Post-Newtonian accelerations of a Mercury orbiter

TL;DR

This paper develops a high-precision relativistic orbital model for Mercury orbiters by analyzing post-Newtonian perturbations, including local and third-body effects, to improve spacecraft navigation accuracy.

Contribution

It introduces a comprehensive approach to modeling Mercury's relativistic gravitational effects, including often-neglected third-body perturbations, for spacecraft orbit determination.

Findings

Post-Newtonian terms are significant along BepiColombo trajectories.

Relativistic third-body perturbations can be comparable to local effects.

A practical method for high-accuracy relativistic orbital modeling is proposed.

Abstract

We investigate the relativistic modeling of spacecraft motion in Mercury's post-Newtonian local coordinates. This investigation is motivated by the fact that Mercury's post-Newtonian gravitational field (as well as that of any other planet) admits an expansion in terms of multipole moments, which are most appropriately defined in the local reference system. The equations of motion in the Mercury-centric local frame include relativistic local perturbations, given by the Schwarzschild term, Lense-Thirring precession, and the acceleration due to the quadrupole moment, and relativistic third-body perturbations, which are the gravito-electric and gravito-magnetic accelerations, along with a coupling term between Mercury and other solar system bodies. The relativistic third-body perturbations are usually neglected in all practical applications. In this study, we analyze the magnitude of the post-Newtonian terms of the equations of motion formulated in the Mercury-centric frame, evaluating them along the trajectories of the two BepiColombo spacecrafts. Based on this analysis, we provide a practical approach for constructing a high-accuracy relativistic orbital model suitable for a Mercury orbiter.