Tttai", "j")
}
func TestTttcg(t *testing.T) {
var g1, g2 float64
var j int
j = gofa.Tttcg(2453750.5, 0.892482639, &g1, &g2)
vvd(t, g1, 2453750.5, 1e-6, "Tttcg", "g1")
vvd(t, g2, 0.8924900312508587113, 1e-12, "Tttcg", "g2")
viv(t, j, 0, "Tttcg", "j")
}
func TestTttdb(t *testing.T) {
var b1, b2 float64
var j int
j = gofa.Tttdb(2453750.5, 0.892855139, -0.000201, &b1, &b2)
vvd(t, b1, 2453750.5, 1e-6, "Tttdb", "b1")
vvd(t, b2, 0.8928551366736111111, 1e-12, "Tttdb", "b2")
viv(t, j, 0, "Tttdb", "j")
}
func TestTtut1(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Ttut1(2453750.5, 0.892855139, 64.8499, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Ttut1", "u1")
vvd(t, u2, 0.8921045614537037037, 1e-12, "Ttut1", "u2")
viv(t, j, 0, "Ttut1", "j")
}
func TestUt1tai(t *testing.T) {
var a1, a2 float64
var j int
j = gofa.Ut1tai(2453750.5, 0.892104561, -32.6659, &a1, &a2)
vvd(t, a1, 2453750.5, 1e-6, "Ut1tai", "a1")
vvd(t, a2, 0.8924826385462962963, 1e-12, "Ut1tai", "a2")
viv(t, j, 0, "Ut1tai", "j")
}
func TestUt1tt(t *testing.T) {
var t1, t2 float64
var j int
j = gofa.Ut1tt(2453750.5, 0.892104561, 64.8499, &t1, &t2)
vvd(t, t1, 2453750.5, 1e-6, "Ut1tt", "t1")
vvd(t, t2, 0.8928551385462962963, 1e-12, "Ut1tt", "t2")
viv(t, j, 0, "Ut1tt", "j")
}
func TestUt1utc(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Ut1utc(2453750.5, 0.892104561, 0.3341, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Ut1utc", "u1")
vvd(t, u2, 0.8921006941018518519, 1e-12, "Ut1utc", "u2")
viv(t, j, 0, "Ut1utc", "j")
}
func TestUtctai(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Utctai(2453750.5, 0.892100694, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Utctai", "u1")
vvd(t, u2, 0.8924826384444444444, 1e-12, "Utctai", "u2")
viv(t, j, 0, "Utctai", "j")
}
func TestUtcut1(t *testing.T) {
var u1, u2 float64
var j int
j = gofa.Utcut1(2453750.5, 0.892100694, 0.3341, &u1, &u2)
vvd(t, u1, 2453750.5, 1e-6, "Utcut1", "u1")
vvd(t, u2, 0.8921045608981481481, 1e-12, "Utcut1", "u2")
viv(t, j, 0, "Utcut1", "j")
}
gofa-1.19.1/test/vml_test.go 0000664 0000000 0000000 00000046010 14535740236 0015674 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa_test
import (
"testing"
"github.com/hebl/gofa"
)
func TestIr(t *testing.T) {
var r [3][3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Ir(&r)
vvd(t, r[0][0], 1.0, 0.0, "Ir", "11")
vvd(t, r[0][1], 0.0, 0.0, "Ir", "12")
vvd(t, r[0][2], 0.0, 0.0, "Ir", "13")
vvd(t, r[1][0], 0.0, 0.0, "Ir", "21")
vvd(t, r[1][1], 1.0, 0.0, "Ir", "22")
vvd(t, r[1][2], 0.0, 0.0, "Ir", "23")
vvd(t, r[2][0], 0.0, 0.0, "Ir", "31")
vvd(t, r[2][1], 0.0, 0.0, "Ir", "32")
vvd(t, r[2][2], 1.0, 0.0, "Ir", "33")
}
func TestZp(t *testing.T) {
var p [3]float64
p[0] = 0.3
p[1] = 1.2
p[2] = -2.5
gofa.Zp(&p)
vvd(t, p[0], 0.0, 0.0, "Zp", "1")
vvd(t, p[1], 0.0, 0.0, "Zp", "2")
vvd(t, p[2], 0.0, 0.0, "Zp", "3")
}
func TestZr(t *testing.T) {
var r [3][3]float64
r[0][0] = 2.0
r[1][0] = 3.0
r[2][0] = 2.0
r[0][1] = 3.0
r[1][1] = 2.0
r[2][1] = 3.0
r[0][2] = 3.0
r[1][2] = 4.0
r[2][2] = 5.0
gofa.Zr(&r)
vvd(t, r[0][0], 0.0, 0.0, "Zr", "00")
vvd(t, r[1][0], 0.0, 0.0, "Zr", "01")
vvd(t, r[2][0], 0.0, 0.0, "Zr", "02")
vvd(t, r[0][1], 0.0, 0.0, "Zr", "10")
vvd(t, r[1][1], 0.0, 0.0, "Zr", "11")
vvd(t, r[2][1], 0.0, 0.0, "Zr", "12")
vvd(t, r[0][2], 0.0, 0.0, "Zr", "20")
vvd(t, r[1][2], 0.0, 0.0, "Zr", "21")
vvd(t, r[2][2], 0.0, 0.0, "Zr", "22")
}
func TestZpv(t *testing.T) {
var pv [2][3]float64
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = -0.5
pv[1][1] = 3.1
pv[1][2] = 0.9
gofa.Zpv(&pv)
vvd(t, pv[0][0], 0.0, 0.0, "Zpv", "p1")
vvd(t, pv[0][1], 0.0, 0.0, "Zpv", "p2")
vvd(t, pv[0][2], 0.0, 0.0, "Zpv", "p3")
vvd(t, pv[1][0], 0.0, 0.0, "Zpv", "v1")
vvd(t, pv[1][1], 0.0, 0.0, "Zpv", "v2")
vvd(t, pv[1][2], 0.0, 0.0, "Zpv", "v3")
}
func TestCp(t *testing.T) {
var p, c [3]float64
p[0] = 0.3
p[1] = 1.2
p[2] = -2.5
gofa.Cp(p, &c)
vvd(t, c[0], 0.3, 0.0, "Cp", "1")
vvd(t, c[1], 1.2, 0.0, "Cp", "2")
vvd(t, c[2], -2.5, 0.0, "Cp", "3")
}
func TestCr(t *testing.T) {
var r, c [3][3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Cr(r, &c)
vvd(t, c[0][0], 2.0, 0.0, "Cr", "11")
vvd(t, c[0][1], 3.0, 0.0, "Cr", "12")
vvd(t, c[0][2], 2.0, 0.0, "Cr", "13")
vvd(t, c[1][0], 3.0, 0.0, "Cr", "21")
vvd(t, c[1][1], 2.0, 0.0, "Cr", "22")
vvd(t, c[1][2], 3.0, 0.0, "Cr", "23")
vvd(t, c[2][0], 3.0, 0.0, "Cr", "31")
vvd(t, c[2][1], 4.0, 0.0, "Cr", "32")
vvd(t, c[2][2], 5.0, 0.0, "Cr", "33")
}
func TestCpv(t *testing.T) {
var pv, c [2][3]float64
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = -0.5
pv[1][1] = 3.1
pv[1][2] = 0.9
gofa.Cpv(pv, &c)
vvd(t, c[0][0], 0.3, 0.0, "Cpv", "p1")
vvd(t, c[0][1], 1.2, 0.0, "Cpv", "p2")
vvd(t, c[0][2], -2.5, 0.0, "Cpv", "p3")
vvd(t, c[1][0], -0.5, 0.0, "Cpv", "v1")
vvd(t, c[1][1], 3.1, 0.0, "Cpv", "v2")
vvd(t, c[1][2], 0.9, 0.0, "Cpv", "v3")
}
func TestP2pv(t *testing.T) {
var p [3]float64
var pv [2][3]float64
p[0] = 0.25
p[1] = 1.2
p[2] = 3.0
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = -0.5
pv[1][1] = 3.1
pv[1][2] = 0.9
gofa.P2pv(p, &pv)
vvd(t, pv[0][0], 0.25, 0.0, "P2pv", "p1")
vvd(t, pv[0][1], 1.2, 0.0, "P2pv", "p2")
vvd(t, pv[0][2], 3.0, 0.0, "P2pv", "p3")
vvd(t, pv[1][0], 0.0, 0.0, "P2pv", "v1")
vvd(t, pv[1][1], 0.0, 0.0, "P2pv", "v2")
vvd(t, pv[1][2], 0.0, 0.0, "P2pv", "v3")
}
func TestPv2p(t *testing.T) {
var pv [2][3]float64
var p [3]float64
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = -0.5
pv[1][1] = 3.1
pv[1][2] = 0.9
gofa.Pv2p(pv, &p)
vvd(t, p[0], 0.3, 0.0, "Pv2p", "1")
vvd(t, p[1], 1.2, 0.0, "Pv2p", "2")
vvd(t, p[2], -2.5, 0.0, "Pv2p", "3")
}
func TestRx(t *testing.T) {
var phi float64
var r [3][3]float64
phi = 0.3456789
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Rx(phi, &r)
vvd(t, r[0][0], 2.0, 0.0, "Rx", "11")
vvd(t, r[0][1], 3.0, 0.0, "Rx", "12")
vvd(t, r[0][2], 2.0, 0.0, "Rx", "13")
vvd(t, r[1][0], 3.839043388235612460, 1e-12, "Rx", "21")
vvd(t, r[1][1], 3.237033249594111899, 1e-12, "Rx", "22")
vvd(t, r[1][2], 4.516714379005982719, 1e-12, "Rx", "23")
vvd(t, r[2][0], 1.806030415924501684, 1e-12, "Rx", "31")
vvd(t, r[2][1], 3.085711545336372503, 1e-12, "Rx", "32")
vvd(t, r[2][2], 3.687721683977873065, 1e-12, "Rx", "33")
}
func TestRy(t *testing.T) {
var theta float64
var r [3][3]float64
theta = 0.3456789
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Ry(theta, &r)
vvd(t, r[0][0], 0.8651847818978159930, 1e-12, "Ry", "11")
vvd(t, r[0][1], 1.467194920539316554, 1e-12, "Ry", "12")
vvd(t, r[0][2], 0.1875137911274457342, 1e-12, "Ry", "13")
vvd(t, r[1][0], 3, 1e-12, "Ry", "21")
vvd(t, r[1][1], 2, 1e-12, "Ry", "22")
vvd(t, r[1][2], 3, 1e-12, "Ry", "23")
vvd(t, r[2][0], 3.500207892850427330, 1e-12, "Ry", "31")
vvd(t, r[2][1], 4.779889022262298150, 1e-12, "Ry", "32")
vvd(t, r[2][2], 5.381899160903798712, 1e-12, "Ry", "33")
}
func TestRz(t *testing.T) {
var psi float64
var r [3][3]float64
psi = 0.3456789
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Rz(psi, &r)
vvd(t, r[0][0], 2.898197754208926769, 1e-12, "Rz", "11")
vvd(t, r[0][1], 3.500207892850427330, 1e-12, "Rz", "12")
vvd(t, r[0][2], 2.898197754208926769, 1e-12, "Rz", "13")
vvd(t, r[1][0], 2.144865911309686813, 1e-12, "Rz", "21")
vvd(t, r[1][1], 0.865184781897815993, 1e-12, "Rz", "22")
vvd(t, r[1][2], 2.144865911309686813, 1e-12, "Rz", "23")
vvd(t, r[2][0], 3.0, 1e-12, "Rz", "31")
vvd(t, r[2][1], 4.0, 1e-12, "Rz", "32")
vvd(t, r[2][2], 5.0, 1e-12, "Rz", "33")
}
func TestS2c(t *testing.T) {
var c [3]float64
gofa.S2c(3.0123, -0.999, &c)
vvd(t, c[0], -0.5366267667260523906, 1e-12, "S2c", "1")
vvd(t, c[1], 0.0697711109765145365, 1e-12, "S2c", "2")
vvd(t, c[2], -0.8409302618566214041, 1e-12, "S2c", "3")
}
func TestC2s(t *testing.T) {
var p [3]float64
var theta, phi float64
p[0] = 100.0
p[1] = -50.0
p[2] = 25.0
gofa.C2s(p, &theta, &phi)
vvd(t, theta, -0.4636476090008061162, 1e-14, "C2s", "theta")
vvd(t, phi, 0.2199879773954594463, 1e-14, "C2s", "phi")
}
func TestP2s(t *testing.T) {
var p [3]float64
var theta, phi, r float64
p[0] = 100.0
p[1] = -50.0
p[2] = 25.0
gofa.P2s(p, &theta, &phi, &r)
vvd(t, theta, -0.4636476090008061162, 1e-12, "P2s", "theta")
vvd(t, phi, 0.2199879773954594463, 1e-12, "P2s", "phi")
vvd(t, r, 114.5643923738960002, 1e-9, "P2s", "r")
}
func TestS2p(t *testing.T) {
var p [3]float64
gofa.S2p(-3.21, 0.123, 0.456, &p)
vvd(t, p[0], -0.4514964673880165228, 1e-12, "S2p", "x")
vvd(t, p[1], 0.0309339427734258688, 1e-12, "S2p", "y")
vvd(t, p[2], 0.0559466810510877933, 1e-12, "S2p", "z")
}
func TestS2pv(t *testing.T) {
var pv [2][3]float64
gofa.S2pv(-3.21, 0.123, 0.456, -7.8e-6, 9.01e-6, -1.23e-5, &pv)
vvd(t, pv[0][0], -0.4514964673880165228, 1e-12, "S2pv", "x")
vvd(t, pv[0][1], 0.0309339427734258688, 1e-12, "S2pv", "y")
vvd(t, pv[0][2], 0.0559466810510877933, 1e-12, "S2pv", "z")
vvd(t, pv[1][0], 0.1292270850663260170e-4, 1e-16, "S2pv", "vx")
vvd(t, pv[1][1], 0.2652814182060691422e-5, 1e-16, "S2pv", "vy")
vvd(t, pv[1][2], 0.2568431853930292259e-5, 1e-16, "S2pv", "vz")
}
func TestPv2s(t *testing.T) {
var pv [2][3]float64
var theta, phi, r, td, pd, rd float64
pv[0][0] = -0.4514964673880165
pv[0][1] = 0.03093394277342585
pv[0][2] = 0.05594668105108779
pv[1][0] = 1.292270850663260e-5
pv[1][1] = 2.652814182060692e-6
pv[1][2] = 2.568431853930293e-6
gofa.Pv2s(pv, &theta, &phi, &r, &td, &pd, &rd)
vvd(t, theta, 3.073185307179586515, 1e-12, "Pv2s", "theta")
vvd(t, phi, 0.1229999999999999992, 1e-12, "Pv2s", "phi")
vvd(t, r, 0.4559999999999999757, 1e-12, "Pv2s", "r")
vvd(t, td, -0.7800000000000000364e-5, 1e-16, "Pv2s", "td")
vvd(t, pd, 0.9010000000000001639e-5, 1e-16, "Pv2s", "pd")
vvd(t, rd, -0.1229999999999999832e-4, 1e-16, "Pv2s", "rd")
}
func TestPpp(t *testing.T) {
var a, b, apb [3]float64
a[0] = 2.0
a[1] = 2.0
a[2] = 3.0
b[0] = 1.0
b[1] = 3.0
b[2] = 4.0
gofa.Ppp(a, b, &apb)
vvd(t, apb[0], 3.0, 1e-12, "Ppp", "0")
vvd(t, apb[1], 5.0, 1e-12, "Ppp", "1")
vvd(t, apb[2], 7.0, 1e-12, "Ppp", "2")
}
func TestPmp(t *testing.T) {
var a, b, amb [3]float64
a[0] = 2.0
a[1] = 2.0
a[2] = 3.0
b[0] = 1.0
b[1] = 3.0
b[2] = 4.0
gofa.Pmp(a, b, &amb)
vvd(t, amb[0], 1.0, 1e-12, "Pmp", "0")
vvd(t, amb[1], -1.0, 1e-12, "Pmp", "1")
vvd(t, amb[2], -1.0, 1e-12, "Pmp", "2")
}
func TestPpsp(t *testing.T) {
var a, b, apsb [3]float64
var s float64
a[0] = 2.0
a[1] = 2.0
a[2] = 3.0
s = 5.0
b[0] = 1.0
b[1] = 3.0
b[2] = 4.0
gofa.Ppsp(a, s, b, &apsb)
vvd(t, apsb[0], 7.0, 1e-12, "Ppsp", "0")
vvd(t, apsb[1], 17.0, 1e-12, "Ppsp", "1")
vvd(t, apsb[2], 23.0, 1e-12, "Ppsp", "2")
}
func TestPdp(t *testing.T) {
var a, b [3]float64
var adb float64
a[0] = 2.0
a[1] = 2.0
a[2] = 3.0
b[0] = 1.0
b[1] = 3.0
b[2] = 4.0
adb = gofa.Pdp(a, b)
vvd(t, adb, 20, 1e-12, "Pdp", "")
}
func TestPxp(t *testing.T) {
var a, b, axb [3]float64
a[0] = 2.0
a[1] = 2.0
a[2] = 3.0
b[0] = 1.0
b[1] = 3.0
b[2] = 4.0
gofa.Pxp(a, b, &axb)
vvd(t, axb[0], -1.0, 1e-12, "Pxp", "1")
vvd(t, axb[1], -5.0, 1e-12, "Pxp", "2")
vvd(t, axb[2], 4.0, 1e-12, "Pxp", "3")
}
func TestPm(t *testing.T) {
var p [3]float64
var r float64
p[0] = 0.3
p[1] = 1.2
p[2] = -2.5
r = gofa.Pm(p)
vvd(t, r, 2.789265136196270604, 1e-12, "Pm", "")
}
func TestPn(t *testing.T) {
var p, u [3]float64
var r float64
p[0] = 0.3
p[1] = 1.2
p[2] = -2.5
gofa.Pn(p, &r, &u)
vvd(t, r, 2.789265136196270604, 1e-12, "Pn", "r")
vvd(t, u[0], 0.1075552109073112058, 1e-12, "Pn", "u1")
vvd(t, u[1], 0.4302208436292448232, 1e-12, "Pn", "u2")
vvd(t, u[2], -0.8962934242275933816, 1e-12, "Pn", "u3")
}
func TestSxp(t *testing.T) {
var s float64
var p, sp [3]float64
s = 2.0
p[0] = 0.3
p[1] = 1.2
p[2] = -2.5
gofa.Sxp(s, p, &sp)
vvd(t, sp[0], 0.6, 0.0, "Sxp", "1")
vvd(t, sp[1], 2.4, 0.0, "Sxp", "2")
vvd(t, sp[2], -5.0, 0.0, "Sxp", "3")
}
func TestPvppv(t *testing.T) {
var a, b, apb [2][3]float64
a[0][0] = 2.0
a[0][1] = 2.0
a[0][2] = 3.0
a[1][0] = 5.0
a[1][1] = 6.0
a[1][2] = 3.0
b[0][0] = 1.0
b[0][1] = 3.0
b[0][2] = 4.0
b[1][0] = 3.0
b[1][1] = 2.0
b[1][2] = 1.0
gofa.Pvppv(a, b, &apb)
vvd(t, apb[0][0], 3.0, 1e-12, "Pvppv", "p1")
vvd(t, apb[0][1], 5.0, 1e-12, "Pvppv", "p2")
vvd(t, apb[0][2], 7.0, 1e-12, "Pvppv", "p3")
vvd(t, apb[1][0], 8.0, 1e-12, "Pvppv", "v1")
vvd(t, apb[1][1], 8.0, 1e-12, "Pvppv", "v2")
vvd(t, apb[1][2], 4.0, 1e-12, "Pvppv", "v3")
}
func TestPvmpv(t *testing.T) {
var a, b, amb [2][3]float64
a[0][0] = 2.0
a[0][1] = 2.0
a[0][2] = 3.0
a[1][0] = 5.0
a[1][1] = 6.0
a[1][2] = 3.0
b[0][0] = 1.0
b[0][1] = 3.0
b[0][2] = 4.0
b[1][0] = 3.0
b[1][1] = 2.0
b[1][2] = 1.0
gofa.Pvmpv(a, b, &amb)
vvd(t, amb[0][0], 1.0, 1e-12, "Pvmpv", "11")
vvd(t, amb[0][1], -1.0, 1e-12, "Pvmpv", "21")
vvd(t, amb[0][2], -1.0, 1e-12, "Pvmpv", "31")
vvd(t, amb[1][0], 2.0, 1e-12, "Pvmpv", "12")
vvd(t, amb[1][1], 4.0, 1e-12, "Pvmpv", "22")
vvd(t, amb[1][2], 2.0, 1e-12, "Pvmpv", "32")
}
func TestPvdpv(t *testing.T) {
var a, b [2][3]float64
var adb [2]float64
a[0][0] = 2.0
a[0][1] = 2.0
a[0][2] = 3.0
a[1][0] = 6.0
a[1][1] = 0.0
a[1][2] = 4.0
b[0][0] = 1.0
b[0][1] = 3.0
b[0][2] = 4.0
b[1][0] = 0.0
b[1][1] = 2.0
b[1][2] = 8.0
gofa.Pvdpv(a, b, &adb)
vvd(t, adb[0], 20.0, 1e-12, "Pvdpv", "1")
vvd(t, adb[1], 50.0, 1e-12, "Pvdpv", "2")
}
func TestPvxpv(t *testing.T) {
var a, b, axb [2][3]float64
a[0][0] = 2.0
a[0][1] = 2.0
a[0][2] = 3.0
a[1][0] = 6.0
a[1][1] = 0.0
a[1][2] = 4.0
b[0][0] = 1.0
b[0][1] = 3.0
b[0][2] = 4.0
b[1][0] = 0.0
b[1][1] = 2.0
b[1][2] = 8.0
gofa.Pvxpv(a, b, &axb)
vvd(t, axb[0][0], -1.0, 1e-12, "Pvxpv", "p1")
vvd(t, axb[0][1], -5.0, 1e-12, "Pvxpv", "p2")
vvd(t, axb[0][2], 4.0, 1e-12, "Pvxpv", "p3")
vvd(t, axb[1][0], -2.0, 1e-12, "Pvxpv", "v1")
vvd(t, axb[1][1], -36.0, 1e-12, "Pvxpv", "v2")
vvd(t, axb[1][2], 22.0, 1e-12, "Pvxpv", "v3")
}
func TestPvm(t *testing.T) {
var pv [2][3]float64
var r, s float64
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = 0.45
pv[1][1] = -0.25
pv[1][2] = 1.1
gofa.Pvm(pv, &r, &s)
vvd(t, r, 2.789265136196270604, 1e-12, "Pvm", "r")
vvd(t, s, 1.214495780149111922, 1e-12, "Pvm", "s")
}
func TestSxpv(t *testing.T) {
var s float64
var pv, spv [2][3]float64
s = 2.0
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = 0.5
pv[1][1] = 3.2
pv[1][2] = -0.7
gofa.Sxpv(s, pv, &spv)
vvd(t, spv[0][0], 0.6, 0.0, "Sxpv", "p1")
vvd(t, spv[0][1], 2.4, 0.0, "Sxpv", "p2")
vvd(t, spv[0][2], -5.0, 0.0, "Sxpv", "p3")
vvd(t, spv[1][0], 1.0, 0.0, "Sxpv", "v1")
vvd(t, spv[1][1], 6.4, 0.0, "Sxpv", "v2")
vvd(t, spv[1][2], -1.4, 0.0, "Sxpv", "v3")
}
func TestS2xpv(t *testing.T) {
var s1, s2 float64
var pv, spv [2][3]float64
s1 = 2.0
s2 = 3.0
pv[0][0] = 0.3
pv[0][1] = 1.2
pv[0][2] = -2.5
pv[1][0] = 0.5
pv[1][1] = 2.3
pv[1][2] = -0.4
gofa.S2xpv(s1, s2, pv, &spv)
vvd(t, spv[0][0], 0.6, 1e-12, "S2xpv", "p1")
vvd(t, spv[0][1], 2.4, 1e-12, "S2xpv", "p2")
vvd(t, spv[0][2], -5.0, 1e-12, "S2xpv", "p3")
vvd(t, spv[1][0], 1.5, 1e-12, "S2xpv", "v1")
vvd(t, spv[1][1], 6.9, 1e-12, "S2xpv", "v2")
vvd(t, spv[1][2], -1.2, 1e-12, "S2xpv", "v3")
}
func TestPvu(t *testing.T) {
var pv, upv [2][3]float64
pv[0][0] = 126668.5912743160734
pv[0][1] = 2136.792716839935565
pv[0][2] = -245251.2339876830229
pv[1][0] = -0.4051854035740713039e-2
pv[1][1] = -0.6253919754866175788e-2
pv[1][2] = 0.1189353719774107615e-1
gofa.Pvu(2920.0, pv, &upv)
vvd(t, upv[0][0], 126656.7598605317105, 1e-6, "Pvu", "p1")
vvd(t, upv[0][1], 2118.531271155726332, 1e-8, "Pvu", "p2")
vvd(t, upv[0][2], -245216.5048590656190, 1e-6, "Pvu", "p3")
vvd(t, upv[1][0], -0.4051854035740713039e-2, 1e-12, "Pvu", "v1")
vvd(t, upv[1][1], -0.6253919754866175788e-2, 1e-12, "Pvu", "v2")
vvd(t, upv[1][2], 0.1189353719774107615e-1, 1e-12, "Pvu", "v3")
}
func TestPvup(t *testing.T) {
var pv [2][3]float64
var p [3]float64
pv[0][0] = 126668.5912743160734
pv[0][1] = 2136.792716839935565
pv[0][2] = -245251.2339876830229
pv[1][0] = -0.4051854035740713039e-2
pv[1][1] = -0.6253919754866175788e-2
pv[1][2] = 0.1189353719774107615e-1
gofa.Pvup(2920.0, pv, &p)
vvd(t, p[0], 126656.7598605317105, 1e-6, "Pvup", "1")
vvd(t, p[1], 2118.531271155726332, 1e-8, "Pvup", "2")
vvd(t, p[2], -245216.5048590656190, 1e-6, "Pvup", "3")
}
func TestRxr(t *testing.T) {
var a, b, atb [3][3]float64
a[0][0] = 2.0
a[0][1] = 3.0
a[0][2] = 2.0
a[1][0] = 3.0
a[1][1] = 2.0
a[1][2] = 3.0
a[2][0] = 3.0
a[2][1] = 4.0
a[2][2] = 5.0
b[0][0] = 1.0
b[0][1] = 2.0
b[0][2] = 2.0
b[1][0] = 4.0
b[1][1] = 1.0
b[1][2] = 1.0
b[2][0] = 3.0
b[2][1] = 0.0
b[2][2] = 1.0
gofa.Rxr(a, b, &atb)
vvd(t, atb[0][0], 20.0, 1e-12, "Rxr", "11")
vvd(t, atb[0][1], 7.0, 1e-12, "Rxr", "12")
vvd(t, atb[0][2], 9.0, 1e-12, "Rxr", "13")
vvd(t, atb[1][0], 20.0, 1e-12, "Rxr", "21")
vvd(t, atb[1][1], 8.0, 1e-12, "Rxr", "22")
vvd(t, atb[1][2], 11.0, 1e-12, "Rxr", "23")
vvd(t, atb[2][0], 34.0, 1e-12, "Rxr", "31")
vvd(t, atb[2][1], 10.0, 1e-12, "Rxr", "32")
vvd(t, atb[2][2], 15.0, 1e-12, "Rxr", "33")
}
func TestTr(t *testing.T) {
var r, rt [3][3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
gofa.Tr(r, &rt)
vvd(t, rt[0][0], 2.0, 0.0, "Tr", "11")
vvd(t, rt[0][1], 3.0, 0.0, "Tr", "12")
vvd(t, rt[0][2], 3.0, 0.0, "Tr", "13")
vvd(t, rt[1][0], 3.0, 0.0, "Tr", "21")
vvd(t, rt[1][1], 2.0, 0.0, "Tr", "22")
vvd(t, rt[1][2], 4.0, 0.0, "Tr", "23")
vvd(t, rt[2][0], 2.0, 0.0, "Tr", "31")
vvd(t, rt[2][1], 3.0, 0.0, "Tr", "32")
vvd(t, rt[2][2], 5.0, 0.0, "Tr", "33")
}
func TestRxp(t *testing.T) {
var r [3][3]float64
var p, rp [3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
p[0] = 0.2
p[1] = 1.5
p[2] = 0.1
gofa.Rxp(r, p, &rp)
vvd(t, rp[0], 5.1, 1e-12, "iauRxp", "1")
vvd(t, rp[1], 3.9, 1e-12, "iauRxp", "2")
vvd(t, rp[2], 7.1, 1e-12, "iauRxp", "3")
}
func TestTrxp(t *testing.T) {
var r [3][3]float64
var p, trp [3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
p[0] = 0.2
p[1] = 1.5
p[2] = 0.1
gofa.Trxp(r, p, &trp)
vvd(t, trp[0], 5.2, 1e-12, "iauTrxp", "1")
vvd(t, trp[1], 4.0, 1e-12, "iauTrxp", "2")
vvd(t, trp[2], 5.4, 1e-12, "iauTrxp", "3")
}
func TestRxpv(t *testing.T) {
var r [3][3]float64
var pv, rpv [2][3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
pv[0][0] = 0.2
pv[0][1] = 1.5
pv[0][2] = 0.1
pv[1][0] = 1.5
pv[1][1] = 0.2
pv[1][2] = 0.1
gofa.Rxpv(r, pv, &rpv)
vvd(t, rpv[0][0], 5.1, 1e-12, "iauRxpv", "11")
vvd(t, rpv[1][0], 3.8, 1e-12, "iauRxpv", "12")
vvd(t, rpv[0][1], 3.9, 1e-12, "iauRxpv", "21")
vvd(t, rpv[1][1], 5.2, 1e-12, "iauRxpv", "22")
vvd(t, rpv[0][2], 7.1, 1e-12, "iauRxpv", "31")
vvd(t, rpv[1][2], 5.8, 1e-12, "iauRxpv", "32")
}
func TestTrxpv(t *testing.T) {
var r [3][3]float64
var pv, trpv [2][3]float64
r[0][0] = 2.0
r[0][1] = 3.0
r[0][2] = 2.0
r[1][0] = 3.0
r[1][1] = 2.0
r[1][2] = 3.0
r[2][0] = 3.0
r[2][1] = 4.0
r[2][2] = 5.0
pv[0][0] = 0.2
pv[0][1] = 1.5
pv[0][2] = 0.1
pv[1][0] = 1.5
pv[1][1] = 0.2
pv[1][2] = 0.1
gofa.Trxpv(r, pv, &trpv)
vvd(t, trpv[0][0], 5.2, 1e-12, "iauTrxpv", "p1")
vvd(t, trpv[0][1], 4.0, 1e-12, "iauTrxpv", "p1")
vvd(t, trpv[0][2], 5.4, 1e-12, "iauTrxpv", "p1")
vvd(t, trpv[1][0], 3.9, 1e-12, "iauTrxpv", "v1")
vvd(t, trpv[1][1], 5.3, 1e-12, "iauTrxpv", "v2")
vvd(t, trpv[1][2], 4.1, 1e-12, "iauTrxpv", "v3")
}
func TestRv2m(t *testing.T) {
var w [3]float64
var r [3][3]float64
w[0] = 0.0
w[1] = 1.41371669
w[2] = -1.88495559
gofa.Rv2m(w, &r)
vvd(t, r[0][0], -0.7071067782221119905, 1e-14, "iauRv2m", "11")
vvd(t, r[0][1], -0.5656854276809129651, 1e-14, "iauRv2m", "12")
vvd(t, r[0][2], -0.4242640700104211225, 1e-14, "iauRv2m", "13")
vvd(t, r[1][0], 0.5656854276809129651, 1e-14, "iauRv2m", "21")
vvd(t, r[1][1], -0.0925483394532274246, 1e-14, "iauRv2m", "22")
vvd(t, r[1][2], -0.8194112531408833269, 1e-14, "iauRv2m", "23")
vvd(t, r[2][0], 0.4242640700104211225, 1e-14, "iauRv2m", "31")
vvd(t, r[2][1], -0.8194112531408833269, 1e-14, "iauRv2m", "32")
vvd(t, r[2][2], 0.3854415612311154341, 1e-14, "iauRv2m", "33")
}
func TestRm2v(t *testing.T) {
var r [3][3]float64
var w [3]float64
r[0][0] = 0.00
r[0][1] = -0.80
r[0][2] = -0.60
r[1][0] = 0.80
r[1][1] = -0.36
r[1][2] = 0.48
r[2][0] = 0.60
r[2][1] = 0.48
r[2][2] = -0.64
gofa.Rm2v(r, &w)
vvd(t, w[0], 0.0, 1e-12, "iauRm2v", "1")
vvd(t, w[1], 1.413716694115406957, 1e-12, "iauRm2v", "2")
vvd(t, w[2], -1.884955592153875943, 1e-12, "iauRm2v", "3")
}
gofa-1.19.1/ts.go 0000664 0000000 0000000 00000262647 14535740236 0013526 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
import (
"math"
"strings"
)
// SOFA Time Scale and Calendar Tools
// Time Scales (20)
/*
D2dtf Format 2-part JD for output
Format for output a 2-part Julian Date (or in the case of UTC a
quasi-JD form that includes special provision for leap seconds).
Given:
scale string time scale ID (Note 1)
ndp int resolution (Note 2)
d1,d2 float64 time as a 2-part Julian Date (Notes 3,4)
Returned:
iy,im,id int year, month, day in Gregorian calendar (Note 5)
ihmsf [4]int hours, minutes, seconds, fraction (Note 1)
Returned (function value):
int status: +1 = dubious year (Note 5)
0 = OK
-1 = unacceptable date (Note 6)
Notes:
1. scale identifies the time scale. Only the value "UTC" (in upper
case) is significant, and enables handling of leap seconds (see
Note 4).
2. ndp is the number of decimal places in the seconds field, and can
have negative as well as positive values, such as:
ndp resolution
-4 1 00 00
-3 0 10 00
-2 0 01 00
-1 0 00 10
0 0 00 01
1 0 00 00.1
2 0 00 00.01
3 0 00 00.001
The limits are platform dependent, but a safe range is -5 to +9.
3. d1+d2 is Julian Date, apportioned in any convenient way between
the two arguments, for example where d1 is the Julian Day Number
and d2 is the fraction of a day. In the case of UTC, where the
use of JD is problematical, special conventions apply: see the
next note.
4. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The SOFA internal convention is that
the quasi-JD day represents UTC days whether the length is 86399,
86400 or 86401 SI seconds. In the 1960-1972 era there were
smaller jumps (in either direction) each time the linear UTC(TAI)
expression was changed, and these "mini-leaps" are also included
in the SOFA convention.
5. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
6. For calendar conventions and limitations, see Cal2jd.
Called:
Jd2cal JD to Gregorian calendar
D2tf decompose days to hms
Dat delta(AT) = TAI-UTC
*/
func D2dtf(scale string, ndp int, d1, d2 float64, iy, im, id *int, ihmsf *[4]int) int {
var leap bool
var s byte
var iy1, im1, id1, js, iy2, im2, id2, i int
var ihmsf1 [4]int
var a1, b1, fd, dat0, dat12, w, dat24, dleap float64
/* The two-part JD. */
a1 = d1
b1 = d2
/* Provisional calendar date. */
js = Jd2cal(a1, b1, &iy1, &im1, &id1, &fd)
if js != 0 {
return -1
}
/* Is this a leap second day? */
leap = false
//if ( ! strcmp(scale,"UTC") ) {
if strings.Compare(scale, "UTC") == 0 {
/* TAI-UTC at 0h today. */
js = Dat(iy1, im1, id1, 0.0, &dat0)
if js < 0 {
return -1
}
/* TAI-UTC at 12h today (to detect drift). */
js = Dat(iy1, im1, id1, 0.5, &dat12)
if js < 0 {
return -1
}
/* TAI-UTC at 0h tomorrow (to detect jumps). */
js = Jd2cal(a1+1.5, b1-fd, &iy2, &im2, &id2, &w)
if js != 0 {
return -1
}
js = Dat(iy2, im2, id2, 0.0, &dat24)
if js < 0 {
return -1
}
/* Any sudden change in TAI-UTC (seconds). */
dleap = dat24 - (2.0*dat12 - dat0)
/* If leap second day, scale the fraction of a day into SI. */
// leap = (math.Abs(dleap) > 0.5)
// if math.Abs(dleap) > 0.5 {
// leap = 1
// }
leap = (math.Abs(dleap) > 0.5)
if leap {
fd += fd * dleap / DAYSEC
}
}
/* Provisional time of day. */
D2tf(ndp, fd, &s, &ihmsf1)
/* Has the (rounded) time gone past 24h? */
if ihmsf1[0] > 23 {
/* Yes. We probably need tomorrow's calendar date. */
js = Jd2cal(a1+1.5, b1-fd, &iy2, &im2, &id2, &w)
if js != 0 {
return -1
}
/* Is today a leap second day? */
if !leap {
/* No. Use 0h tomorrow. */
iy1 = iy2
im1 = im2
id1 = id2
ihmsf1[0] = 0
ihmsf1[1] = 0
ihmsf1[2] = 0
} else {
/* Yes. Are we past the leap second itself? */
if ihmsf1[2] > 0 {
/* Yes. Use tomorrow but allow for the leap second. */
iy1 = iy2
im1 = im2
id1 = id2
ihmsf1[0] = 0
ihmsf1[1] = 0
ihmsf1[2] = 0
} else {
/* No. Use 23 59 60... today. */
ihmsf1[0] = 23
ihmsf1[1] = 59
ihmsf1[2] = 60
}
/* If rounding to 10s or coarser always go up to new day. */
if ndp < 0 && ihmsf1[2] == 60 {
iy1 = iy2
im1 = im2
id1 = id2
ihmsf1[0] = 0
ihmsf1[1] = 0
ihmsf1[2] = 0
}
}
}
/* Results. */
*iy = iy1
*im = im1
*id = id1
for i = 0; i < 4; i++ {
ihmsf[i] = ihmsf1[i]
}
/* Status. */
return js
}
/*
Dtf2d Encode time and date fields into 2-part JD
Encode date and time fields into 2-part Julian Date (or in the case
of UTC a quasi-JD form that includes special provision for leap
seconds).
Given:
scale string time scale ID (Note 1)
iy,im,id int year, month, day in Gregorian calendar (Note 2)
ihr,imn int hour, minute
sec float64 seconds
Returned:
d1,d2 float64 2-part Julian Date (Notes 3,4)
Returned (function value):
int status: +3 = both of next two
+2 = time is after end of day (Note 5)
+1 = dubious year (Note 6)
0 = OK
-1 = bad year
-2 = bad month
-3 = bad day
-4 = bad hour
-5 = bad minute
-6 = bad second (<0)
Notes:
1. scale identifies the time scale. Only the value "UTC" (in upper
case) is significant, and enables handling of leap seconds (see
Note 4).
2. For calendar conventions and limitations, see Cal2jd.
3. The sum of the results, d1+d2, is Julian Date, where normally d1
is the Julian Day Number and d2 is the fraction of a day. In the
case of UTC, where the use of JD is problematical, special
conventions apply: see the next note.
4. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The SOFA internal convention is that
the quasi-JD day represents UTC days whether the length is 86399,
86400 or 86401 SI seconds. In the 1960-1972 era there were
smaller jumps (in either direction) each time the linear UTC(TAI)
expression was changed, and these "mini-leaps" are also included
in the SOFA convention.
5. The warning status "time is after end of day" usually means that
the sec argument is greater than 60.0. However, in a day ending
in a leap second the limit changes to 61.0 (or 59.0 in the case
of a negative leap second).
6. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
7. Only in the case of continuous and regular time scales (TAI, TT,
TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly
speaking. In the other cases (UT1 and UTC) the result must be
used with circumspection; in particular the difference between
two such results cannot be interpreted as a precise time
interval.
Called:
Cal2jd Gregorian calendar to JD
Dat delta(AT) = TAI-UTC
Jd2cal JD to Gregorian calendar
*/
func Dtf2d(scale string, iy, im, id, ihr, imn int, sec float64, d1, d2 *float64) int {
var js, iy2, im2, id2 int
var dj, w, day, seclim, dat0, dat12, dat24, dleap, time float64
/* Today's Julian Day Number. */
js = Cal2jd(iy, im, id, &dj, &w)
if js != 0 {
return js
}
dj += w
/* Day length and final minute length in seconds (provisional). */
day = DAYSEC
seclim = 60.0
/* Deal with the UTC leap second case. */
if strings.Compare(scale, "UTC") == 0 {
/* TAI-UTC at 0h today. */
js = Dat(iy, im, id, 0.0, &dat0)
if js < 0 {
return js
}
/* TAI-UTC at 12h today (to detect drift). */
js = Dat(iy, im, id, 0.5, &dat12)
if js < 0 {
return js
}
/* TAI-UTC at 0h tomorrow (to detect jumps). */
js = Jd2cal(dj, 1.5, &iy2, &im2, &id2, &w)
if js != 0 {
return js
}
js = Dat(iy2, im2, id2, 0.0, &dat24)
if js < 0 {
return js
}
/* Any sudden change in TAI-UTC between today and tomorrow. */
dleap = dat24 - (2.0*dat12 - dat0)
/* If leap second day, correct the day and final minute lengths. */
day += dleap
if ihr == 23 && imn == 59 {
seclim += dleap
}
/* End of UTC-specific actions. */
}
/* Validate the time. */
if ihr >= 0 && ihr <= 23 {
if imn >= 0 && imn <= 59 {
if sec >= 0 {
if sec >= seclim {
js += 2
}
} else {
js = -6
}
} else {
js = -5
}
} else {
js = -4
}
if js < 0 {
return js
}
/* The time in days. */
time = (60.0*(float64(60*ihr+imn)) + sec) / float64(day)
/* Return the date and time. */
*d1 = dj
*d2 = time
/* Status. */
return js
}
/*
Dat Delta(AT) (=TAI-UTC) for a given UTC date
For a given UTC date, calculate Delta(AT) = TAI-UTC.
:------------------------------------------:
: :
: IMPORTANT :
: :
: A new version of this function must be :
: produced whenever a new leap second is :
: announced. There are four items to :
: change on each such occasion: :
: :
: 1) A new line must be added to the set :
: of statements that initialize the :
: array "changes". :
: :
: 2) The constant IYV must be set to the :
: current year. :
: :
: 3) The "Latest leap second" comment :
: below must be set to the new leap :
: second date. :
: :
: 4) The "This revision" comment, later, :
: must be set to the current date. :
: :
: Change (2) must also be carried out :
: whenever the function is re-issued, :
: even if no leap seconds have been :
: added. :
: :
: Latest leap second: 2016 December 31 :
: :
:__________________________________________:
Given:
iy int UTC: year (Notes 1 and 2)
im int month (Note 2)
id int day (Notes 2 and 3)
fd float64 fraction of day (Note 4)
Returned:
deltat float64 TAI minus UTC, seconds
Returned (function value):
int status (Note 5):
1 = dubious year (Note 1)
0 = OK
-1 = bad year
-2 = bad month
-3 = bad day (Note 3)
-4 = bad fraction (Note 4)
-5 = internal error (Note 5)
Notes:
1. UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
to call the function with an earlier date. If this is attempted,
zero is returned together with a warning status.
Because leap seconds cannot, in principle, be predicted in
advance, a reliable check for dates beyond the valid range is
impossible. To guard against gross errors, a year five or more
after the release year of the present function (see the constant
IYV) is considered dubious. In this case a warning status is
returned but the result is computed in the normal way.
For both too-early and too-late years, the warning status is +1.
This is distinct from the error status -1, which signifies a year
so early that JD could not be computed.
2. If the specified date is for a day which ends with a leap second,
the TAI-UTC value returned is for the period leading up to the
leap second. If the date is for a day which begins as a leap
second ends, the TAI-UTC returned is for the period following the
leap second.
3. The day number must be in the normal calendar range, for example
1 through 30 for April. The "almanac" convention of allowing
such dates as January 0 and December 32 is not supported in this
function, in order to avoid confusion near leap seconds.
4. The fraction of day is used only for dates before the
introduction of leap seconds, the first of which occurred at the
end of 1971. It is tested for validity (0 to 1 is the valid
range) even if not used; if invalid, zero is used and status -4
is returned. For many applications, setting fd to zero is
acceptable; the resulting error is always less than 3 ms (and
occurs only pre-1972).
5. The status value returned in the case where there are multiple
errors refers to the first error detected. For example, if the
month and day are 13 and 32 respectively, status -2 (bad month)
will be returned. The "internal error" status refers to a
case that is impossible but causes some compilers to issue a
warning.
6. In cases where a valid result is not available, zero is returned.
References:
1. For dates from 1961 January 1 onwards, the expressions from the
file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
2. The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of
the 1992 Explanatory Supplement.
Called:
Cal2jd Gregorian calendar to JD
*/
func Dat(iy, im, id int, fd float64, deltat *float64) int {
/* Release year for this version of Dat */
const IYV = 2023
/* Reference dates (MJD) and drift rates (s/day), pre leap seconds */
drift := [...][2]float64{
{37300.0, 0.0012960},
{37300.0, 0.0012960},
{37300.0, 0.0012960},
{37665.0, 0.0011232},
{37665.0, 0.0011232},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{38761.0, 0.0012960},
{39126.0, 0.0025920},
{39126.0, 0.0025920},
}
/* Number of Delta(AT) expressions before leap seconds were introduced */
// enum { NERA1 = (int) (sizeof drift / sizeof (double) / 2) };
NERA1 := len(drift)
/* Dates and Delta(AT)s */
changes := [...]struct {
iyear int
month int
delat float64
}{
{1960, 1, 1.4178180},
{1961, 1, 1.4228180},
{1961, 8, 1.3728180},
{1962, 1, 1.8458580},
{1963, 11, 1.9458580},
{1964, 1, 3.2401300},
{1964, 4, 3.3401300},
{1964, 9, 3.4401300},
{1965, 1, 3.5401300},
{1965, 3, 3.6401300},
{1965, 7, 3.7401300},
{1965, 9, 3.8401300},
{1966, 1, 4.3131700},
{1968, 2, 4.2131700},
{1972, 1, 10.0},
{1972, 7, 11.0},
{1973, 1, 12.0},
{1974, 1, 13.0},
{1975, 1, 14.0},
{1976, 1, 15.0},
{1977, 1, 16.0},
{1978, 1, 17.0},
{1979, 1, 18.0},
{1980, 1, 19.0},
{1981, 7, 20.0},
{1982, 7, 21.0},
{1983, 7, 22.0},
{1985, 7, 23.0},
{1988, 1, 24.0},
{1990, 1, 25.0},
{1991, 1, 26.0},
{1992, 7, 27.0},
{1993, 7, 28.0},
{1994, 7, 29.0},
{1996, 1, 30.0},
{1997, 7, 31.0},
{1999, 1, 32.0},
{2006, 1, 33.0},
{2009, 1, 34.0},
{2012, 7, 35.0},
{2015, 7, 36.0},
{2017, 1, 37.0},
}
/* Number of Delta(AT) changes */
// enum { NDAT = (int) (sizeof changes / sizeof changes[0]) };
NDAT := len(changes)
/* Miscellaneous local variables */
var j, i, m int
var da, djm0, djm float64
/* Initialize the result to zero. */
// *deltat = da = 0.0;
*deltat = 0.0
// da = 0.0
/* If invalid fraction of a day, set error status and give up. */
if fd < 0.0 || fd > 1.0 {
return -4
}
/* Convert the date into an MJD. */
j = Cal2jd(iy, im, id, &djm0, &djm)
/* If invalid year, month, or day, give up. */
if j < 0 {
return j
}
/* If pre-UTC year, set warning status and give up. */
if iy < changes[0].iyear {
return 1
}
/* If suspiciously late year, set warning status but proceed. */
if iy > IYV+5 {
j = 1
}
/* Combine year and month to form a date-ordered integer... */
m = 12*iy + im
/* ...and use it to find the preceding table entry. */
for i = NDAT - 1; i >= 0; i-- {
if m >= (12*changes[i].iyear + changes[i].month) {
break
}
}
/* Prevent underflow warnings. */
if i < 0 {
return -5
}
/* Get the Delta(AT). */
da = changes[i].delat
/* If pre-1972, adjust for drift. */
if i < NERA1 {
da += (djm + fd - drift[i][0]) * drift[i][1]
}
/* Return the Delta(AT) value. */
*deltat = da
/* Return the status. */
return j
}
/*
Dtdb TDB-TT
An approximation to TDB-TT, the difference between barycentric
dynamical time and terrestrial time, for an observer on the Earth.
The different time scales - proper, coordinate and realized - are
related to each other:
TAI <- physically realized
:
offset <- observed (nominally +32.184s)
:
TT <- terrestrial time
:
rate adjustment (L_G) <- definition of TT
:
TCG <- time scale for GCRS
:
"periodic" terms <- Dtdb is an implementation
:
rate adjustment (L_C) <- function of solar-system ephemeris
:
TCB <- time scale for BCRS
:
rate adjustment (-L_B) <- definition of TDB
:
TDB <- TCB scaled to track TT
:
"periodic" terms <- -Dtdb is an approximation
:
TT <- terrestrial time
Adopted values for the various constants can be found in the IERS
Conventions (McCarthy & Petit 2003).
Given:
date1,date2 float64 date, TDB (Notes 1-3)
ut float64 universal time (UT1, fraction of one day)
elong float64 longitude (east positive, radians)
u float64 distance from Earth spin axis (km)
v float64 distance north of equatorial plane (km)
Returned (function value):
float64 TDB-TT (seconds)
Notes:
1. The date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments. For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable. The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution. The MJD method and the date & time methods
are both good compromises between resolution and convenience.
Although the date is, formally, barycentric dynamical time (TDB),
the terrestrial dynamical time (TT) can be used with no practical
effect on the accuracy of the prediction.
2. TT can be regarded as a coordinate time that is realized as an
offset of 32.184s from International Atomic Time, TAI. TT is a
specific linear transformation of geocentric coordinate time TCG,
which is the time scale for the Geocentric Celestial Reference
System, GCRS.
3. TDB is a coordinate time, and is a specific linear transformation
of barycentric coordinate time TCB, which is the time scale for
the Barycentric Celestial Reference System, BCRS.
4. The difference TCG-TCB depends on the masses and positions of the
bodies of the solar system and the velocity of the Earth. It is
dominated by a rate difference, the residual being of a periodic
character. The latter, which is modeled by the present function,
comprises a main (annual) sinusoidal term of amplitude
approximately 0.00166 seconds, plus planetary terms up to about
20 microseconds, and lunar and diurnal terms up to 2 microseconds.
These effects come from the changing transverse Doppler effect
and gravitational red-shift as the observer (on the Earth's
surface) experiences variations in speed (with respect to the
BCRS) and gravitational potential.
5. TDB can be regarded as the same as TCB but with a rate adjustment
to keep it close to TT, which is convenient for many applications.
The history of successive attempts to define TDB is set out in
Resolution 3 adopted by the IAU General Assembly in 2006, which
defines a fixed TDB(TCB) transformation that is consistent with
contemporary solar-system ephemerides. Future ephemerides will
imply slightly changed transformations between TCG and TCB, which
could introduce a linear drift between TDB and TT; however, any
such drift is unlikely to exceed 1 nanosecond per century.
6. The geocentric TDB-TT model used in the present function is that of
Fairhead & Bretagnon (1990), in its full form. It was originally
supplied by Fairhead (private communications with P.T.Wallace,
1990. as a Fortran subroutine. The present C function contains an
adaptation of the Fairhead code. The numerical results are
essentially unaffected by the changes, the differences with
respect to the Fairhead & Bretagnon original being at the 1e-20 s
level.
The topocentric part of the model is from Moyer (1981) and
Murray (1983), with fundamental arguments adapted from
Simon et al. 1994. It is an approximation to the expression
( v / c ) . ( r / c ), where v is the barycentric velocity of
the Earth, r is the geocentric position of the observer and
c is the speed of light.
By supplying zeroes for u and v, the topocentric part of the
model can be nullified, and the function will return the Fairhead
& Bretagnon result alone.
7. During the interval 1950-2050, the absolute accuracy is better
than +/- 3 nanoseconds relative to time ephemerides obtained by
direct numerical integrations based on the JPL DE405 solar system
ephemeris.
8. It must be stressed that the present function is merely a model,
and that numerical integration of solar-system ephemerides is the
definitive method for predicting the relationship between TCG and
TCB and hence between TT and TDB.
References:
Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
(1990).
IAU 2006 Resolution 3.
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Moyer, T.D., Cel.Mech., 23, 33 (1981).
Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
Seidelmann, P.K. et al., Explanatory Supplement to the
Astronomical Almanac, Chapter 2, University Science Books (1992).
Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).
*/
func Dtdb(date1, date2 float64, ut, elong, u, v float64) float64 {
var t, tsol, w, elsun, emsun, d, elj, els, wt, w0, w1, w2, w3, w4,
wf, wj float64
var j int
/*
=====================
Fairhead et al. model
=====================
787 sets of three coefficients.
Each set is
amplitude (microseconds)
frequency (radians per Julian millennium since J2000.0)
phase (radians)
Sets 1-474 are the T0 terms
" 475-679 " " T1
" 680-764 " " T2
" 765-784 " " T3
" 785-787 " " T4
*/
fairhd := [787][3]float64{
/* 1, 10 */
{1656.674564e-6, 6283.075849991, 6.240054195},
{22.417471e-6, 5753.384884897, 4.296977442},
{13.839792e-6, 12566.151699983, 6.196904410},
{4.770086e-6, 529.690965095, 0.444401603},
{4.676740e-6, 6069.776754553, 4.021195093},
{2.256707e-6, 213.299095438, 5.543113262},
{1.694205e-6, -3.523118349, 5.025132748},
{1.554905e-6, 77713.771467920, 5.198467090},
{1.276839e-6, 7860.419392439, 5.988822341},
{1.193379e-6, 5223.693919802, 3.649823730},
/* 11, 20 */
{1.115322e-6, 3930.209696220, 1.422745069},
{0.794185e-6, 11506.769769794, 2.322313077},
{0.447061e-6, 26.298319800, 3.615796498},
{0.435206e-6, -398.149003408, 4.349338347},
{0.600309e-6, 1577.343542448, 2.678271909},
{0.496817e-6, 6208.294251424, 5.696701824},
{0.486306e-6, 5884.926846583, 0.520007179},
{0.432392e-6, 74.781598567, 2.435898309},
{0.468597e-6, 6244.942814354, 5.866398759},
{0.375510e-6, 5507.553238667, 4.103476804},
/* 21, 30 */
{0.243085e-6, -775.522611324, 3.651837925},
{0.173435e-6, 18849.227549974, 6.153743485},
{0.230685e-6, 5856.477659115, 4.773852582},
{0.203747e-6, 12036.460734888, 4.333987818},
{0.143935e-6, -796.298006816, 5.957517795},
{0.159080e-6, 10977.078804699, 1.890075226},
{0.119979e-6, 38.133035638, 4.551585768},
{0.118971e-6, 5486.777843175, 1.914547226},
{0.116120e-6, 1059.381930189, 0.873504123},
{0.137927e-6, 11790.629088659, 1.135934669},
/* 31, 40 */
{0.098358e-6, 2544.314419883, 0.092793886},
{0.101868e-6, -5573.142801634, 5.984503847},
{0.080164e-6, 206.185548437, 2.095377709},
{0.079645e-6, 4694.002954708, 2.949233637},
{0.062617e-6, 20.775395492, 2.654394814},
{0.075019e-6, 2942.463423292, 4.980931759},
{0.064397e-6, 5746.271337896, 1.280308748},
{0.063814e-6, 5760.498431898, 4.167901731},
{0.048042e-6, 2146.165416475, 1.495846011},
{0.048373e-6, 155.420399434, 2.251573730},
/* 41, 50 */
{0.058844e-6, 426.598190876, 4.839650148},
{0.046551e-6, -0.980321068, 0.921573539},
{0.054139e-6, 17260.154654690, 3.411091093},
{0.042411e-6, 6275.962302991, 2.869567043},
{0.040184e-6, -7.113547001, 3.565975565},
{0.036564e-6, 5088.628839767, 3.324679049},
{0.040759e-6, 12352.852604545, 3.981496998},
{0.036507e-6, 801.820931124, 6.248866009},
{0.036955e-6, 3154.687084896, 5.071801441},
{0.042732e-6, 632.783739313, 5.720622217},
/* 51, 60 */
{0.042560e-6, 161000.685737473, 1.270837679},
{0.040480e-6, 15720.838784878, 2.546610123},
{0.028244e-6, -6286.598968340, 5.069663519},
{0.033477e-6, 6062.663207553, 4.144987272},
{0.034867e-6, 522.577418094, 5.210064075},
{0.032438e-6, 6076.890301554, 0.749317412},
{0.030215e-6, 7084.896781115, 3.389610345},
{0.029247e-6, -71430.695617928, 4.183178762},
{0.033529e-6, 9437.762934887, 2.404714239},
{0.032423e-6, 8827.390269875, 5.541473556},
/* 61, 70 */
{0.027567e-6, 6279.552731642, 5.040846034},
{0.029862e-6, 12139.553509107, 1.770181024},
{0.022509e-6, 10447.387839604, 1.460726241},
{0.020937e-6, 8429.241266467, 0.652303414},
{0.020322e-6, 419.484643875, 3.735430632},
{0.024816e-6, -1194.447010225, 1.087136918},
{0.025196e-6, 1748.016413067, 2.901883301},
{0.021691e-6, 14143.495242431, 5.952658009},
{0.017673e-6, 6812.766815086, 3.186129845},
{0.022567e-6, 6133.512652857, 3.307984806},
/* 71, 80 */
{0.016155e-6, 10213.285546211, 1.331103168},
{0.014751e-6, 1349.867409659, 4.308933301},
{0.015949e-6, -220.412642439, 4.005298270},
{0.015974e-6, -2352.866153772, 6.145309371},
{0.014223e-6, 17789.845619785, 2.104551349},
{0.017806e-6, 73.297125859, 3.475975097},
{0.013671e-6, -536.804512095, 5.971672571},
{0.011942e-6, 8031.092263058, 2.053414715},
{0.014318e-6, 16730.463689596, 3.016058075},
{0.012462e-6, 103.092774219, 1.737438797},
/* 81, 90 */
{0.010962e-6, 3.590428652, 2.196567739},
{0.015078e-6, 19651.048481098, 3.969480770},
{0.010396e-6, 951.718406251, 5.717799605},
{0.011707e-6, -4705.732307544, 2.654125618},
{0.010453e-6, 5863.591206116, 1.913704550},
{0.012420e-6, 4690.479836359, 4.734090399},
{0.011847e-6, 5643.178563677, 5.489005403},
{0.008610e-6, 3340.612426700, 3.661698944},
{0.011622e-6, 5120.601145584, 4.863931876},
{0.010825e-6, 553.569402842, 0.842715011},
/* 91, 100 */
{0.008666e-6, -135.065080035, 3.293406547},
{0.009963e-6, 149.563197135, 4.870690598},
{0.009858e-6, 6309.374169791, 1.061816410},
{0.007959e-6, 316.391869657, 2.465042647},
{0.010099e-6, 283.859318865, 1.942176992},
{0.007147e-6, -242.728603974, 3.661486981},
{0.007505e-6, 5230.807466803, 4.920937029},
{0.008323e-6, 11769.853693166, 1.229392026},
{0.007490e-6, -6256.777530192, 3.658444681},
{0.009370e-6, 149854.400134205, 0.673880395},
/* 101, 110 */
{0.007117e-6, 38.027672636, 5.294249518},
{0.007857e-6, 12168.002696575, 0.525733528},
{0.007019e-6, 6206.809778716, 0.837688810},
{0.006056e-6, 955.599741609, 4.194535082},
{0.008107e-6, 13367.972631107, 3.793235253},
{0.006731e-6, 5650.292110678, 5.639906583},
{0.007332e-6, 36.648562930, 0.114858677},
{0.006366e-6, 4164.311989613, 2.262081818},
{0.006858e-6, 5216.580372801, 0.642063318},
{0.006919e-6, 6681.224853400, 6.018501522},
/* 111, 120 */
{0.006826e-6, 7632.943259650, 3.458654112},
{0.005308e-6, -1592.596013633, 2.500382359},
{0.005096e-6, 11371.704689758, 2.547107806},
{0.004841e-6, 5333.900241022, 0.437078094},
{0.005582e-6, 5966.683980335, 2.246174308},
{0.006304e-6, 11926.254413669, 2.512929171},
{0.006603e-6, 23581.258177318, 5.393136889},
{0.005123e-6, -1.484472708, 2.999641028},
{0.004648e-6, 1589.072895284, 1.275847090},
{0.005119e-6, 6438.496249426, 1.486539246},
/* 121, 130 */
{0.004521e-6, 4292.330832950, 6.140635794},
{0.005680e-6, 23013.539539587, 4.557814849},
{0.005488e-6, -3.455808046, 0.090675389},
{0.004193e-6, 7234.794256242, 4.869091389},
{0.003742e-6, 7238.675591600, 4.691976180},
{0.004148e-6, -110.206321219, 3.016173439},
{0.004553e-6, 11499.656222793, 5.554998314},
{0.004892e-6, 5436.993015240, 1.475415597},
{0.004044e-6, 4732.030627343, 1.398784824},
{0.004164e-6, 12491.370101415, 5.650931916},
/* 131, 140 */
{0.004349e-6, 11513.883316794, 2.181745369},
{0.003919e-6, 12528.018664345, 5.823319737},
{0.003129e-6, 6836.645252834, 0.003844094},
{0.004080e-6, -7058.598461315, 3.690360123},
{0.003270e-6, 76.266071276, 1.517189902},
{0.002954e-6, 6283.143160294, 4.447203799},
{0.002872e-6, 28.449187468, 1.158692983},
{0.002881e-6, 735.876513532, 0.349250250},
{0.003279e-6, 5849.364112115, 4.893384368},
{0.003625e-6, 6209.778724132, 1.473760578},
/* 141, 150 */
{0.003074e-6, 949.175608970, 5.185878737},
{0.002775e-6, 9917.696874510, 1.030026325},
{0.002646e-6, 10973.555686350, 3.918259169},
{0.002575e-6, 25132.303399966, 6.109659023},
{0.003500e-6, 263.083923373, 1.892100742},
{0.002740e-6, 18319.536584880, 4.320519510},
{0.002464e-6, 202.253395174, 4.698203059},
{0.002409e-6, 2.542797281, 5.325009315},
{0.003354e-6, -90955.551694697, 1.942656623},
{0.002296e-6, 6496.374945429, 5.061810696},
/* 151, 160 */
{0.003002e-6, 6172.869528772, 2.797822767},
{0.003202e-6, 27511.467873537, 0.531673101},
{0.002954e-6, -6283.008539689, 4.533471191},
{0.002353e-6, 639.897286314, 3.734548088},
{0.002401e-6, 16200.772724501, 2.605547070},
{0.003053e-6, 233141.314403759, 3.029030662},
{0.003024e-6, 83286.914269554, 2.355556099},
{0.002863e-6, 17298.182327326, 5.240963796},
{0.002103e-6, -7079.373856808, 5.756641637},
{0.002303e-6, 83996.847317911, 2.013686814},
/* 161, 170 */
{0.002303e-6, 18073.704938650, 1.089100410},
{0.002381e-6, 63.735898303, 0.759188178},
{0.002493e-6, 6386.168624210, 0.645026535},
{0.002366e-6, 3.932153263, 6.215885448},
{0.002169e-6, 11015.106477335, 4.845297676},
{0.002397e-6, 6243.458341645, 3.809290043},
{0.002183e-6, 1162.474704408, 6.179611691},
{0.002353e-6, 6246.427287062, 4.781719760},
{0.002199e-6, -245.831646229, 5.956152284},
{0.001729e-6, 3894.181829542, 1.264976635},
/* 171, 180 */
{0.001896e-6, -3128.388765096, 4.914231596},
{0.002085e-6, 35.164090221, 1.405158503},
{0.002024e-6, 14712.317116458, 2.752035928},
{0.001737e-6, 6290.189396992, 5.280820144},
{0.002229e-6, 491.557929457, 1.571007057},
{0.001602e-6, 14314.168113050, 4.203664806},
{0.002186e-6, 454.909366527, 1.402101526},
{0.001897e-6, 22483.848574493, 4.167932508},
{0.001825e-6, -3738.761430108, 0.545828785},
{0.001894e-6, 1052.268383188, 5.817167450},
/* 181, 190 */
{0.001421e-6, 20.355319399, 2.419886601},
{0.001408e-6, 10984.192351700, 2.732084787},
{0.001847e-6, 10873.986030480, 2.903477885},
{0.001391e-6, -8635.942003763, 0.593891500},
{0.001388e-6, -7.046236698, 1.166145902},
{0.001810e-6, -88860.057071188, 0.487355242},
{0.001288e-6, -1990.745017041, 3.913022880},
{0.001297e-6, 23543.230504682, 3.063805171},
{0.001335e-6, -266.607041722, 3.995764039},
{0.001376e-6, 10969.965257698, 5.152914309},
/* 191, 200 */
{0.001745e-6, 244287.600007027, 3.626395673},
{0.001649e-6, 31441.677569757, 1.952049260},
{0.001416e-6, 9225.539273283, 4.996408389},
{0.001238e-6, 4804.209275927, 5.503379738},
{0.001472e-6, 4590.910180489, 4.164913291},
{0.001169e-6, 6040.347246017, 5.841719038},
{0.001039e-6, 5540.085789459, 2.769753519},
{0.001004e-6, -170.672870619, 0.755008103},
{0.001284e-6, 10575.406682942, 5.306538209},
{0.001278e-6, 71.812653151, 4.713486491},
/* 201, 210 */
{0.001321e-6, 18209.330263660, 2.624866359},
{0.001297e-6, 21228.392023546, 0.382603541},
{0.000954e-6, 6282.095528923, 0.882213514},
{0.001145e-6, 6058.731054289, 1.169483931},
{0.000979e-6, 5547.199336460, 5.448375984},
{0.000987e-6, -6262.300454499, 2.656486959},
{0.001070e-6, -154717.609887482, 1.827624012},
{0.000991e-6, 4701.116501708, 4.387001801},
{0.001155e-6, -14.227094002, 3.042700750},
{0.001176e-6, 277.034993741, 3.335519004},
/* 211, 220 */
{0.000890e-6, 13916.019109642, 5.601498297},
{0.000884e-6, -1551.045222648, 1.088831705},
{0.000876e-6, 5017.508371365, 3.969902609},
{0.000806e-6, 15110.466119866, 5.142876744},
{0.000773e-6, -4136.910433516, 0.022067765},
{0.001077e-6, 175.166059800, 1.844913056},
{0.000954e-6, -6284.056171060, 0.968480906},
{0.000737e-6, 5326.786694021, 4.923831588},
{0.000845e-6, -433.711737877, 4.749245231},
{0.000819e-6, 8662.240323563, 5.991247817},
/* 221, 230 */
{0.000852e-6, 199.072001436, 2.189604979},
{0.000723e-6, 17256.631536341, 6.068719637},
{0.000940e-6, 6037.244203762, 6.197428148},
{0.000885e-6, 11712.955318231, 3.280414875},
{0.000706e-6, 12559.038152982, 2.824848947},
{0.000732e-6, 2379.164473572, 2.501813417},
{0.000764e-6, -6127.655450557, 2.236346329},
{0.000908e-6, 131.541961686, 2.521257490},
{0.000907e-6, 35371.887265976, 3.370195967},
{0.000673e-6, 1066.495477190, 3.876512374},
/* 231, 240 */
{0.000814e-6, 17654.780539750, 4.627122566},
{0.000630e-6, 36.027866677, 0.156368499},
{0.000798e-6, 515.463871093, 5.151962502},
{0.000798e-6, 148.078724426, 5.909225055},
{0.000806e-6, 309.278322656, 6.054064447},
{0.000607e-6, -39.617508346, 2.839021623},
{0.000601e-6, 412.371096874, 3.984225404},
{0.000646e-6, 11403.676995575, 3.852959484},
{0.000704e-6, 13521.751441591, 2.300991267},
{0.000603e-6, -65147.619767937, 4.140083146},
/* 241, 250 */
{0.000609e-6, 10177.257679534, 0.437122327},
{0.000631e-6, 5767.611978898, 4.026532329},
{0.000576e-6, 11087.285125918, 4.760293101},
{0.000674e-6, 14945.316173554, 6.270510511},
{0.000726e-6, 5429.879468239, 6.039606892},
{0.000710e-6, 28766.924424484, 5.672617711},
{0.000647e-6, 11856.218651625, 3.397132627},
{0.000678e-6, -5481.254918868, 6.249666675},
{0.000618e-6, 22003.914634870, 2.466427018},
{0.000738e-6, 6134.997125565, 2.242668890},
/* 251, 260 */
{0.000660e-6, 625.670192312, 5.864091907},
{0.000694e-6, 3496.032826134, 2.668309141},
{0.000531e-6, 6489.261398429, 1.681888780},
{0.000611e-6, -143571.324284214, 2.424978312},
{0.000575e-6, 12043.574281889, 4.216492400},
{0.000553e-6, 12416.588502848, 4.772158039},
{0.000689e-6, 4686.889407707, 6.224271088},
{0.000495e-6, 7342.457780181, 3.817285811},
{0.000567e-6, 3634.621024518, 1.649264690},
{0.000515e-6, 18635.928454536, 3.945345892},
/* 261, 270 */
{0.000486e-6, -323.505416657, 4.061673868},
{0.000662e-6, 25158.601719765, 1.794058369},
{0.000509e-6, 846.082834751, 3.053874588},
{0.000472e-6, -12569.674818332, 5.112133338},
{0.000461e-6, 6179.983075773, 0.513669325},
{0.000641e-6, 83467.156352816, 3.210727723},
{0.000520e-6, 10344.295065386, 2.445597761},
{0.000493e-6, 18422.629359098, 1.676939306},
{0.000478e-6, 1265.567478626, 5.487314569},
{0.000472e-6, -18.159247265, 1.999707589},
/* 271, 280 */
{0.000559e-6, 11190.377900137, 5.783236356},
{0.000494e-6, 9623.688276691, 3.022645053},
{0.000463e-6, 5739.157790895, 1.411223013},
{0.000432e-6, 16858.482532933, 1.179256434},
{0.000574e-6, 72140.628666286, 1.758191830},
{0.000484e-6, 17267.268201691, 3.290589143},
{0.000550e-6, 4907.302050146, 0.864024298},
{0.000399e-6, 14.977853527, 2.094441910},
{0.000491e-6, 224.344795702, 0.878372791},
{0.000432e-6, 20426.571092422, 6.003829241},
/* 281, 290 */
{0.000481e-6, 5749.452731634, 4.309591964},
{0.000480e-6, 5757.317038160, 1.142348571},
{0.000485e-6, 6702.560493867, 0.210580917},
{0.000426e-6, 6055.549660552, 4.274476529},
{0.000480e-6, 5959.570433334, 5.031351030},
{0.000466e-6, 12562.628581634, 4.959581597},
{0.000520e-6, 39302.096962196, 4.788002889},
{0.000458e-6, 12132.439962106, 1.880103788},
{0.000470e-6, 12029.347187887, 1.405611197},
{0.000416e-6, -7477.522860216, 1.082356330},
/* 291, 300 */
{0.000449e-6, 11609.862544012, 4.179989585},
{0.000465e-6, 17253.041107690, 0.353496295},
{0.000362e-6, -4535.059436924, 1.583849576},
{0.000383e-6, 21954.157609398, 3.747376371},
{0.000389e-6, 17.252277143, 1.395753179},
{0.000331e-6, 18052.929543158, 0.566790582},
{0.000430e-6, 13517.870106233, 0.685827538},
{0.000368e-6, -5756.908003246, 0.731374317},
{0.000330e-6, 10557.594160824, 3.710043680},
{0.000332e-6, 20199.094959633, 1.652901407},
/* 301, 310 */
{0.000384e-6, 11933.367960670, 5.827781531},
{0.000387e-6, 10454.501386605, 2.541182564},
{0.000325e-6, 15671.081759407, 2.178850542},
{0.000318e-6, 138.517496871, 2.253253037},
{0.000305e-6, 9388.005909415, 0.578340206},
{0.000352e-6, 5749.861766548, 3.000297967},
{0.000311e-6, 6915.859589305, 1.693574249},
{0.000297e-6, 24072.921469776, 1.997249392},
{0.000363e-6, -640.877607382, 5.071820966},
{0.000323e-6, 12592.450019783, 1.072262823},
/* 311, 320 */
{0.000341e-6, 12146.667056108, 4.700657997},
{0.000290e-6, 9779.108676125, 1.812320441},
{0.000342e-6, 6132.028180148, 4.322238614},
{0.000329e-6, 6268.848755990, 3.033827743},
{0.000374e-6, 17996.031168222, 3.388716544},
{0.000285e-6, -533.214083444, 4.687313233},
{0.000338e-6, 6065.844601290, 0.877776108},
{0.000276e-6, 24.298513841, 0.770299429},
{0.000336e-6, -2388.894020449, 5.353796034},
{0.000290e-6, 3097.883822726, 4.075291557},
/* 321, 330 */
{0.000318e-6, 709.933048357, 5.941207518},
{0.000271e-6, 13095.842665077, 3.208912203},
{0.000331e-6, 6073.708907816, 4.007881169},
{0.000292e-6, 742.990060533, 2.714333592},
{0.000362e-6, 29088.811415985, 3.215977013},
{0.000280e-6, 12359.966151546, 0.710872502},
{0.000267e-6, 10440.274292604, 4.730108488},
{0.000262e-6, 838.969287750, 1.327720272},
{0.000250e-6, 16496.361396202, 0.898769761},
{0.000325e-6, 20597.243963041, 0.180044365},
/* 331, 340 */
{0.000268e-6, 6148.010769956, 5.152666276},
{0.000284e-6, 5636.065016677, 5.655385808},
{0.000301e-6, 6080.822454817, 2.135396205},
{0.000294e-6, -377.373607916, 3.708784168},
{0.000236e-6, 2118.763860378, 1.733578756},
{0.000234e-6, 5867.523359379, 5.575209112},
{0.000268e-6, -226858.238553767, 0.069432392},
{0.000265e-6, 167283.761587465, 4.369302826},
{0.000280e-6, 28237.233459389, 5.304829118},
{0.000292e-6, 12345.739057544, 4.096094132},
/* 341, 350 */
{0.000223e-6, 19800.945956225, 3.069327406},
{0.000301e-6, 43232.306658416, 6.205311188},
{0.000264e-6, 18875.525869774, 1.417263408},
{0.000304e-6, -1823.175188677, 3.409035232},
{0.000301e-6, 109.945688789, 0.510922054},
{0.000260e-6, 813.550283960, 2.389438934},
{0.000299e-6, 316428.228673312, 5.384595078},
{0.000211e-6, 5756.566278634, 3.789392838},
{0.000209e-6, 5750.203491159, 1.661943545},
{0.000240e-6, 12489.885628707, 5.684549045},
/* 351, 360 */
{0.000216e-6, 6303.851245484, 3.862942261},
{0.000203e-6, 1581.959348283, 5.549853589},
{0.000200e-6, 5642.198242609, 1.016115785},
{0.000197e-6, -70.849445304, 4.690702525},
{0.000227e-6, 6287.008003254, 2.911891613},
{0.000197e-6, 533.623118358, 1.048982898},
{0.000205e-6, -6279.485421340, 1.829362730},
{0.000209e-6, -10988.808157535, 2.636140084},
{0.000208e-6, -227.526189440, 4.127883842},
{0.000191e-6, 415.552490612, 4.401165650},
/* 361, 370 */
{0.000190e-6, 29296.615389579, 4.175658539},
{0.000264e-6, 66567.485864652, 4.601102551},
{0.000256e-6, -3646.350377354, 0.506364778},
{0.000188e-6, 13119.721102825, 2.032195842},
{0.000185e-6, -209.366942175, 4.694756586},
{0.000198e-6, 25934.124331089, 3.832703118},
{0.000195e-6, 4061.219215394, 3.308463427},
{0.000234e-6, 5113.487598583, 1.716090661},
{0.000188e-6, 1478.866574064, 5.686865780},
{0.000222e-6, 11823.161639450, 1.942386641},
/* 371, 380 */
{0.000181e-6, 10770.893256262, 1.999482059},
{0.000171e-6, 6546.159773364, 1.182807992},
{0.000206e-6, 70.328180442, 5.934076062},
{0.000169e-6, 20995.392966449, 2.169080622},
{0.000191e-6, 10660.686935042, 5.405515999},
{0.000228e-6, 33019.021112205, 4.656985514},
{0.000184e-6, -4933.208440333, 3.327476868},
{0.000220e-6, -135.625325010, 1.765430262},
{0.000166e-6, 23141.558382925, 3.454132746},
{0.000191e-6, 6144.558353121, 5.020393445},
/* 381, 390 */
{0.000180e-6, 6084.003848555, 0.602182191},
{0.000163e-6, 17782.732072784, 4.960593133},
{0.000225e-6, 16460.333529525, 2.596451817},
{0.000222e-6, 5905.702242076, 3.731990323},
{0.000204e-6, 227.476132789, 5.636192701},
{0.000159e-6, 16737.577236597, 3.600691544},
{0.000200e-6, 6805.653268085, 0.868220961},
{0.000187e-6, 11919.140866668, 2.629456641},
{0.000161e-6, 127.471796607, 2.862574720},
{0.000205e-6, 6286.666278643, 1.742882331},
/* 391, 400 */
{0.000189e-6, 153.778810485, 4.812372643},
{0.000168e-6, 16723.350142595, 0.027860588},
{0.000149e-6, 11720.068865232, 0.659721876},
{0.000189e-6, 5237.921013804, 5.245313000},
{0.000143e-6, 6709.674040867, 4.317625647},
{0.000146e-6, 4487.817406270, 4.815297007},
{0.000144e-6, -664.756045130, 5.381366880},
{0.000175e-6, 5127.714692584, 4.728443327},
{0.000162e-6, 6254.626662524, 1.435132069},
{0.000187e-6, 47162.516354635, 1.354371923},
/* 401, 410 */
{0.000146e-6, 11080.171578918, 3.369695406},
{0.000180e-6, -348.924420448, 2.490902145},
{0.000148e-6, 151.047669843, 3.799109588},
{0.000157e-6, 6197.248551160, 1.284375887},
{0.000167e-6, 146.594251718, 0.759969109},
{0.000133e-6, -5331.357443741, 5.409701889},
{0.000154e-6, 95.979227218, 3.366890614},
{0.000148e-6, -6418.140930027, 3.384104996},
{0.000128e-6, -6525.804453965, 3.803419985},
{0.000130e-6, 11293.470674356, 0.939039445},
/* 411, 420 */
{0.000152e-6, -5729.506447149, 0.734117523},
{0.000138e-6, 210.117701700, 2.564216078},
{0.000123e-6, 6066.595360816, 4.517099537},
{0.000140e-6, 18451.078546566, 0.642049130},
{0.000126e-6, 11300.584221356, 3.485280663},
{0.000119e-6, 10027.903195729, 3.217431161},
{0.000151e-6, 4274.518310832, 4.404359108},
{0.000117e-6, 6072.958148291, 0.366324650},
{0.000165e-6, -7668.637425143, 4.298212528},
{0.000117e-6, -6245.048177356, 5.379518958},
/* 421, 430 */
{0.000130e-6, -5888.449964932, 4.527681115},
{0.000121e-6, -543.918059096, 6.109429504},
{0.000162e-6, 9683.594581116, 5.720092446},
{0.000141e-6, 6219.339951688, 0.679068671},
{0.000118e-6, 22743.409379516, 4.881123092},
{0.000129e-6, 1692.165669502, 0.351407289},
{0.000126e-6, 5657.405657679, 5.146592349},
{0.000114e-6, 728.762966531, 0.520791814},
{0.000120e-6, 52.596639600, 0.948516300},
{0.000115e-6, 65.220371012, 3.504914846},
/* 431, 440 */
{0.000126e-6, 5881.403728234, 5.577502482},
{0.000158e-6, 163096.180360983, 2.957128968},
{0.000134e-6, 12341.806904281, 2.598576764},
{0.000151e-6, 16627.370915377, 3.985702050},
{0.000109e-6, 1368.660252845, 0.014730471},
{0.000131e-6, 6211.263196841, 0.085077024},
{0.000146e-6, 5792.741760812, 0.708426604},
{0.000146e-6, -77.750543984, 3.121576600},
{0.000107e-6, 5341.013788022, 0.288231904},
{0.000138e-6, 6281.591377283, 2.797450317},
/* 441, 450 */
{0.000113e-6, -6277.552925684, 2.788904128},
{0.000115e-6, -525.758811831, 5.895222200},
{0.000138e-6, 6016.468808270, 6.096188999},
{0.000139e-6, 23539.707386333, 2.028195445},
{0.000146e-6, -4176.041342449, 4.660008502},
{0.000107e-6, 16062.184526117, 4.066520001},
{0.000142e-6, 83783.548222473, 2.936315115},
{0.000128e-6, 9380.959672717, 3.223844306},
{0.000135e-6, 6205.325306007, 1.638054048},
{0.000101e-6, 2699.734819318, 5.481603249},
/* 451, 460 */
{0.000104e-6, -568.821874027, 2.205734493},
{0.000103e-6, 6321.103522627, 2.440421099},
{0.000119e-6, 6321.208885629, 2.547496264},
{0.000138e-6, 1975.492545856, 2.314608466},
{0.000121e-6, 137.033024162, 4.539108237},
{0.000123e-6, 19402.796952817, 4.538074405},
{0.000119e-6, 22805.735565994, 2.869040566},
{0.000133e-6, 64471.991241142, 6.056405489},
{0.000129e-6, -85.827298831, 2.540635083},
{0.000131e-6, 13613.804277336, 4.005732868},
/* 461, 470 */
{0.000104e-6, 9814.604100291, 1.959967212},
{0.000112e-6, 16097.679950283, 3.589026260},
{0.000123e-6, 2107.034507542, 1.728627253},
{0.000121e-6, 36949.230808424, 6.072332087},
{0.000108e-6, -12539.853380183, 3.716133846},
{0.000113e-6, -7875.671863624, 2.725771122},
{0.000109e-6, 4171.425536614, 4.033338079},
{0.000101e-6, 6247.911759770, 3.441347021},
{0.000113e-6, 7330.728427345, 0.656372122},
{0.000113e-6, 51092.726050855, 2.791483066},
/* 471, 480 */
{0.000106e-6, 5621.842923210, 1.815323326},
{0.000101e-6, 111.430161497, 5.711033677},
{0.000103e-6, 909.818733055, 2.812745443},
{0.000101e-6, 1790.642637886, 1.965746028},
/* T */
{102.156724e-6, 6283.075849991, 4.249032005},
{1.706807e-6, 12566.151699983, 4.205904248},
{0.269668e-6, 213.299095438, 3.400290479},
{0.265919e-6, 529.690965095, 5.836047367},
{0.210568e-6, -3.523118349, 6.262738348},
{0.077996e-6, 5223.693919802, 4.670344204},
/* 481, 490 */
{0.054764e-6, 1577.343542448, 4.534800170},
{0.059146e-6, 26.298319800, 1.083044735},
{0.034420e-6, -398.149003408, 5.980077351},
{0.032088e-6, 18849.227549974, 4.162913471},
{0.033595e-6, 5507.553238667, 5.980162321},
{0.029198e-6, 5856.477659115, 0.623811863},
{0.027764e-6, 155.420399434, 3.745318113},
{0.025190e-6, 5746.271337896, 2.980330535},
{0.022997e-6, -796.298006816, 1.174411803},
{0.024976e-6, 5760.498431898, 2.467913690},
/* 491, 500 */
{0.021774e-6, 206.185548437, 3.854787540},
{0.017925e-6, -775.522611324, 1.092065955},
{0.013794e-6, 426.598190876, 2.699831988},
{0.013276e-6, 6062.663207553, 5.845801920},
{0.011774e-6, 12036.460734888, 2.292832062},
{0.012869e-6, 6076.890301554, 5.333425680},
{0.012152e-6, 1059.381930189, 6.222874454},
{0.011081e-6, -7.113547001, 5.154724984},
{0.010143e-6, 4694.002954708, 4.044013795},
{0.009357e-6, 5486.777843175, 3.416081409},
/* 501, 510 */
{0.010084e-6, 522.577418094, 0.749320262},
{0.008587e-6, 10977.078804699, 2.777152598},
{0.008628e-6, 6275.962302991, 4.562060226},
{0.008158e-6, -220.412642439, 5.806891533},
{0.007746e-6, 2544.314419883, 1.603197066},
{0.007670e-6, 2146.165416475, 3.000200440},
{0.007098e-6, 74.781598567, 0.443725817},
{0.006180e-6, -536.804512095, 1.302642751},
{0.005818e-6, 5088.628839767, 4.827723531},
{0.004945e-6, -6286.598968340, 0.268305170},
/* 511, 520 */
{0.004774e-6, 1349.867409659, 5.808636673},
{0.004687e-6, -242.728603974, 5.154890570},
{0.006089e-6, 1748.016413067, 4.403765209},
{0.005975e-6, -1194.447010225, 2.583472591},
{0.004229e-6, 951.718406251, 0.931172179},
{0.005264e-6, 553.569402842, 2.336107252},
{0.003049e-6, 5643.178563677, 1.362634430},
{0.002974e-6, 6812.766815086, 1.583012668},
{0.003403e-6, -2352.866153772, 2.552189886},
{0.003030e-6, 419.484643875, 5.286473844},
/* 521, 530 */
{0.003210e-6, -7.046236698, 1.863796539},
{0.003058e-6, 9437.762934887, 4.226420633},
{0.002589e-6, 12352.852604545, 1.991935820},
{0.002927e-6, 5216.580372801, 2.319951253},
{0.002425e-6, 5230.807466803, 3.084752833},
{0.002656e-6, 3154.687084896, 2.487447866},
{0.002445e-6, 10447.387839604, 2.347139160},
{0.002990e-6, 4690.479836359, 6.235872050},
{0.002890e-6, 5863.591206116, 0.095197563},
{0.002498e-6, 6438.496249426, 2.994779800},
/* 531, 540 */
{0.001889e-6, 8031.092263058, 3.569003717},
{0.002567e-6, 801.820931124, 3.425611498},
{0.001803e-6, -71430.695617928, 2.192295512},
{0.001782e-6, 3.932153263, 5.180433689},
{0.001694e-6, -4705.732307544, 4.641779174},
{0.001704e-6, -1592.596013633, 3.997097652},
{0.001735e-6, 5849.364112115, 0.417558428},
{0.001643e-6, 8429.241266467, 2.180619584},
{0.001680e-6, 38.133035638, 4.164529426},
{0.002045e-6, 7084.896781115, 0.526323854},
/* 541, 550 */
{0.001458e-6, 4292.330832950, 1.356098141},
{0.001437e-6, 20.355319399, 3.895439360},
{0.001738e-6, 6279.552731642, 0.087484036},
{0.001367e-6, 14143.495242431, 3.987576591},
{0.001344e-6, 7234.794256242, 0.090454338},
{0.001438e-6, 11499.656222793, 0.974387904},
{0.001257e-6, 6836.645252834, 1.509069366},
{0.001358e-6, 11513.883316794, 0.495572260},
{0.001628e-6, 7632.943259650, 4.968445721},
{0.001169e-6, 103.092774219, 2.838496795},
/* 551, 560 */
{0.001162e-6, 4164.311989613, 3.408387778},
{0.001092e-6, 6069.776754553, 3.617942651},
{0.001008e-6, 17789.845619785, 0.286350174},
{0.001008e-6, 639.897286314, 1.610762073},
{0.000918e-6, 10213.285546211, 5.532798067},
{0.001011e-6, -6256.777530192, 0.661826484},
{0.000753e-6, 16730.463689596, 3.905030235},
{0.000737e-6, 11926.254413669, 4.641956361},
{0.000694e-6, 3340.612426700, 2.111120332},
{0.000701e-6, 3894.181829542, 2.760823491},
/* 561, 570 */
{0.000689e-6, -135.065080035, 4.768800780},
{0.000700e-6, 13367.972631107, 5.760439898},
{0.000664e-6, 6040.347246017, 1.051215840},
{0.000654e-6, 5650.292110678, 4.911332503},
{0.000788e-6, 6681.224853400, 4.699648011},
{0.000628e-6, 5333.900241022, 5.024608847},
{0.000755e-6, -110.206321219, 4.370971253},
{0.000628e-6, 6290.189396992, 3.660478857},
{0.000635e-6, 25132.303399966, 4.121051532},
{0.000534e-6, 5966.683980335, 1.173284524},
/* 571, 580 */
{0.000543e-6, -433.711737877, 0.345585464},
{0.000517e-6, -1990.745017041, 5.414571768},
{0.000504e-6, 5767.611978898, 2.328281115},
{0.000485e-6, 5753.384884897, 1.685874771},
{0.000463e-6, 7860.419392439, 5.297703006},
{0.000604e-6, 515.463871093, 0.591998446},
{0.000443e-6, 12168.002696575, 4.830881244},
{0.000570e-6, 199.072001436, 3.899190272},
{0.000465e-6, 10969.965257698, 0.476681802},
{0.000424e-6, -7079.373856808, 1.112242763},
/* 581, 590 */
{0.000427e-6, 735.876513532, 1.994214480},
{0.000478e-6, -6127.655450557, 3.778025483},
{0.000414e-6, 10973.555686350, 5.441088327},
{0.000512e-6, 1589.072895284, 0.107123853},
{0.000378e-6, 10984.192351700, 0.915087231},
{0.000402e-6, 11371.704689758, 4.107281715},
{0.000453e-6, 9917.696874510, 1.917490952},
{0.000395e-6, 149.563197135, 2.763124165},
{0.000371e-6, 5739.157790895, 3.112111866},
{0.000350e-6, 11790.629088659, 0.440639857},
/* 591, 600 */
{0.000356e-6, 6133.512652857, 5.444568842},
{0.000344e-6, 412.371096874, 5.676832684},
{0.000383e-6, 955.599741609, 5.559734846},
{0.000333e-6, 6496.374945429, 0.261537984},
{0.000340e-6, 6055.549660552, 5.975534987},
{0.000334e-6, 1066.495477190, 2.335063907},
{0.000399e-6, 11506.769769794, 5.321230910},
{0.000314e-6, 18319.536584880, 2.313312404},
{0.000424e-6, 1052.268383188, 1.211961766},
{0.000307e-6, 63.735898303, 3.169551388},
/* 601, 610 */
{0.000329e-6, 29.821438149, 6.106912080},
{0.000357e-6, 6309.374169791, 4.223760346},
{0.000312e-6, -3738.761430108, 2.180556645},
{0.000301e-6, 309.278322656, 1.499984572},
{0.000268e-6, 12043.574281889, 2.447520648},
{0.000257e-6, 12491.370101415, 3.662331761},
{0.000290e-6, 625.670192312, 1.272834584},
{0.000256e-6, 5429.879468239, 1.913426912},
{0.000339e-6, 3496.032826134, 4.165930011},
{0.000283e-6, 3930.209696220, 4.325565754},
/* 611, 620 */
{0.000241e-6, 12528.018664345, 3.832324536},
{0.000304e-6, 4686.889407707, 1.612348468},
{0.000259e-6, 16200.772724501, 3.470173146},
{0.000238e-6, 12139.553509107, 1.147977842},
{0.000236e-6, 6172.869528772, 3.776271728},
{0.000296e-6, -7058.598461315, 0.460368852},
{0.000306e-6, 10575.406682942, 0.554749016},
{0.000251e-6, 17298.182327326, 0.834332510},
{0.000290e-6, 4732.030627343, 4.759564091},
{0.000261e-6, 5884.926846583, 0.298259862},
/* 621, 630 */
{0.000249e-6, 5547.199336460, 3.749366406},
{0.000213e-6, 11712.955318231, 5.415666119},
{0.000223e-6, 4701.116501708, 2.703203558},
{0.000268e-6, -640.877607382, 0.283670793},
{0.000209e-6, 5636.065016677, 1.238477199},
{0.000193e-6, 10177.257679534, 1.943251340},
{0.000182e-6, 6283.143160294, 2.456157599},
{0.000184e-6, -227.526189440, 5.888038582},
{0.000182e-6, -6283.008539689, 0.241332086},
{0.000228e-6, -6284.056171060, 2.657323816},
/* 631, 640 */
{0.000166e-6, 7238.675591600, 5.930629110},
{0.000167e-6, 3097.883822726, 5.570955333},
{0.000159e-6, -323.505416657, 5.786670700},
{0.000154e-6, -4136.910433516, 1.517805532},
{0.000176e-6, 12029.347187887, 3.139266834},
{0.000167e-6, 12132.439962106, 3.556352289},
{0.000153e-6, 202.253395174, 1.463313961},
{0.000157e-6, 17267.268201691, 1.586837396},
{0.000142e-6, 83996.847317911, 0.022670115},
{0.000152e-6, 17260.154654690, 0.708528947},
/* 641, 650 */
{0.000144e-6, 6084.003848555, 5.187075177},
{0.000135e-6, 5756.566278634, 1.993229262},
{0.000134e-6, 5750.203491159, 3.457197134},
{0.000144e-6, 5326.786694021, 6.066193291},
{0.000160e-6, 11015.106477335, 1.710431974},
{0.000133e-6, 3634.621024518, 2.836451652},
{0.000134e-6, 18073.704938650, 5.453106665},
{0.000134e-6, 1162.474704408, 5.326898811},
{0.000128e-6, 5642.198242609, 2.511652591},
{0.000160e-6, 632.783739313, 5.628785365},
/* 651, 660 */
{0.000132e-6, 13916.019109642, 0.819294053},
{0.000122e-6, 14314.168113050, 5.677408071},
{0.000125e-6, 12359.966151546, 5.251984735},
{0.000121e-6, 5749.452731634, 2.210924603},
{0.000136e-6, -245.831646229, 1.646502367},
{0.000120e-6, 5757.317038160, 3.240883049},
{0.000134e-6, 12146.667056108, 3.059480037},
{0.000137e-6, 6206.809778716, 1.867105418},
{0.000141e-6, 17253.041107690, 2.069217456},
{0.000129e-6, -7477.522860216, 2.781469314},
/* 661, 670 */
{0.000116e-6, 5540.085789459, 4.281176991},
{0.000116e-6, 9779.108676125, 3.320925381},
{0.000129e-6, 5237.921013804, 3.497704076},
{0.000113e-6, 5959.570433334, 0.983210840},
{0.000122e-6, 6282.095528923, 2.674938860},
{0.000140e-6, -11.045700264, 4.957936982},
{0.000108e-6, 23543.230504682, 1.390113589},
{0.000106e-6, -12569.674818332, 0.429631317},
{0.000110e-6, -266.607041722, 5.501340197},
{0.000115e-6, 12559.038152982, 4.691456618},
/* 671, 680 */
{0.000134e-6, -2388.894020449, 0.577313584},
{0.000109e-6, 10440.274292604, 6.218148717},
{0.000102e-6, -543.918059096, 1.477842615},
{0.000108e-6, 21228.392023546, 2.237753948},
{0.000101e-6, -4535.059436924, 3.100492232},
{0.000103e-6, 76.266071276, 5.594294322},
{0.000104e-6, 949.175608970, 5.674287810},
{0.000101e-6, 13517.870106233, 2.196632348},
{0.000100e-6, 11933.367960670, 4.056084160},
/* T^2 */
{4.322990e-6, 6283.075849991, 2.642893748},
/* 681, 690 */
{0.406495e-6, 0.000000000, 4.712388980},
{0.122605e-6, 12566.151699983, 2.438140634},
{0.019476e-6, 213.299095438, 1.642186981},
{0.016916e-6, 529.690965095, 4.510959344},
{0.013374e-6, -3.523118349, 1.502210314},
{0.008042e-6, 26.298319800, 0.478549024},
{0.007824e-6, 155.420399434, 5.254710405},
{0.004894e-6, 5746.271337896, 4.683210850},
{0.004875e-6, 5760.498431898, 0.759507698},
{0.004416e-6, 5223.693919802, 6.028853166},
/* 691, 700 */
{0.004088e-6, -7.113547001, 0.060926389},
{0.004433e-6, 77713.771467920, 3.627734103},
{0.003277e-6, 18849.227549974, 2.327912542},
{0.002703e-6, 6062.663207553, 1.271941729},
{0.003435e-6, -775.522611324, 0.747446224},
{0.002618e-6, 6076.890301554, 3.633715689},
{0.003146e-6, 206.185548437, 5.647874613},
{0.002544e-6, 1577.343542448, 6.232904270},
{0.002218e-6, -220.412642439, 1.309509946},
{0.002197e-6, 5856.477659115, 2.407212349},
/* 701, 710 */
{0.002897e-6, 5753.384884897, 5.863842246},
{0.001766e-6, 426.598190876, 0.754113147},
{0.001738e-6, -796.298006816, 2.714942671},
{0.001695e-6, 522.577418094, 2.629369842},
{0.001584e-6, 5507.553238667, 1.341138229},
{0.001503e-6, -242.728603974, 0.377699736},
{0.001552e-6, -536.804512095, 2.904684667},
{0.001370e-6, -398.149003408, 1.265599125},
{0.001889e-6, -5573.142801634, 4.413514859},
{0.001722e-6, 6069.776754553, 2.445966339},
/* 711, 720 */
{0.001124e-6, 1059.381930189, 5.041799657},
{0.001258e-6, 553.569402842, 3.849557278},
{0.000831e-6, 951.718406251, 2.471094709},
{0.000767e-6, 4694.002954708, 5.363125422},
{0.000756e-6, 1349.867409659, 1.046195744},
{0.000775e-6, -11.045700264, 0.245548001},
{0.000597e-6, 2146.165416475, 4.543268798},
{0.000568e-6, 5216.580372801, 4.178853144},
{0.000711e-6, 1748.016413067, 5.934271972},
{0.000499e-6, 12036.460734888, 0.624434410},
/* 721, 730 */
{0.000671e-6, -1194.447010225, 4.136047594},
{0.000488e-6, 5849.364112115, 2.209679987},
{0.000621e-6, 6438.496249426, 4.518860804},
{0.000495e-6, -6286.598968340, 1.868201275},
{0.000456e-6, 5230.807466803, 1.271231591},
{0.000451e-6, 5088.628839767, 0.084060889},
{0.000435e-6, 5643.178563677, 3.324456609},
{0.000387e-6, 10977.078804699, 4.052488477},
{0.000547e-6, 161000.685737473, 2.841633844},
{0.000522e-6, 3154.687084896, 2.171979966},
/* 731, 740 */
{0.000375e-6, 5486.777843175, 4.983027306},
{0.000421e-6, 5863.591206116, 4.546432249},
{0.000439e-6, 7084.896781115, 0.522967921},
{0.000309e-6, 2544.314419883, 3.172606705},
{0.000347e-6, 4690.479836359, 1.479586566},
{0.000317e-6, 801.820931124, 3.553088096},
{0.000262e-6, 419.484643875, 0.606635550},
{0.000248e-6, 6836.645252834, 3.014082064},
{0.000245e-6, -1592.596013633, 5.519526220},
{0.000225e-6, 4292.330832950, 2.877956536},
/* 741, 750 */
{0.000214e-6, 7234.794256242, 1.605227587},
{0.000205e-6, 5767.611978898, 0.625804796},
{0.000180e-6, 10447.387839604, 3.499954526},
{0.000229e-6, 199.072001436, 5.632304604},
{0.000214e-6, 639.897286314, 5.960227667},
{0.000175e-6, -433.711737877, 2.162417992},
{0.000209e-6, 515.463871093, 2.322150893},
{0.000173e-6, 6040.347246017, 2.556183691},
{0.000184e-6, 6309.374169791, 4.732296790},
{0.000227e-6, 149854.400134205, 5.385812217},
/* 751, 760 */
{0.000154e-6, 8031.092263058, 5.120720920},
{0.000151e-6, 5739.157790895, 4.815000443},
{0.000197e-6, 7632.943259650, 0.222827271},
{0.000197e-6, 74.781598567, 3.910456770},
{0.000138e-6, 6055.549660552, 1.397484253},
{0.000149e-6, -6127.655450557, 5.333727496},
{0.000137e-6, 3894.181829542, 4.281749907},
{0.000135e-6, 9437.762934887, 5.979971885},
{0.000139e-6, -2352.866153772, 4.715630782},
{0.000142e-6, 6812.766815086, 0.513330157},
/* 761, 770 */
{0.000120e-6, -4705.732307544, 0.194160689},
{0.000131e-6, -71430.695617928, 0.000379226},
{0.000124e-6, 6279.552731642, 2.122264908},
{0.000108e-6, -6256.777530192, 0.883445696},
/* T^3 */
{0.143388e-6, 6283.075849991, 1.131453581},
{0.006671e-6, 12566.151699983, 0.775148887},
{0.001480e-6, 155.420399434, 0.480016880},
{0.000934e-6, 213.299095438, 6.144453084},
{0.000795e-6, 529.690965095, 2.941595619},
{0.000673e-6, 5746.271337896, 0.120415406},
/* 771, 780 */
{0.000672e-6, 5760.498431898, 5.317009738},
{0.000389e-6, -220.412642439, 3.090323467},
{0.000373e-6, 6062.663207553, 3.003551964},
{0.000360e-6, 6076.890301554, 1.918913041},
{0.000316e-6, -21.340641002, 5.545798121},
{0.000315e-6, -242.728603974, 1.884932563},
{0.000278e-6, 206.185548437, 1.266254859},
{0.000238e-6, -536.804512095, 4.532664830},
{0.000185e-6, 522.577418094, 4.578313856},
{0.000245e-6, 18849.227549974, 0.587467082},
/* 781, 787 */
{0.000180e-6, 426.598190876, 5.151178553},
{0.000200e-6, 553.569402842, 5.355983739},
{0.000141e-6, 5223.693919802, 1.336556009},
{0.000104e-6, 5856.477659115, 4.239842759},
/* T^4 */
{0.003826e-6, 6283.075849991, 5.705257275},
{0.000303e-6, 12566.151699983, 5.407132842},
{0.000209e-6, 155.420399434, 1.989815753},
}
/* Time since J2000.0 in Julian millennia. */
t = ((date1 - DJ00) + date2) / DJM
/* ================= */
/* Topocentric terms */
/* ================= */
/* Convert UT to local solar time in radians. */
tsol = math.Mod(ut, 1.0)*D2PI + elong
/* FUNDAMENTAL ARGUMENTS: Simon et al. 1994. */
/* Combine time argument (millennia) with deg/arcsec factor. */
w = t / 3600.0
/* Sun Mean Longitude. */
elsun = math.Mod(280.46645683+1296027711.03429*w, 360.0) * DD2R
/* Sun Mean Anomaly. */
emsun = math.Mod(357.52910918+1295965810.481*w, 360.0) * DD2R
/* Mean Elongation of Moon from Sun. */
d = math.Mod(297.85019547+16029616012.090*w, 360.0) * DD2R
/* Mean Longitude of Jupiter. */
elj = math.Mod(34.35151874+109306899.89453*w, 360.0) * DD2R
/* Mean Longitude of Saturn. */
els = math.Mod(50.07744430+44046398.47038*w, 360.0) * DD2R
/* TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983. */
wt = +0.00029e-10*u*math.Sin(tsol+elsun-els) +
+0.00100e-10*u*math.Sin(tsol-2.0*emsun) +
+0.00133e-10*u*math.Sin(tsol-d) +
+0.00133e-10*u*math.Sin(tsol+elsun-elj) +
-0.00229e-10*u*math.Sin(tsol+2.0*elsun+emsun) +
-0.02200e-10*v*math.Cos(elsun+emsun) +
+0.05312e-10*u*math.Sin(tsol-emsun) +
-0.13677e-10*u*math.Sin(tsol+2.0*elsun) +
-1.31840e-10*v*math.Cos(elsun) +
+3.17679e-10*u*math.Sin(tsol)
/* ===================== */
/* Fairhead et al. model */
/* ===================== */
/* T0 */
w0 = 0
for j = 473; j >= 0; j-- {
w0 += fairhd[j][0] * math.Sin(fairhd[j][1]*t+fairhd[j][2])
}
/* T1 */
w1 = 0
for j = 678; j >= 474; j-- {
w1 += fairhd[j][0] * math.Sin(fairhd[j][1]*t+fairhd[j][2])
}
/* T2 */
w2 = 0
for j = 763; j >= 679; j-- {
w2 += fairhd[j][0] * math.Sin(fairhd[j][1]*t+fairhd[j][2])
}
/* T3 */
w3 = 0
for j = 783; j >= 764; j-- {
w3 += fairhd[j][0] * math.Sin(fairhd[j][1]*t+fairhd[j][2])
}
/* T4 */
w4 = 0
for j = 786; j >= 784; j-- {
w4 += fairhd[j][0] * math.Sin(fairhd[j][1]*t+fairhd[j][2])
}
/* Multiply by powers of T and combine. */
wf = t*(t*(t*(t*w4+w3)+w2)+w1) + w0
/* Adjustments to use JPL planetary masses instead of IAU. */
wj = 0.00065e-6*math.Sin(6069.776754*t+4.021194) +
0.00033e-6*math.Sin(213.299095*t+5.543132) +
(-0.00196e-6 * math.Sin(6208.294251*t+5.696701)) +
(-0.00173e-6 * math.Sin(74.781599*t+2.435900)) +
0.03638e-6*t*t
/* ============ */
/* Final result */
/* ============ */
/* TDB-TT in seconds. */
w = wt + wf + wj
return w
}
/*
Taitt TAI to TT.
Time scale transformation: International Atomic Time, TAI, to
Terrestrial Time, TT.
Given:
tai1,tai2 float64 TAI as a 2-part Julian Date
Returned:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Note:
tai1+tai2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tai1 is the Julian
Day Number and tai2 is the fraction of a day. The returned
tt1,tt2 follow suit.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Taitt(tai1, tai2 float64, tt1, tt2 *float64) int {
/* TT minus TAI (days). */
const dtat = TTMTAI / DAYSEC
/* Result, safeguarding precision. */
if math.Abs(tai1) > math.Abs(tai2) {
*tt1 = tai1
*tt2 = tai2 + dtat
} else {
*tt1 = tai1 + dtat
*tt2 = tai2
}
/* Status (always OK). */
return 0
}
/*
Taiut1 TAI to UT1
Time scale transformation: International Atomic Time, TAI, to
Universal Time, UT1.
Given:
tai1,tai2 float64 TAI as a 2-part Julian Date
dta float64 UT1-TAI in seconds
Returned:
ut11,ut12 float64 UT1 as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tai1+tai2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tai1 is the Julian
Day Number and tai2 is the fraction of a day. The returned
UT11,UT12 follow suit.
2. The argument dta, i.e. UT1-TAI, is an observed quantity, and is
available from IERS tabulations.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Taiut1(tai1, tai2, dta float64, ut11, ut12 *float64) int {
var dtad float64
/* Result, safeguarding precision. */
dtad = dta / DAYSEC
if math.Abs(tai1) > math.Abs(tai2) {
*ut11 = tai1
*ut12 = tai2 + dtad
} else {
*ut11 = tai1 + dtad
*ut12 = tai2
}
/* Status (always OK). */
return 0
}
/*
Taiutc TAI to UTC
Time scale transformation: International Atomic Time, TAI, to
Coordinated Universal Time, UTC.
Given:
tai1,tai2 float64 TAI as a 2-part Julian Date (Note 1)
Returned:
utc1,utc2 float64 UTC as a 2-part quasi Julian Date (Notes 1-3)
Returned (function value):
int status: +1 = dubious year (Note 4)
0 = OK
-1 = unacceptable date
Notes:
1. tai1+tai2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tai1 is the Julian
Day Number and tai2 is the fraction of a day. The returned utc1
and utc2 form an analogous pair, except that a special convention
is used, to deal with the problem of leap seconds - see the next
note.
2. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The convention in the present
function is that the JD day represents UTC days whether the
length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era
there were smaller jumps (in either direction) each time the
linear UTC(TAI) expression was changed, and these "mini-leaps"
are also included in the SOFA convention.
3. The function D2dtf can be used to transform the UTC quasi-JD
into calendar date and clock time, including UTC leap second
handling.
4. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
Called:
Utctai UTC to TAI
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Taiutc(tai1, tai2 float64, utc1, utc2 *float64) int {
var big1 bool
var i, j int
var a1, a2, u1, u2, g1, g2 float64
/* Put the two parts of the TAI into big-first order. */
big1 = (math.Abs(tai1) >= math.Abs(tai2))
if big1 {
a1 = tai1
a2 = tai2
} else {
a1 = tai2
a2 = tai1
}
/* Initial guess for UTC. */
u1 = a1
u2 = a2
/* Iterate (though in most cases just once is enough). */
for i = 0; i < 3; i++ {
/* Guessed UTC to TAI. */
j = Utctai(u1, u2, &g1, &g2)
if j < 0 {
return j
}
/* Adjust guessed UTC. */
u2 += a1 - g1
u2 += a2 - g2
}
/* Return the UTC result, preserving the TAI order. */
if big1 {
*utc1 = u1
*utc2 = u2
} else {
*utc1 = u2
*utc2 = u1
}
/* Status. */
return j
}
/*
Tcbtdb TCB to TDB
Time scale transformation: Barycentric Coordinate Time, TCB, to
Barycentric Dynamical Time, TDB.
Given:
tcb1,tcb2 float64 TCB as a 2-part Julian Date
Returned:
tdb1,tdb2 float64 TDB as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tcb1+tcb2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tcb1 is the Julian
Day Number and tcb2 is the fraction of a day. The returned
tdb1,tdb2 follow suit.
2. The 2006 IAU General Assembly introduced a conventional linear
transformation between TDB and TCB. This transformation
compensates for the drift between TCB and terrestrial time TT,
and keeps TDB approximately centered on TT. Because the
relationship between TT and TCB depends on the adopted solar
system ephemeris, the degree of alignment between TDB and TT over
long intervals will vary according to which ephemeris is used.
Former definitions of TDB attempted to avoid this problem by
stipulating that TDB and TT should differ only by periodic
effects. This is a good description of the nature of the
relationship but eluded precise mathematical formulation. The
conventional linear relationship adopted in 2006 sidestepped
these difficulties whilst delivering a TDB that in practice was
consistent with values before that date.
3. TDB is essentially the same as Teph, the time argument for the
JPL solar system ephemerides.
Reference:
IAU 2006 Resolution B3
*/
func Tcbtdb(tcb1, tcb2 float64, tdb1, tdb2 *float64) int {
/* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
const t77td = DJM0 + DJM77
const t77tf = TTMTAI / DAYSEC
/* TDB (days) at TAI 1977 Jan 1.0 */
const tdb0 = TDB0 / DAYSEC
var d float64
/* Result, safeguarding precision. */
if math.Abs(tcb1) > math.Abs(tcb2) {
d = tcb1 - t77td
*tdb1 = tcb1
*tdb2 = tcb2 + tdb0 - (d+(tcb2-t77tf))*ELB
} else {
d = tcb2 - t77td
*tdb1 = tcb1 + tdb0 - (d+(tcb1-t77tf))*ELB
*tdb2 = tcb2
}
/* Status (always OK). */
return 0
}
/*
Tcgtt TCG to TT
Time scale transformation: Geocentric Coordinate Time, TCG, to
Terrestrial Time, TT.
Given:
tcg1,tcg2 float64 TCG as a 2-part Julian Date
Returned:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Note:
tcg1+tcg2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tcg1 is the Julian
Day Number and tcg22 is the fraction of a day. The returned
tt1,tt2 follow suit.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
IAU 2000 Resolution B1.9
*/
func Tcgtt(tcg1, tcg2 float64, tt1, tt2 *float64) int {
/* 1977 Jan 1 00:00:32.184 TT, as MJD */
const t77t = DJM77 + TTMTAI/DAYSEC
/* Result, safeguarding precision. */
if math.Abs(tcg1) > math.Abs(tcg2) {
*tt1 = tcg1
*tt2 = tcg2 - ((tcg1-DJM0)+(tcg2-t77t))*ELG
} else {
*tt1 = tcg1 - ((tcg2-DJM0)+(tcg1-t77t))*ELG
*tt2 = tcg2
}
/* OK status. */
return 0
}
/*
Tdbtcb TDB to TCB
Time scale transformation: Barycentric Dynamical Time, TDB, to
Barycentric Coordinate Time, TCB.
Given:
tdb1,tdb2 float64 TDB as a 2-part Julian Date
Returned:
tcb1,tcb2 float64 TCB as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tdb1+tdb2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tdb1 is the Julian
Day Number and tdb2 is the fraction of a day. The returned
tcb1,tcb2 follow suit.
2. The 2006 IAU General Assembly introduced a conventional linear
transformation between TDB and TCB. This transformation
compensates for the drift between TCB and terrestrial time TT,
and keeps TDB approximately centered on TT. Because the
relationship between TT and TCB depends on the adopted solar
system ephemeris, the degree of alignment between TDB and TT over
long intervals will vary according to which ephemeris is used.
Former definitions of TDB attempted to avoid this problem by
stipulating that TDB and TT should differ only by periodic
effects. This is a good description of the nature of the
relationship but eluded precise mathematical formulation. The
conventional linear relationship adopted in 2006 sidestepped
these difficulties whilst delivering a TDB that in practice was
consistent with values before that date.
3. TDB is essentially the same as Teph, the time argument for the
JPL solar system ephemerides.
Reference:
IAU 2006 Resolution B3
*/
func Tdbtcb(tdb1, tdb2 float64, tcb1, tcb2 *float64) int {
/* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
const t77td = DJM0 + DJM77
const t77tf = TTMTAI / DAYSEC
/* TDB (days) at TAI 1977 Jan 1.0 */
const tdb0 = TDB0 / DAYSEC
/* TDB to TCB rate */
const elbb = ELB / (1.0 - ELB)
var d, f float64
/* Result, preserving date format but safeguarding precision. */
if math.Abs(tdb1) > math.Abs(tdb2) {
d = t77td - tdb1
f = tdb2 - tdb0
*tcb1 = tdb1
*tcb2 = f - (d-(f-t77tf))*elbb
} else {
d = t77td - tdb2
f = tdb1 - tdb0
*tcb1 = f - (d-(f-t77tf))*elbb
*tcb2 = tdb2
}
/* Status (always OK). */
return 0
}
/*
Tdbtt TDB to TT
Time scale transformation: Barycentric Dynamical Time, TDB, to
Terrestrial Time, TT.
Given:
tdb1,tdb2 float64 TDB as a 2-part Julian Date
dtr float64 TDB-TT in seconds
Returned:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tdb1+tdb2 is Julian Date, apportioned in any convenient way
between the two arguments, for example where tdb1 is the Julian
Day Number and tdb2 is the fraction of a day. The returned
tt1,tt2 follow suit.
2. The argument dtr represents the quasi-periodic component of the
GR transformation between TT and TCB. It is dependent upon the
adopted solar-system ephemeris, and can be obtained by numerical
integration, by interrogating a precomputed time ephemeris or by
evaluating a model such as that implemented in the SOFA function
Dtdb. The quantity is dominated by an annual term of 1.7 ms
amplitude.
3. TDB is essentially the same as Teph, the time argument for the
JPL solar system ephemerides.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
IAU 2006 Resolution 3
*/
func Tdbtt(tdb1, tdb2, dtr float64, tt1, tt2 *float64) int {
var dtrd float64
/* Result, safeguarding precision. */
dtrd = dtr / DAYSEC
if math.Abs(tdb1) > math.Abs(tdb2) {
*tt1 = tdb1
*tt2 = tdb2 - dtrd
} else {
*tt1 = tdb1 - dtrd
*tt2 = tdb2
}
/* Status (always OK). */
return 0
}
/*
Tttai TT to TAI
Time scale transformation: Terrestrial Time, TT, to International
Atomic Time, TAI.
Given:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned:
tai1,tai2 float64 TAI as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Note:
tt1+tt2 is Julian Date, apportioned in any convenient way between
the two arguments, for example where tt1 is the Julian Day Number
and tt2 is the fraction of a day. The returned tai1,tai2 follow
suit.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Tttai(tt1, tt2 float64, tai1, tai2 *float64) int {
/* TT minus TAI (days). */
const dtat = TTMTAI / DAYSEC
/* Result, safeguarding precision. */
if math.Abs(tt1) > math.Abs(tt2) {
*tai1 = tt1
*tai2 = tt2 - dtat
} else {
*tai1 = tt1 - dtat
*tai2 = tt2
}
/* Status (always OK). */
return 0
}
/*
Tttcg TT to TCG
Time scale transformation: Terrestrial Time, TT, to Geocentric
Coordinate Time, TCG.
Given:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned:
tcg1,tcg2 float64 TCG as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Note:
tt1+tt2 is Julian Date, apportioned in any convenient way between
the two arguments, for example where tt1 is the Julian Day Number
and tt2 is the fraction of a day. The returned tcg1,tcg2 follow
suit.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
IAU 2000 Resolution B1.9
*/
func Tttcg(tt1, tt2 float64, tcg1, tcg2 *float64) int {
/* 1977 Jan 1 00:00:32.184 TT, as MJD */
const t77t = DJM77 + TTMTAI/DAYSEC
/* TT to TCG rate */
const elgg = ELG / (1.0 - ELG)
/* Result, safeguarding precision. */
if math.Abs(tt1) > math.Abs(tt2) {
*tcg1 = tt1
*tcg2 = tt2 + ((tt1-DJM0)+(tt2-t77t))*elgg
} else {
*tcg1 = tt1 + ((tt2-DJM0)+(tt1-t77t))*elgg
*tcg2 = tt2
}
/* Status (always OK). */
return 0
}
/*
Tttdb TT to TDB
Time scale transformation: Terrestrial Time, TT, to Barycentric
Dynamical Time, TDB.
Given:
tt1,tt2 float64 TT as a 2-part Julian Date
dtr float64 TDB-TT in seconds
Returned:
tdb1,tdb2 float64 TDB as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tt1+tt2 is Julian Date, apportioned in any convenient way between
the two arguments, for example where tt1 is the Julian Day Number
and tt2 is the fraction of a day. The returned tdb1,tdb2 follow
suit.
2. The argument dtr represents the quasi-periodic component of the
GR transformation between TT and TCB. It is dependent upon the
adopted solar-system ephemeris, and can be obtained by numerical
integration, by interrogating a precomputed time ephemeris or by
evaluating a model such as that implemented in the SOFA function
Dtdb. The quantity is dominated by an annual term of 1.7 ms
amplitude.
3. TDB is essentially the same as Teph, the time argument for the JPL
solar system ephemerides.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
IAU 2006 Resolution 3
*/
func Tttdb(tt1, tt2, dtr float64, tdb1, tdb2 *float64) int {
var dtrd float64
/* Result, safeguarding precision. */
dtrd = dtr / DAYSEC
if math.Abs(tt1) > math.Abs(tt2) {
*tdb1 = tt1
*tdb2 = tt2 + dtrd
} else {
*tdb1 = tt1 + dtrd
*tdb2 = tt2
}
/* Status (always OK). */
return 0
}
/*
Ttut1 TT to UT1
Time scale transformation: Terrestrial Time, TT, to Universal Time,
UT1.
Given:
tt1,tt2 float64 TT as a 2-part Julian Date
dt float64 TT-UT1 in seconds
Returned:
ut11,ut12 float64 UT1 as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. tt1+tt2 is Julian Date, apportioned in any convenient way between
the two arguments, for example where tt1 is the Julian Day Number
and tt2 is the fraction of a day. The returned ut11,ut12 follow
suit.
2. The argument dt is classical Delta T.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Ttut1(tt1, tt2, dt float64, ut11, ut12 *float64) int {
var dtd float64
/* Result, safeguarding precision. */
dtd = dt / DAYSEC
if math.Abs(tt1) > math.Abs(tt2) {
*ut11 = tt1
*ut12 = tt2 - dtd
} else {
*ut11 = tt1 - dtd
*ut12 = tt2
}
/* Status (always OK). */
return 0
}
/*
Ut1tai UT1 to TAI
Time scale transformation: Universal Time, UT1, to International
Atomic Time, TAI.
Given:
ut11,ut12 float64 UT1 as a 2-part Julian Date
dta float64 UT1-TAI in seconds
Returned:
tai1,tai2 float64 TAI as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. ut11+ut12 is Julian Date, apportioned in any convenient way
between the two arguments, for example where ut11 is the Julian
Day Number and ut12 is the fraction of a day. The returned
tai1,tai2 follow suit.
2. The argument dta, i.e. UT1-TAI, is an observed quantity, and is
available from IERS tabulations.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Ut1tai(ut11, ut12, dta float64, tai1, tai2 *float64) int {
var dtad float64
/* Result, safeguarding precision. */
dtad = dta / DAYSEC
if math.Abs(ut11) > math.Abs(ut12) {
*tai1 = ut11
*tai2 = ut12 - dtad
} else {
*tai1 = ut11 - dtad
*tai2 = ut12
}
/* Status (always OK). */
return 0
}
/*
Ut1tt UT1 to TT
Time scale transformation: Universal Time, UT1, to Terrestrial
Time, TT.
Given:
ut11,ut12 float64 UT1 as a 2-part Julian Date
dt float64 TT-UT1 in seconds
Returned:
tt1,tt2 float64 TT as a 2-part Julian Date
Returned (function value):
int status: 0 = OK
Notes:
1. ut11+ut12 is Julian Date, apportioned in any convenient way
between the two arguments, for example where ut11 is the Julian
Day Number and ut12 is the fraction of a day. The returned
tt1,tt2 follow suit.
2. The argument dt is classical Delta T.
Reference:
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Ut1tt(ut11, ut12, dt float64, tt1, tt2 *float64) int {
var dtd float64
/* Result, safeguarding precision. */
dtd = dt / DAYSEC
if math.Abs(ut11) > math.Abs(ut12) {
*tt1 = ut11
*tt2 = ut12 + dtd
} else {
*tt1 = ut11 + dtd
*tt2 = ut12
}
/* Status (always OK). */
return 0
}
/*
Ut1utc UT1 to UTC
Time scale transformation: Universal Time, UT1, to Coordinated
Universal Time, UTC.
Given:
ut11,ut12 float64 UT1 as a 2-part Julian Date (Note 1)
dut1 float64 Delta UT1: UT1-UTC in seconds (Note 2)
Returned:
utc1,utc2 float64 UTC as a 2-part quasi Julian Date (Notes 3,4)
Returned (function value):
int status: +1 = dubious year (Note 5)
0 = OK
-1 = unacceptable date
Notes:
1. ut11+ut12 is Julian Date, apportioned in any convenient way
between the two arguments, for example where ut11 is the Julian
Day Number and ut12 is the fraction of a day. The returned utc1
and utc2 form an analogous pair, except that a special convention
is used, to deal with the problem of leap seconds - see Note 3.
2. Delta UT1 can be obtained from tabulations provided by the
International Earth Rotation and Reference Systems Service. The
value changes abruptly by 1s at a leap second; however, close to
a leap second the algorithm used here is tolerant of the "wrong"
choice of value being made.
3. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The convention in the present
function is that the returned quasi-JD UTC1+UTC2 represents UTC
days whether the length is 86399, 86400 or 86401 SI seconds.
4. The function D2dtf can be used to transform the UTC quasi-JD
into calendar date and clock time, including UTC leap second
handling.
5. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
Called:
Jd2cal JD to Gregorian calendar
Dat delta(AT) = TAI-UTC
Cal2jd Gregorian calendar to JD
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Ut1utc(ut11, ut12, dut1 float64, utc1, utc2 *float64) int {
var big1 bool
var i, iy, im, id, js int
var duts, u1, u2, d1, dats1, d2, fd, dats2, ddats, us1, us2, du float64
/* UT1-UTC in seconds. */
duts = dut1
/* Put the two parts of the UT1 into big-first order. */
big1 = (math.Abs(ut11) >= math.Abs(ut12))
if big1 {
u1 = ut11
u2 = ut12
} else {
u1 = ut12
u2 = ut11
}
/* See if the UT1 can possibly be in a leap-second day. */
d1 = u1
dats1 = 0
for i = -1; i <= 3; i++ {
d2 = u2 + float64(i)
if Jd2cal(d1, d2, &iy, &im, &id, &fd) != 0 {
return -1
}
js = Dat(iy, im, id, 0.0, &dats2)
if js < 0 {
return -1
}
if i == -1 {
dats1 = dats2
}
ddats = dats2 - dats1
if math.Abs(ddats) >= 0.5 {
/* Yes, leap second nearby: ensure UT1-UTC is "before" value. */
if ddats*duts >= 0 {
duts -= ddats
}
/* UT1 for the start of the UTC day that ends in a leap. */
if Cal2jd(iy, im, id, &d1, &d2) != 0 {
return -1
}
us1 = d1
us2 = d2 - 1.0 + duts/DAYSEC
/* Is the UT1 after this point? */
du = u1 - us1
du += u2 - us2
if du > 0 {
/* Yes: fraction of the current UTC day that has elapsed. */
fd = du * DAYSEC / (DAYSEC + ddats)
/* Ramp UT1-UTC to bring about SOFA's JD(UTC) convention. */
//duts += ddats * ( fd <= 1.0 ? fd : 1.0 );
if fd <= 1.0 {
duts += ddats * fd
} else {
duts += ddats
}
}
/* Done. */
break
}
dats1 = dats2
}
/* Subtract the (possibly adjusted) UT1-UTC from UT1 to give UTC. */
u2 -= duts / DAYSEC
/* Result, safeguarding precision. */
if big1 {
*utc1 = u1
*utc2 = u2
} else {
*utc1 = u2
*utc2 = u1
}
/* Status. */
return js
}
/*
Utctai UTC to TAI
Time scale transformation: Coordinated Universal Time, UTC, to
International Atomic Time, TAI.
Given:
utc1,utc2 float64 UTC as a 2-part quasi Julian Date (Notes 1-4)
Returned:
tai1,tai2 float64 TAI as a 2-part Julian Date (Note 5)
Returned (function value):
int status: +1 = dubious year (Note 3)
0 = OK
-1 = unacceptable date
Notes:
1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
2. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The convention in the present
function is that the JD day represents UTC days whether the
length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era
there were smaller jumps (in either direction) each time the
linear UTC(TAI) expression was changed, and these "mini-leaps"
are also included in the SOFA convention.
3. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
4. The function Dtf2d converts from calendar date and time of day
into 2-part Julian Date, and in the case of UTC implements the
leap-second-ambiguity convention described above.
5. The returned TAI1,TAI2 are such that their sum is the TAI Julian
Date.
Called:
Jd2cal JD to Gregorian calendar
Dat delta(AT) = TAI-UTC
Cal2jd Gregorian calendar to JD
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
*/
func Utctai(utc1, utc2 float64, tai1, tai2 *float64) int {
var big1 bool
var iy, im, id, j, iyt, imt, idt int
var u1, u2, fd, dat0, dat12, w, dat24, dlod, dleap, z1, z2, a2 float64
/* Put the two parts of the UTC into big-first order. */
big1 = (math.Abs(utc1) >= math.Abs(utc2))
if big1 {
u1 = utc1
u2 = utc2
} else {
u1 = utc2
u2 = utc1
}
/* Get TAI-UTC at 0h today. */
j = Jd2cal(u1, u2, &iy, &im, &id, &fd)
if j != 0 {
return j
}
j = Dat(iy, im, id, 0.0, &dat0)
if j < 0 {
return j
}
/* Get TAI-UTC at 12h today (to detect drift). */
j = Dat(iy, im, id, 0.5, &dat12)
if j < 0 {
return j
}
/* Get TAI-UTC at 0h tomorrow (to detect jumps). */
j = Jd2cal(u1+1.5, u2-fd, &iyt, &imt, &idt, &w)
if j != 0 {
return j
}
j = Dat(iyt, imt, idt, 0.0, &dat24)
if j < 0 {
return j
}
/* Separate TAI-UTC change into per-day (DLOD) and any jump (DLEAP). */
dlod = 2.0 * (dat12 - dat0)
dleap = dat24 - (dat0 + dlod)
/* Remove any scaling applied to spread leap into preceding day. */
fd *= (DAYSEC + dleap) / DAYSEC
/* Scale from (pre-1972) UTC seconds to SI seconds. */
fd *= (DAYSEC + dlod) / DAYSEC
/* Today's calendar date to 2-part JD. */
if Cal2jd(iy, im, id, &z1, &z2) != 0 {
return -1
}
/* Assemble the TAI result, preserving the UTC split and order. */
a2 = z1 - u1
a2 += z2
a2 += fd + dat0/DAYSEC
if big1 {
*tai1 = u1
*tai2 = a2
} else {
*tai1 = a2
*tai2 = u1
}
/* Status. */
return j
}
/*
Utcut1 UTC to UT1
Time scale transformation: Coordinated Universal Time, UTC, to
Universal Time, UT1.
Given:
utc1,utc2 float64 UTC as a 2-part quasi Julian Date (Notes 1-4)
dut1 float64 Delta UT1 = UT1-UTC in seconds (Note 5)
Returned:
ut11,ut12 float64 UT1 as a 2-part Julian Date (Note 6)
Returned (function value):
int status: +1 = dubious year (Note 3)
0 = OK
-1 = unacceptable date
Notes:
1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
convenient way between the two arguments, for example where utc1
is the Julian Day Number and utc2 is the fraction of a day.
2. JD cannot unambiguously represent UTC during a leap second unless
special measures are taken. The convention in the present
function is that the JD day represents UTC days whether the
length is 86399, 86400 or 86401 SI seconds.
3. The warning status "dubious year" flags UTCs that predate the
introduction of the time scale or that are too far in the future
to be trusted. See Dat for further details.
4. The function Dtf2d converts from calendar date and time of
day into 2-part Julian Date, and in the case of UTC implements
the leap-second-ambiguity convention described above.
5. Delta UT1 can be obtained from tabulations provided by the
International Earth Rotation and Reference Systems Service.
It is the caller's responsibility to supply a dut1 argument
containing the UT1-UTC value that matches the given UTC.
6. The returned ut11,ut12 are such that their sum is the UT1 Julian
Date.
References:
McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)
Explanatory Supplement to the Astronomical Almanac,
P. Kenneth Seidelmann (ed), University Science Books (1992)
Called:
Jd2cal JD to Gregorian calendar
Dat delta(AT) = TAI-UTC
Utctai UTC to TAI
Taiut1 TAI to UT1
*/
func Utcut1(utc1, utc2, dut1 float64, ut11, ut12 *float64) int {
var iy, im, id, js, jw int
var w, dat, dta, tai1, tai2 float64
/* Look up TAI-UTC. */
if Jd2cal(utc1, utc2, &iy, &im, &id, &w) != 0 {
return -1
}
js = Dat(iy, im, id, 0.0, &dat)
if js < 0 {
return -1
}
/* Form UT1-TAI. */
dta = dut1 - dat
/* UTC to TAI to UT1. */
jw = Utctai(utc1, utc2, &tai1, &tai2)
if jw < 0 {
return -1
} else if jw > 0 {
js = jw
}
if Taiut1(tai1, tai2, dta, ut11, ut12) != 0 {
return -1
}
/* Status. */
return js
}
gofa-1.19.1/vml.go 0000664 0000000 0000000 00000061465 14535740236 0013671 0 ustar 00root root 0000000 0000000 // Copyright 2022 HE Boliang
// All rights reserved.
package gofa
// Vector/Matrix Library
// 1. Initialization (4)
// Operations involving p-vectors and r-matrices (3)
/*
Zp Zero a p-vector.
Returned:
p [3]float64 zero p-vector
*/
func Zp(p *[3]float64) {
p[0] = 0.0
p[1] = 0.0
p[2] = 0.0
}
/*
Zr Initialize an r-matrix to the null matrix.
Returned:
r [3][3]float64 r-matrix
*/
func Zr(r *[3][3]float64) {
r[0][0] = 0.0
r[0][1] = 0.0
r[0][2] = 0.0
r[1][0] = 0.0
r[1][1] = 0.0
r[1][2] = 0.0
r[2][0] = 0.0
r[2][1] = 0.0
r[2][2] = 0.0
}
/*
Ir Initialize an r-matrix to the identity matrix.
Returned:
r [3][3]float64 r-matrix
*/
func Ir(r *[3][3]float64) {
r[0][0] = 1.0
r[0][1] = 0.0
r[0][2] = 0.0
r[1][0] = 0.0
r[1][1] = 1.0
r[1][2] = 0.0
r[2][0] = 0.0
r[2][1] = 0.0
r[2][2] = 1.0
}
/*
Zpv Zero a pv-vector.
Returned:
pv [2][3]float64 zero pv-vector
Called:
Zp zero p-vector
*/
func Zpv(pv *[2][3]float64) {
Zp(&pv[0])
Zp(&pv[1])
}
// 2. Copy/Extend/Extract (5)
// Operations involving p-vectors and r-matrices (2)
/*
Cp Copy a p-vector.
Given:
p [3]float64 p-vector to be copied
Returned:
c [3]float64 copy
*/
func Cp(p [3]float64, c *[3]float64) {
c[0] = p[0]
c[1] = p[1]
c[2] = p[2]
}
/*
Cr Copy an r-matrix.
Given:
r [3][3]float64 r-matrix to be copied
Returned:
c [3][3]float64 copy
Called:
Cp copy p-vector
*/
func Cr(r [3][3]float64, c *[3][3]float64) {
Cp(r[0], &c[0])
Cp(r[1], &c[1])
Cp(r[2], &c[2])
}
// Operations involving pv-vectors (3)
/*
Cpv Copy a position/velocity vector.
Given:
pv [2][3]float64 position/velocity vector to be copied
Returned:
c [2][3]float64 copy
*/
func Cpv(pv [2][3]float64, c *[2][3]float64) {
Cp(pv[0], &c[0])
Cp(pv[1], &c[1])
}
/*
P2pv Extend a p-vector to a pv-vector by appending a zero velocity.
Given:
p [3]float64 p-vector
Returned:
pv [2][3]float64 pv-vector
Called:
Cp copy p-vector
Zp zero p-vector
*/
func P2pv(p [3]float64, pv *[2][3]float64) {
Cp(p, &pv[0])
Zp(&pv[1])
}
/*
Pv2p Discard velocity component of a pv-vector.
Given:
pv [2][3]float64 pv-vector
Returned:
p [3]float64 p-vector
Called:
Cp copy p-vector
*/
func Pv2p(pv [2][3]float64, p *[3]float64) {
Cp(pv[0], p)
}
// 3. Build Rotations (3)
/*
Rx Rotate an r-matrix about the x-axis.
Given:
phi float64 angle (radians)
Given and returned:
r [3][3]float64 r-matrix, rotated
Notes:
1) Calling this function with positive phi incorporates in the
supplied r-matrix r an additional rotation, about the x-axis,
anticlockwise as seen looking towards the origin from positive x.
2) The additional rotation can be represented by this matrix:
( 1 0 0 )
( )
( 0 + cos(phi) + sin(phi) )
( )
( 0 - sin(phi) + cos(phi) )
*/
func Rx(phi float64, r *[3][3]float64) {
var s, c, a10, a11, a12, a20, a21, a22 float64
s = sin(phi)
c = cos(phi)
a10 = c*r[1][0] + s*r[2][0]
a11 = c*r[1][1] + s*r[2][1]
a12 = c*r[1][2] + s*r[2][2]
a20 = -s*r[1][0] + c*r[2][0]
a21 = -s*r[1][1] + c*r[2][1]
a22 = -s*r[1][2] + c*r[2][2]
r[1][0] = a10
r[1][1] = a11
r[1][2] = a12
r[2][0] = a20
r[2][1] = a21
r[2][2] = a22
}
/*
Ry Rotate an r-matrix about the y-axis.
Given:
theta float64 angle (radians)
Given and returned:
r [3][3]float64 r-matrix, rotated
Notes:
1) Calling this function with positive theta incorporates in the
supplied r-matrix r an additional rotation, about the y-axis,
anticlockwise as seen looking towards the origin from positive y.
2) The additional rotation can be represented by this matrix:
( + cos(theta) 0 - sin(theta) )
( )
( 0 1 0 )
( )
( + sin(theta) 0 + cos(theta) )
*/
func Ry(theta float64, r *[3][3]float64) {
var s, c, a00, a01, a02, a20, a21, a22 float64
s = sin(theta)
c = cos(theta)
a00 = c*r[0][0] - s*r[2][0]
a01 = c*r[0][1] - s*r[2][1]
a02 = c*r[0][2] - s*r[2][2]
a20 = s*r[0][0] + c*r[2][0]
a21 = s*r[0][1] + c*r[2][1]
a22 = s*r[0][2] + c*r[2][2]
r[0][0] = a00
r[0][1] = a01
r[0][2] = a02
r[2][0] = a20
r[2][1] = a21
r[2][2] = a22
}
/*
Rz Rotate an r-matrix about the z-axis.
Given:
psi float64 angle (radians)
Given and returned:
r [3][3]float64 r-matrix, rotated
Notes:
1) Calling this function with positive psi incorporates in the
supplied r-matrix r an additional rotation, about the z-axis,
anticlockwise as seen looking towards the origin from positive z.
2) The additional rotation can be represented by this matrix:
( + cos(psi) + sin(psi) 0 )
( )
( - sin(psi) + cos(psi) 0 )
( )
( 0 0 1 )
*/
func Rz(psi float64, r *[3][3]float64) {
var s, c, a00, a01, a02, a10, a11, a12 float64
s = sin(psi)
c = cos(psi)
a00 = c*r[0][0] + s*r[1][0]
a01 = c*r[0][1] + s*r[1][1]
a02 = c*r[0][2] + s*r[1][2]
a10 = -s*r[0][0] + c*r[1][0]
a11 = -s*r[0][1] + c*r[1][1]
a12 = -s*r[0][2] + c*r[1][2]
r[0][0] = a00
r[0][1] = a01
r[0][2] = a02
r[1][0] = a10
r[1][1] = a11
r[1][2] = a12
}
// 4. Spherical/Cartesian Conversions (6)
// Operations involving p-vectors and r-matrices (4)
/*
S2c Convert spherical coordinates to Cartesian.
Given:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
Returned:
c [3]float64 direction cosines
*/
func S2c(theta, phi float64, c *[3]float64) {
var cp float64
cp = cos(phi)
c[0] = cos(theta) * cp
c[1] = sin(theta) * cp
c[2] = sin(phi)
}
/*
C2s P-vector to spherical coordinates.
Given:
p [3]float64 p-vector
Returned:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
Notes:
1) The vector p can have any magnitude; only its direction is used.
2) If p is null, zero theta and phi are returned.
3) At either pole, zero theta is returned.
*/
func C2s(p [3]float64, theta *float64, phi *float64) {
var x, y, z, d2 float64
x = p[0]
y = p[1]
z = p[2]
d2 = x*x + y*y
if d2 == 0.0 {
*theta = 0.0
} else {
*theta = atan2(y, x)
}
if z == 0.0 {
*phi = 0.0
} else {
*phi = atan2(z, sqrt(d2))
}
}
/*
S2p Convert spherical polar coordinates to p-vector.
Given:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
r float64 radial distance
Returned:
p [3]float64 Cartesian coordinates
Called:
S2c spherical coordinates to unit vector
Sxp multiply p-vector by scalar
*/
func S2p(theta, phi, r float64, p *[3]float64) {
u := [3]float64{}
S2c(theta, phi, &u)
Sxp(r, u, p)
}
/*
P2s P-vector to spherical polar coordinates.
Given:
p [3]float64 p-vector
Returned:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
r float64 radial distance
Notes:
1) If P is null, zero theta, phi and r are returned.
2) At either pole, zero theta is returned.
Called:
C2s p-vector to spherical
Pm modulus of p-vector
*/
func P2s(p [3]float64, theta *float64, phi *float64, r *float64) {
C2s(p, theta, phi)
*r = Pm(p)
}
// Operations involving pv-vectors (2)
/*
S2pv Convert position/velocity from spherical to Cartesian coordinates.
Given:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
r float64 radial distance
td float64 rate of change of theta
pd float64 rate of change of phi
rd float64 rate of change of r
Returned:
pv [2][3]float64 pv-vector
*/
func S2pv(theta, phi, r float64, td, pd, rd float64, pv *[2][3]float64) {
var st, ct, sp, cp, rcp, x, y, rpd, w float64
st = sin(theta)
ct = cos(theta)
sp = sin(phi)
cp = cos(phi)
rcp = r * cp
x = rcp * ct
y = rcp * st
rpd = r * pd
w = rpd*sp - cp*rd
pv[0][0] = x
pv[0][1] = y
pv[0][2] = r * sp
pv[1][0] = -y*td - w*ct
pv[1][1] = x*td - w*st
pv[1][2] = rpd*cp + sp*rd
}
/*
Pv2s Convert position/velocity from Cartesian to spherical coordinates.
Given:
pv [2][3]float64 pv-vector
Returned:
theta float64 longitude angle (radians)
phi float64 latitude angle (radians)
r float64 radial distance
td float64 rate of change of theta
pd float64 rate of change of phi
rd float64 rate of change of r
Notes:
1) If the position part of pv is null, theta, phi, td and pd
are indeterminate. This is handled by extrapolating the
position through unit time by using the velocity part of
pv. This moves the origin without changing the direction
of the velocity component. If the position and velocity
components of pv are both null, zeroes are returned for all
six results.
2) If the position is a pole, theta, td and pd are indeterminate.
In such cases zeroes are returned for all three.
*/
func Pv2s(pv [2][3]float64, theta, phi, r *float64, td, pd, rd *float64) {
var x, y, z, xd, yd, zd, rxy2, rxy, r2, rtrue, rw, xyp float64
/* Components of position/velocity vector. */
x = pv[0][0]
y = pv[0][1]
z = pv[0][2]
xd = pv[1][0]
yd = pv[1][1]
zd = pv[1][2]
/* Component of r in XY plane squared. */
rxy2 = x*x + y*y
/* Modulus squared. */
r2 = rxy2 + z*z
/* Modulus. */
rtrue = sqrt(r2)
/* If null vector, move the origin along the direction of movement. */
rw = rtrue
if rtrue == 0.0 {
x = xd
y = yd
z = zd
rxy2 = x*x + y*y
r2 = rxy2 + z*z
rw = sqrt(r2)
}
/* Position and velocity in spherical coordinates. */
rxy = sqrt(rxy2)
xyp = x*xd + y*yd
if rxy2 != 0.0 {
*theta = atan2(y, x)
*phi = atan2(z, rxy)
*td = (x*yd - y*xd) / rxy2
*pd = (zd*rxy2 - z*xyp) / (r2 * rxy)
} else {
*theta = 0.0
if z != 0.0 {
*phi = atan2(z, rxy)
} else {
*phi = 0.0
}
*td = 0.0
*pd = 0.0
}
*r = rtrue
if rw != 0.0 {
*rd = (xyp + z*zd) / rw
} else {
*rd = 0.0
}
}
// 5. Operations on Vectors (17)
// Operations involving p-vectors and r-matrices (8)
/*
Ppp P-vector addition.
Given:
a [3]float64 first p-vector
b [3]float64 second p-vector
Returned:
apb [3]float64 a + b
Note:
It is permissible to re-use the same array for any of the
arguments.
*/
func Ppp(a, b [3]float64, apb *[3]float64) {
apb[0] = a[0] + b[0]
apb[1] = a[1] + b[1]
apb[2] = a[2] + b[2]
}
/*
Pmp P-vector subtraction.
Given:
a [3]float64 first p-vector
b [3]float64 second p-vector
Returned:
amb [3]float64 a - b
Note:
It is permissible to re-use the same array for any of the
arguments.
*/
func Pmp(a, b [3]float64, amb *[3]float64) {
amb[0] = a[0] - b[0]
amb[1] = a[1] - b[1]
amb[2] = a[2] - b[2]
}
/*
Ppsp P-vector plus scaled p-vector.
Given:
a [3]float64 first p-vector
s float64 scalar (multiplier for b)
b [3]float64 second p-vector
Returned:
apsb [3]float64 a + s*b
Note:
It is permissible for any of a, b and apsb to be the same array.
Called:
Sxp multiply p-vector by scalar
Ppp p-vector plus p-vector
*/
func Ppsp(a [3]float64, s float64, b [3]float64, apsb *[3]float64) {
var sb [3]float64
/* s*b. */
Sxp(s, b, &sb)
/* a + s*b. */
Ppp(a, sb, apsb)
}
/*
Pdp p-vector inner (=scalar=dot) product.
Given:
a [3]float64 first p-vector
b [3]float64 second p-vector
Returned (function value):
float64 a . b
*/
func Pdp(a, b [3]float64) float64 {
w := a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
return w
}
/*
Pxp p-vector outer (=vector=cross) product.
Given:
a [3]float64 first p-vector
b [3]float64 second p-vector
Returned:
axb [3]float64 a x b
Note:
It is permissible to re-use the same array for any of the
arguments.
*/
func Pxp(a, b [3]float64, axb *[3]float64) {
var xa, ya, za, xb, yb, zb float64
xa = a[0]
ya = a[1]
za = a[2]
xb = b[0]
yb = b[1]
zb = b[2]
axb[0] = ya*zb - za*yb
axb[1] = za*xb - xa*zb
axb[2] = xa*yb - ya*xb
}
/*
Pm Modulus of p-vector.
Given:
p [3]float64 p-vector
Returned (function value):
float64 modulus
*/
func Pm(p [3]float64) float64 {
return sqrt(p[0]*p[0] + p[1]*p[1] + p[2]*p[2])
}
/*
Pn Convert a p-vector into modulus and unit vector.
Given:
p [3]float64 p-vector
Returned:
r float64 modulus
u [3]float64 unit vector
Notes:
1) If p is null, the result is null. Otherwise the result is a unit
vector.
2) It is permissible to re-use the same array for any of the
arguments.
Called:
Pm modulus of p-vector
Zp zero p-vector
Sxp multiply p-vector by scalar
*/
func Pn(p [3]float64, r *float64, u *[3]float64) {
var w float64
/* Obtain the modulus and test for zero. */
w = Pm(p)
if w == 0.0 {
/* Null vector. */
Zp(u)
} else {
/* Unit vector. */
Sxp(1.0/w, p, u)
}
/* Return the modulus. */
*r = w
}
/*
Sxp Multiply a p-vector by a scalar.
Given:
s float64 scalar
p [3]float64 p-vector
Returned:
sp [3]float64 s * p
Note:
It is permissible for p and sp to be the same array.
*/
func Sxp(s float64, p [3]float64, sp *[3]float64) {
sp[0] = s * p[0]
sp[1] = s * p[1]
sp[2] = s * p[2]
}
// Operations involving pv-vectors (9)
/*
Pvppv Add one pv-vector to another.
Given:
a [2][3]float64 first pv-vector
b [2][3]float64 second pv-vector
Returned:
apb [2][3]float64 a + b
Note:
It is permissible to re-use the same array for any of the
arguments.
Called:
Ppp p-vector plus p-vector
*/
func Pvppv(a, b [2][3]float64, apb *[2][3]float64) {
Ppp(a[0], b[0], &apb[0])
Ppp(a[1], b[1], &apb[1])
}
/*
Pvmpv Subtract one pv-vector from another.
Given:
a [2][3]float64 first pv-vector
b [2][3]float64 second pv-vector
Returned:
amb [2][3]float64 a - b
Note:
It is permissible to re-use the same array for any of the
arguments.
Called:
Pmp p-vector minus p-vector
*/
func Pvmpv(a, b [2][3]float64, amb *[2][3]float64) {
Pmp(a[0], b[0], &amb[0])
Pmp(a[1], b[1], &amb[1])
}
/*
Pvdpv Inner (=scalar=dot) product of two pv-vectors.
Given:
a [2][3]float64 first pv-vector
b [2][3]float64 second pv-vector
Returned:
adb [2]float64 a . b (see note)
Note:
If the position and velocity components of the two pv-vectors are
( ap, av ) and ( bp, bv ), the result, a . b, is the pair of
numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the
dot-product of the two p-vectors and its derivative.
Called:
Pdp scalar product of two p-vectors
*/
func Pvdpv(a, b [2][3]float64, adb *[2]float64) {
var adbd, addb float64
/* a . b = constant part of result. */
adb[0] = Pdp(a[0], b[0])
/* a . bdot */
adbd = Pdp(a[0], b[1])
/* adot . b */
addb = Pdp(a[1], b[0])
/* Velocity part of result. */
adb[1] = adbd + addb
}
/*
Pvxpv Outer (=vector=cross) product of two pv-vectors.
Given:
a [2][3]float64 first pv-vector
b [2][3]float64 second pv-vector
Returned:
axb [2][3]float64 a x b
Notes:
1) If the position and velocity components of the two pv-vectors are
( ap, av ) and ( bp, bv ), the result, a x b, is the pair of
vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the
cross-product of the two p-vectors and its derivative.
2) It is permissible to re-use the same array for any of the
arguments.
Called:
Cpv copy pv-vector
Pxp vector product of two p-vectors
Ppp p-vector plus p-vector
*/
func Pvxpv(a, b [2][3]float64, axb *[2][3]float64) {
var wa, wb [2][3]float64
var axbd, adxb [3]float64
/* Make copies of the inputs. */
Cpv(a, &wa)
Cpv(b, &wb)
/* a x b = position part of result. */
Pxp(wa[0], wb[0], &axb[0])
/* a x bdot + adot x b = velocity part of result. */
Pxp(wa[0], wb[1], &axbd)
Pxp(wa[1], wb[0], &adxb)
Ppp(axbd, adxb, &axb[1])
}
/*
Pvm Modulus of pv-vector.
Given:
pv [2][3]float64 pv-vector
Returned:
r float64 modulus of position component
s float64 modulus of velocity component
Called:
Pm modulus of p-vector
*/
func Pvm(pv [2][3]float64, r, s *float64) {
/* Distance. */
*r = Pm(pv[0])
/* Speed. */
*s = Pm(pv[1])
}
/*
Sxpv Multiply a pv-vector by a scalar.
Given:
s float64 scalar
pv [2][3]float64 pv-vector
Returned:
spv [2][3]float64 s * pv
Note:
It is permissible for pv and spv to be the same array.
Called:
S2xpv multiply pv-vector by two scalars
*/
func Sxpv(s float64, pv [2][3]float64, spv *[2][3]float64) {
S2xpv(s, s, pv, spv)
}
/*
S2xpv Multiply a pv-vector by two scalars.
Given:
s1 float64 scalar to multiply position component by
s2 float64 scalar to multiply velocity component by
pv [2][3]float64 pv-vector
Returned:
spv [2][3]float64 pv-vector: p scaled by s1, v scaled by s2
Note:
It is permissible for pv and spv to be the same array.
Called:
Sxp multiply p-vector by scalar
*/
func S2xpv(s1, s2 float64, pv [2][3]float64, spv *[2][3]float64) {
Sxp(s1, pv[0], &spv[0])
Sxp(s2, pv[1], &spv[1])
}
/*
Pvu Update a pv-vector.
Given:
dt float64 time interval
pv [2][3]float64 pv-vector
Returned:
upv [2][3]float64 p updated, v unchanged
Notes:
1) "Update" means "refer the position component of the vector
to a new date dt time units from the existing date".
2) The time units of dt must match those of the velocity.
3) It is permissible for pv and upv to be the same array.
Called:
Ppsp p-vector plus scaled p-vector
Cp copy p-vector
*/
func Pvu(dt float64, pv [2][3]float64, upv *[2][3]float64) {
Ppsp(pv[0], dt, pv[1], &upv[0])
Cp(pv[1], &upv[1])
}
/*
Pvup Update a pv-vector, discarding the velocity component.
Status: vector/matrix support function.
Given:
dt float64 time interval
pv [2][3]float64 pv-vector
Returned:
p [3]float64 p-vector
Notes:
1) "Update" means "refer the position component of the vector to a
new date dt time units from the existing date".
2) The time units of dt must match those of the velocity.
*/
func Pvup(dt float64, pv [2][3]float64, p *[3]float64) {
p[0] = pv[0][0] + dt*pv[1][0]
p[1] = pv[0][1] + dt*pv[1][1]
p[2] = pv[0][2] + dt*pv[1][2]
}
// 6. Operations on matrices (2)
/*
Rxr Multiply two r-matrices.
Given:
a [3][3]float64 first r-matrix
b [3][3]float64 second r-matrix
Returned:
atb [3][3]float64 a * b
Note:
It is permissible to re-use the same array for any of the
arguments.
Called:
Cr copy r-matrix
*/
func Rxr(a, b [3][3]float64, atb *[3][3]float64) {
var w float64
var wm [3][3]float64
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
w = 0.0
for k := 0; k < 3; k++ {
w += a[i][k] * b[k][j]
}
wm[i][j] = w
}
}
Cr(wm, atb)
}
/*
Tr Transpose an r-matrix.
Given:
r [3][3]float64 r-matrix
Returned:
rt [3][3]float64 transpose
Note:
It is permissible for r and rt to be the same array.
Called:
Cr copy r-matrix
*/
func Tr(r [3][3]float64, rt *[3][3]float64) {
var wm [3][3]float64
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
wm[i][j] = r[j][i]
}
}
Cr(wm, rt)
}
// 7. Matrix-vector products (4)
// Operations involving p-vectors and r-matrices (2)
/*
Rxp Multiply a p-vector by an r-matrix.
Given:
r [3][3]float64 r-matrix
p [3]float64 p-vector
Returned:
rp [3]float64 r * p
Note:
It is permissible for p and rp to be the same array.
Called:
Cp copy p-vector
*/
func Rxp(r [3][3]float64, p [3]float64, rp *[3]float64) {
var w float64
var wrp [3]float64
//var i, j int
/* Matrix r * vector p. */
for j := 0; j < 3; j++ {
w = 0.0
for i := 0; i < 3; i++ {
w += r[j][i] * p[i]
}
wrp[j] = w
}
/* Return the result. */
Cp(wrp, rp)
}
/*
Trxp Multiply a p-vector by the transpose of an r-matrix.
Given:
r [3][3]float64 r-matrix
p [3]float64 p-vector
Returned:
trp [3]float64 r^T * p
Note:
It is permissible for p and trp to be the same array.
Called:
Tr transpose r-matrix
Rxp product of r-matrix and p-vector
*/
func Trxp(r [3][3]float64, p [3]float64, trp *[3]float64) {
var tr [3][3]float64
/* Transpose of matrix r. */
Tr(r, &tr)
/* Matrix tr * vector p -> vector trp. */
Rxp(tr, p, trp)
}
// Operations involving pv-vectors (2)
/*
Rxpv Multiply a pv-vector by an r-matrix.
Given:
r [3][3]float64 r-matrix
pv [2][3]float64 pv-vector
Returned:
rpv [2][3]float64 r * pv
Notes:
1) The algorithm is for the simple case where the r-matrix r is not
a function of time. The case where r is a function of time leads
to an additional velocity component equal to the product of the
derivative of r and the position vector.
2) It is permissible for pv and rpv to be the same array.
Called:
Rxp product of r-matrix and p-vector
*/
func Rxpv(r [3][3]float64, pv [2][3]float64, rpv *[2][3]float64) {
Rxp(r, pv[0], &rpv[0])
Rxp(r, pv[1], &rpv[1])
}
/*
Trxpv Multiply a pv-vector by the transpose of an r-matrix.
Given:
r [3][3]float64 r-matrix
pv [2][3]float64 pv-vector
Returned:
trpv [2][3]float64 r^T * pv
Notes:
1) The algorithm is for the simple case where the r-matrix r is not
a function of time. The case where r is a function of time leads
to an additional velocity component equal to the product of the
derivative of the transpose of r and the position vector.
2) It is permissible for pv and rpv to be the same array.
Called:
Tr transpose r-matrix
Rxpv product of r-matrix and pv-vector
*/
func Trxpv(r [3][3]float64, pv [2][3]float64, trpv *[2][3]float64) {
var tr [3][3]float64
/* Transpose of matrix r. */
Tr(r, &tr)
/* Matrix tr * vector pv -> vector trpv. */
Rxpv(tr, pv, trpv)
}
// 9. Rotation vectors (2)
/*
Rv2m Form the r-matrix corresponding to a given r-vector.
Given:
w [3]float64 rotation vector (Note 1)
Returned:
r [3][3]float64 rotation matrix
Notes:
1) A rotation matrix describes a rotation through some angle about
some arbitrary axis called the Euler axis. The "rotation vector"
supplied to This function has the same direction as the Euler
axis, and its magnitude is the angle in radians.
2) If w is null, the identity matrix is returned.
3) The reference frame rotates clockwise as seen looking along the
rotation vector from the origin.
*/
func Rv2m(w [3]float64, r *[3][3]float64) {
var x, y, z, phi, s, c, f float64
/* Euler angle (magnitude of rotation vector) and functions. */
x = w[0]
y = w[1]
z = w[2]
phi = sqrt(x*x + y*y + z*z)
s = sin(phi)
c = cos(phi)
f = 1.0 - c
/* Euler axis (direction of rotation vector), perhaps null. */
if phi > 0.0 {
x /= phi
y /= phi
z /= phi
}
/* Form the rotation matrix. */
r[0][0] = x*x*f + c
r[0][1] = x*y*f + z*s
r[0][2] = x*z*f - y*s
r[1][0] = y*x*f - z*s
r[1][1] = y*y*f + c
r[1][2] = y*z*f + x*s
r[2][0] = z*x*f + y*s
r[2][1] = z*y*f - x*s
r[2][2] = z*z*f + c
}
/*
Rm2v Express an r-matrix as an r-vector.
Given:
r [3][3]float64 rotation matrix
Returned:
w [3]float64 rotation vector (Note 1)
Notes:
1) A rotation matrix describes a rotation through some angle about
some arbitrary axis called the Euler axis. The "rotation vector"
returned by this function has the same direction as the Euler axis,
and its magnitude is the angle in radians. (The magnitude and
direction can be separated by means of the function iauPn.)
2) If r is null, so is the result. If r is not a rotation matrix
the result is undefined; r must be proper (i.e. have a positive
determinant) and real orthogonal (inverse = transpose).
3) The reference frame rotates clockwise as seen looking along
the rotation vector from the origin.
*/
func Rm2v(r [3][3]float64, w *[3]float64) {
var x, y, z, s2, c2, phi, f float64
x = r[1][2] - r[2][1]
y = r[2][0] - r[0][2]
z = r[0][1] - r[1][0]
s2 = sqrt(x*x + y*y + z*z)
if s2 > 0 {
c2 = r[0][0] + r[1][1] + r[2][2] - 1.0
phi = atan2(s2, c2)
f = phi / s2
w[0] = x * f
w[1] = y * f
w[2] = z * f
} else {
w[0] = 0.0
w[1] = 0.0
w[2] = 0.0
}
}