Powered lunar flyby for transfers between non-coplanar orbits around Earth

This work studies transfer between non-coplanar circular orbits around Earth with the space vehicle performing a powered lunar flyby maneuver. The complete transfer trajectory is accomplished by an application of two or three impulsive velocity increments. First and final velocity increments are applied tangentially, respectively, to the departing and the arrival orbits around Earth. An optional second velocity increment is applied at the perilune in order to increase the effects of the flyby maneuver. Despite many works consider the powered lunar flyby instead of a natural lunar flyby, it is important to compare both maneuvers in the context of the complete trajectory. In this direction, the present work formulates and solves multiple point boundary value problems that determine the transfer trajectories considering three models: a three-dimensional patched-conic approximation, a model based on the spatial restricted three-body problem, and, a model based on the spatial bi-circular restricted four-body in which the influence of the Sun is included. The transfer trajectory solutions are compared with classical maneuvers and with transfers that perform a natural flyby maneuver. An interesting result shows that a decelerating propulsion during the flyby maneuver can provide a transfer trajectory with a fuel consumption smaller than the one of bi-parabolic maneuver even if the Sun's attraction is considered. Moreover, the influence of the Sun can decrease the time of flight and the apogee of the trajectory and it can save fuel consumption if the Sun's initial phase angle is properly chosen.