Quadratic-Based Computation of Four-Impulse Optimal Rendezvous near Circular Orbit

Abstract

Thewell-knownproblemofminimizingthetotalcharacteristicvelocityofaspacecraftinanimpulsiverendezvous with a satellite in circular orbit is considered by using the Clohessy ‐Wiltshire equations. It is well known that, for boundary conditions in the plane of the orbit, four impulses at most are required. The mathematical framework is presented for four-impulse optimal rendezvous near a circular orbit resulting in relatively simple formulas that determine if four impulses are required and, if so, how the four optimal velocity increments can be calculated.