Analytic Maneuver Sequence for Safety Ellipse Reconfigurations Using Relative Orbital Elements

Abstract

This paper presents an analytic solution for a three-impulse maneuver sequence that reconfigures safety ellipses. Safety ellipses are relative motion trajectories that do not require thrusting to ensure a high probability of short-term collision avoidance. Primer vector theory is used to derive analytic expressions that relate the necessary conditions for optimality to properties of the initial and final safety ellipses. The primer vector analysis is validated numerically using convex optimization and Monte Carlo methods. A general passive safety parameter for relative motion trajectories in near-circular orbits is also introduced. It is shown that for practical safety ellipse reconfiguration scenarios, the maneuver sequence generates optimal transfer trajectories that also remain passively safe.