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.
