Collision avoidance dynamics for optimal impulsive collision avoidance maneuvers

This paper describes a method to calculate the optimal impulsive maneuver to avoid the collisions using Simplified General Perturbation 4 (SGP4) and Two Line Element (TLE). It also presents a rigorous analysis of the method to investigate the relative dynamics of the two colliding space objects assuming the encounter is instantaneous. Different collision geometries are used for test cases. For all collision geometries, the relative velocity and the relative miss distance vectors are parallel, which is the worst case because the encounter occurs along the direction of the relative velocity vector. Test cases are satellites with distinctive orbital characteristics that are obtained from the official Spacetrack catalog. A precise numerical orbit propagator is used both to create ephemerides for test cases and to evaluate the accuracy of the proposed method. This work is significant because this is the first comprehensive investigation of the relative dynamics of the optimal impulsive collision avoidance maneuvers for satellites. Moreover, the proposed method isn't compute-intensive because it is a semi-numerical method.