Optimal transfers from Moon to $L_2$ halo orbit of the Earth-Moon system

Abstract: In this paper, we seek optimal solutions for a transfer from a parking orbit around the Moon to a halo orbit around $L_2$ of the Earth-Moon system, by applying a single maneuver and exploiting the stable invariant manifold of the hyperbolic parking solution at arrival. For that, we propose an optimization problem considering as variables both the orbital characteristics of a parking solution around the Moon, (namely, its Keplerian elements) and the characteristics of a transfer trajectory guided by the stable manifold of the arrival Halo orbit. The problem is solved by a nonlinear programming method (NLP), aiming to minimize the cost of $\Delta V$ to perform a single maneuver transfer, within the framework of the Earth-Moon system of the circular restricted three-body problem. Results with low $\Delta V$ and suitable time of flight show the feasibility of this kind of transfer for a Cubesat.