Quadratic-based computation of four-impulse optimal rendezvous near circular orbit

The well-known problem of minimizing the total characteristic velocity of a spacecraft in an impulsive rendezvous 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.