Optimal Free-Return Trajectories to Near-Earth Asteroids

An algorithm is presented to generate an initial guess and converge a trajectory to reach a near-Earth asteroid in a fuel-optimal sense with emphasis on manned-mission risk reduction. The trajectory is designed such that the departing vehicle will return to Earth with no extra maneuvers, and incorporates a lunar flyby on the outbound segment to reduce fuel cost. The nominal mission departs the free-return trajectory to rendezvous with the asteroid for a minimum period of time before returning to Earth. The optimization scheme incorporates a full ephemeris model and analytical gradients for accurate convergence. The method is useful for fuel cost reduction of interplanetary trajectories in general that include a lunar flyby. An example case is presented to rendezvous with asteroid 2000 SG344 that depart