Optimization of Biimpulsive Trajectories in the Earth-Moon Restricted Three-Body System

The problem is addressed of transferring a spacecraft from a low Earth to a low lunar orbit in a planar circular restricted three-body framework. A closed-form approximate expression for the total velocity variation is developed under the assumption of minimum ΔV biimpulsive maneuvers. This approximation quantifies the link between the transfer orbit energy and the minimum ΔV needed to complete the maneuver, but it gives no information on the corresponding mission time. This last problem is addressed in a systematic framework using an optimization process, and the totalΔV is minimized with the constraint that a maximum transfer time is not exceeded. Using a set of mission data taken from the literature, it is found that almost equivalent ΔV and transfer times (compared a weak stability boundary approach) are obtained without the use of solar perturbations. More important, a consistent methodology is proposed to exploit fully the fundamental tradeoff between the time of flight and the required ΔV.