New fly-around formations for an elliptical reference orbit

Fly-around technology, as applied to maintain a chasing spacecraft flying periodically around the chief spacecraft, has received widespread attention in recent years. The conventional impulsive or continuous-thrust control approaches for maintaining non-natural formations put a high demand on the engine and limit the applicability of engineering. In this study, which is based on the relative orbital elements, we propose a series of analytic natural fly-around formations for the two-body case, which can revisit specific points or be maintained within a certain range. In addition to maintaining the fly-around formation when considering the J2 perturbation, we present a two-stage constant thrust control method solved with the linearized sensitive matrix. Furthermore, based on this method, we present several maintaining strategies that guarantee a periodic revisit to a specified relative position. We conduct numerical simulations to demonstrate the efficacy of these proposed methods.