Geometric Perspectives on Fundamental Solutions in the Linearized Satellite Relative Motion Problem

TL;DR

This paper introduces a geometric framework for analyzing and efficiently computing natural relative motion trajectories in satellite constellations, enhancing understanding of close-proximity dynamics in complex orbital environments.

Contribution

It establishes an analytic relationship between Lyapunov-Floquet transformations across coordinate systems, enabling rapid computation and exploration of relative motion solutions.

Findings

Analytic methods for Keplerian relative motion with eccentric orbits

New geometric insights into linearized relative motion dynamics

Comparison with prior solutions demonstrates improved understanding

Abstract

Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov-Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.