Low-energy transfers to a Lunar multi-revolution elliptic halo orbit

The spatial Sun-Earth/Moon Patched Elliptic and Circular Restricted three-body Problem model is utilized to construct low-energy transfers to a strictly periodic orbit, the Multi-revolution Elliptic Halo (ME-Halo), around the lunar L2 point region. This patched model is elaborated, and the low-energy transfers are defined by eight parameters. The ME-Halo orbit in this paper is not a simple repetition of a halo orbit, which has a three-dimensional stable manifold. A survey of all feasible low-energy transfers is presented, and the impact of the redundant dimension of the stable manifold is considered. The survey reveals that it is feasible to design a transfer considering the eccentricity perturbation, but some points on the target orbit are hard to reach no matter what the phase of the patched model is. It also reveals that the redundant stable manifold affects the probability of feasible transfers in the whole parameter space.