The Neptunian gravity estimated from the motion of Triton based on astrometric observations
Authors: Wang Bo , Yan Jianguo , Gao Wutong , Yuan Ye , Sun Shangbiao , Ye Mao , Barriot Jean-Pierre 
Published: February 2023

Context. Accurate gravity and ephemerides estimations for Neptune and its satellites are necessary for the forthcoming deep space exploration missions targeting its system. In addition, these estimations are also meaningful for the modeling of Neptune's interior and for solar system dynamics studies. The body of astrometric data concerning Triton has been accumulating for about two hundred years, but more accurate updates to the ephemerides of this moon and revisions to the relevant gravity parameters would be possible with more precise astrometric data. The new Gaia catalog of star positions plus observations from Voyager 2 and the Hubble Space Telescope provide such a basis for high-precision astrometry and to complement and extend the existing body of data.
Aims. We aim to report integrated orbital fits for Triton based on all the available astrometric data from 1847 to 2020, including observations from Earth-based telescopes, Voyager 2, and the Hubble Space Telescope. We also estimate the Neptunian gravity using the motion of Triton.
Methods. Triton’s orbital solution was determined by a weighted least-squares method to fit the model to the most complete astrometric data set to date. The DOP853 algorithm was adopted in the numerical integration calculations. For the dynamical model parameters, our orbital model for Triton is similar to the NEP081 but with an update. The perturbations from the inner satellites (Naiad, Thalassa, Despina, Galatea, Larissa, Proteus, and Hippocamp) were considered by adding corrections to J2 and J4 for Neptune. As the gravitational oblateness coefficient of Neptune is correlated with its orientation, the pole parameters were thus kept fixed in the integration when estimating Neptunian gravity. A Monte Carlo analysis was performed, however, to obtain reliable accuracy estimations and to assess the uncertainty of pole parameters on the results’ formal error.
Results. We provide a new orbit and dynamical model values for Triton. The estimated accuracy of the model we built and updated fit all the astrometric data. The RMS of the residuals was 0.074 arcsec in the right ascension and 0.071 arcsec in declination. The RMS was 0.102 arcsec for X and 0.139 arcsec for Y in differential coordinates. The RMS for the position angle was 0.834 degrees, and the angular separation distance was 0.257 arcsec for the data collected before 1960. The orbit of Triton was well determined with the orbit differences from NEP081 and NEP097 (so far the latest Triton ephemerides from Jet Propulsion Laboratory) as being less than 300 km (about 15 mas) during the observation coverage period of this study. The large body of astrometric data for Triton over a time interval from 1847 to 2020 was used to constrain its position at the initial epoch, allowing us to reduce formal uncertainty to about 3 km. Based on the most complete weighting astrometric observations of Triton, the estimated mass of the Neptune system is GMs = 6 836 525.210 ±19.526 km3 s−2. Our revised gravity model yields J2 = 3401.655 ±1.850 × 10−6 and J4 = −33.294 ±10.000 × 10−6. The astrometric observations showed little sensitivity to GMs and J4, but acted well on J2. A Monte Carlo method was used to analyze the error caused by a variation in the pole parameters and showed that J2 = 3401.655 ± 3.994 × 10−6 was a more realistic error.