A Relativistic Motion Integrator: Numerical accuracy and illustration with BepiColombo and Mars-NEXT

TL;DR

This paper introduces the Relativistic Motion Integrator (RMI) for numerically solving relativistic equations of spacecraft motion, demonstrating its accuracy and relevance through comparisons with traditional methods for BepiColombo and Mars-NEXT.

Contribution

The paper presents the RMI approach as a precise numerical method for relativistic spacecraft orbit integration, improving upon classical Newtonian plus correction techniques.

Findings

RMI provides accurate relativistic orbit calculations.

RMI results agree with traditional methods within acceptable margins.

RMI is suitable for high-precision spacecraft orbit studies.

Abstract

Today, the motion of spacecraft is still described by the classical Newtonian equations of motion plus some relativistic corrections. This approach might become cumbersome due to the increasing precision required. We use the Relativistic Motion Integrator (RMI) approach to numerically integrate the native relativistic equations of motion for a spacecraft. The principle of RMI is presented. We compare the results obtained with the RMI method with those from the usual Newton plus correction approach for the orbit of the BepiColombo (around Mercury) and Mars-NEXT (around Mars) orbiters. Finally, we present a numerical study of RMI and we show that the RMI approach is relevant to study the orbit of spacecraft.