Indirect optimization of low-thrust capture trajectories

A numerical procedure based on the optimal control theory (OCT) for the optimization of Earth-capture trajectories of a spacecraft that employs electric propulsion (EP), is discussed. The trajectories are split into two phases, approach phase, which involve ballistic arcs inserts the spacecraft into a high circular orbit, and the spiral phase, brings the probe to the final LEO. The boundary conditions for optimality are provided by OCT to complete the differential system and define a multipoint boundary value problem. The procedure yields a long trajectory, which enters the spiral during the second revolution and, the switching structure is modified by adding two coast arcs. The engine perform a first braking at the perigee passage and thrusts again to perform a braking maneuver for the insertion.