Relative Orbit Elements for Satellites in Elliptical Orbits

摘要

The purpose of this research was to describe the unperturbed relative motion of Earth satellites in elliptical orbits using a simple dynamics model whose parameters allow significant geometrical insight and operational efficacy. The goal was to retain the advantages of the Relative Orbit Elements (ROE) realization of the Hill-Clohessy-Wiltshire (HCW) equations, a linearized dynamics model for circular reference orbits. Specifically, this thesis analyzed the geometry of satellite rendezvous and proximity operations using the ROE parameters to characterize the model's utility. Next, through a comprehensive literature review, this thesis sought possible approaches for developing a similarly useful parameterization for chief orbits with nonzero eccentricity. The approach selected was a novel linear time-varying system which requires both chief and deputy satellites to remain close to a virtual chief on a known circular orbit. The research derived and solved the equations of motion, expressing the solution in terms of simple geometric parameters. Numerical simulations compared the new model against both HCW and Keplerian two- body motion, revealing less accurate performance than HCW for some cases. Error analysis explained this behavior and found restricted regions where the new model performed accurately. Finally, this study identified new approaches for researching relative satellite motion on elliptical orbits.