Fuel-optimal rendezvous near a point in general Keplerian orbit

Based on the linearized equations of motion of a spacecraft near a satellite in general Keplerian orbit and the assumptions of a bounded thrust magnitude and constant exhaust velocity, a fixed-duration, fuel-optimal rendezvous problem is formulated and is investigated for the constant-mass case through the solution for the primer vector, which is shown to satisfy the original differential equations that describe the spacecraft motion during unpowered flight. It is shown that there are no singular solutions to this rendezvous problem for noncircular Keplerian orbits and that consequently all optimal solutions for orbit eccentricities greater than zero are constructed from a finite number of intervals of full thrust and coast where the switches are determined from the primer vector.