Context. New observations and new planetary and satellite ephemerides provide opportunities to improve the ephemerides for Triton and Nereid as well as relevant parameters. In particular, the observations include a lot of new accurate Earth-based positions reduced with Gaia astrometic catalogs and accurate positions obtained from Hubble Space Telescope.

Aims. We aim to reliably improve the ephemerides for Triton and Nereid along with some parameters by using all the available astrometric data from 1847 to 2020 and by updating the dynamical model. We also aim to improve the geometrical descriptions based on the improved orbits of the two satellites and the pole orientation of Neptune.

Methods. The orbits of Triton and Nereid are determined by fitting dynamical and observational model parameters to observations in a weighted least-squares sense. The dynamical model makes use of the new ephemerides from Jet Propulsion Laboratory for planets, DE440, and those for the inner satellites of Neptune, NEP090. For completeness, in addition to the gravitational effects considered by NEP081, the model also includes perturbations from inner satellites and a revised model for the motion of the pole orientation of Neptune. Moreover, model simplifications are investigated to speed up the motion equation integration. Since the pole orientation angles of Neptune at epoch are possibly improvable according to the preliminary post-fit sensitivity analysis, these angles are adjusted together with the satellite state vectors at epoch. Linear mapping of the covariance matrix is a measure of formal uncertainties of our orbit and pole solutions. However, to obtain more reliable accuracy estimations, it is necessary to consider the uncertainties in the observations and the unadjusted model parameters. To accomplish this, a method (BR-RS) that performs bootstrap resampling of observations (BR) and random sampling of unadjusted model parameters (RS) is used. Analytical representations are fitted to the orbit and pole solutions to provide their geometric descriptions.

Results. The model we use can be fitted to the observations with their estimated accuracies. The new ephemerides, FORCES-8-MAIN-2020, covering years 1600–2650 are available online in SPICE format. The orbits are well determined with the orbital uncertainties expected to be within 200 km (about 10 mas as seen from the Earth) for Triton and 1000 km (50 mas) for Nereid for the next 100 yr as estimated by the BR-RS method. In particular, the correction in the Nereid mean orbit motion from the NEP081 solution is +4.′′9 yr−1, and has a BR-RS uncertainty of 0.′′24 yr−1. In the fitting process, we also determine the pole orientation of Neptune. At the initial epoch 1989 September 1 TDB, the right ascension and declination of the new pole orientation referred to the International Celestial Reference System are αp = 299.°339 ± 0.°012 (formal)∕ ± 0.°014 (BR-RS) and δp = 42.°985 ± 0.°016 (formal)∕ ± 0.°045 (BR-RS), respectively. From 1800 to 2200, the motion of the pole orientation is well constrained with a BR-RS uncertainty of about 0.°01–0.°05. We also provide geometrical descriptions for the new orbits and pole orientation.