Optimal Free-Return Trajectories to Near-Earth Asteroids

Abstract

A method is presented to calculate optimal trajectories to near-Earth asteroids that incorporate free-return trajectory segments. These trajectories are useful because they return to Earth with no fuel penalty, which is useful for risk mitigation on manned missions. The algorithm minimizes total velocity change over an entire nominal mission, encompassing a single impulsive maneuver each for Earth departure, leaving the free-return trajectory, rendezvous with and departure from the asteroid, culminating with unpowered reentry into Earth’s atmosphere. Two example cases are presented in the circular restricted three-body model: a mission to 2000 SG344 from 23 August 2028 to 9 October 2029 with a cost of , and a mission to 2006 BZ147 from 9 February 2033 to 21 December 2033 with a cost of . The results presented here showcase the usage of the algorithm, which may be applied to free-return trajectories to a wide variety of near-Earth objects.