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 Delta V biimpulsive maneuvers. This approximation quantifies the link between the transfer orbit energy and the minimum Delta V 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 total Delta V 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 Delta V and transfer times (compared to 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 Delta V.