Bounds on maximal and minimal distances for coplanar satellite relative motion under given initial conditions

Maximal and minimal distances are the key parameters for a typical leader-follower satellite formation. For the mission designers, the definition of the initial relative orbital elements that are constrained by extreme distances is a difficult but meaningful problem. In this paper, the analytic distance bounds for the coplanar relative motion are obtained. These solutions are accurate for those periodic close formations in which the follower and leader satellite have equal semi-major axis. Besides, the assumption that the leader satellite has a circular orbit is adopted. Five kinds of special positions that are located on a single axis and generated the given extremum distances are derived and discussed. The simulation results are also provided to corroborate the analytic developments.