Optimal transfers from Moon to L2 halo orbit of the Earth-Moon system

In this paper, optimal solutions are investigated for a transfer from a parking orbit around the Moon to a halo orbit around L2 of the Earth-Moon system. The transfers are executed by applying a single maneuver and exploiting the stable invariant manifold of the hyperbolic parking solution at arrival. In this regard, an optimization problem is proposed where both the orbital characteristics of a parking solution around the Moon (its Keplerian elements) and the characteristics of a transfer trajectory (guided by the stable manifold of the arrival Halo orbit) are considered as variables. The problem involved in the single maneuver transfer is solved using a nonlinear programming method (NLP), which aims to minimize the cost of ΔV within the framework of the Earth-Moon system using the circular restricted three-body problem. The feasibility of this kind of transfer for a Cubesat is shown in this paper through results with low ΔV combined with suitable times of flight.