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 i s considered by using the Clohessy-Wiltshire equations. It is well known th at, for boundary conditions in the plane of the orbit, four impulses at mos t are required. The mathematical framework is presented for four-impulse op timal rendezvous near a circular orbit resulting in relatively simple formu las that determine if four impulses are required and, if so, how the four o ptimal velocity increments can be calculated.