Decomposition analysis of spacecraft relative motion with different inter-satellite ranges

Abstract

With the development of satellite cluster and giant constellations in recent years, the orbit design and long-term maintenance of these systems become more difficult with the restriction of fuel consumption and the influence of orbital perturbations. It's necessary to study the analytical model of relative motion which applicable to different inter-satellite ranges. Then, considering the perturbed evolutions of orbital elements, the decomposed relative motion model was proposed by separating the higher-fidelity relative motion model into two different parts, which reflect the circling motion around chief, and their overall motion relative to chief respectively. Eccentricity expansions had been carried out to provide a time-explicit analytical solution of the decomposed model. Based on this first order time-explicit analytical solution, the bound relative motions with different inter-satellite ranges were studied in Kepler orbit. The initial condition calculation formula for general chief centered circular relative motion was derived at the same time. The accuracy of first order analytical solution of the decomposed model was estimated both theoretically and numerically, to show the effect of inter-satellite range and chief's eccentricity. At last, the first order analytical solution using mean orbital elements was compared with high precision numerical solution under perturbations to validate it's effective in long-term stability analysis.