Relativistic Dynamics of Relative Motions (I): Post-Newtonian Extension of the Hill-Clohessy-Wiltshire Equations

TL;DR

This paper extends the classical Hill-Clohessy-Wiltshire equations to include first-order post-Newtonian effects from general relativity, improving the accuracy of modeling relative orbital motions in deep space.

Contribution

It provides a systematic extension of the Hill-Clohessy-Wiltshire equations to incorporate relativistic corrections, a novel approach in orbital dynamics.

Findings

Derived post-Newtonian corrections to classical equations.

Worked out solutions for general periodic motions with relativistic effects.

Enhanced modeling accuracy for deep space satellite dynamics.

Abstract

With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we extend,in a systematic way, the Hill-Clohessy-Wiltshire Equations to include the complete first order post-Newtonian effects from general relativity. Within certain short time limit, post-Newtonian corrections to general periodic solutions of the Hill-Clohessy-Wiltshire Equations are also worked out.