Leveraging L3 to transfer to L4 in the Sun-perturbed Earth-Moon system

Abstract This paper is devoted to a new approach to construct the transfers from the Earth to the Earth-Moon (EM) L4 using stable and unstable manifolds of planar quasi-periodic Lyapunov orbits (QPLOs) of the EM L3 in the planar bicircular Sun-Earth-Moon system. Some planar QPLOs have stable manifolds intersecting the Earth parking orbits and unstable manifolds passing through the EM L4 region, which gives a skeleton to design such transfers. Tentatively, the stable and unstable manifolds of a planar QPLO are employed to construct transfer segments connecting the Earth and L4 vicinity, respectively. The trajectories near the stable manifolds spent some time moving around L3 and then approach the unstable manifolds towards L4. To reduce the multi-revolution behavior around EM L3, a multiple shooting algorithm is developed to switch from the stable to the unstable manifold, where additional maneuvers are performed at some distance from the planar QPLO to reduce the time spent in the EM L3 vicinity. By such construction a spacecraft can visit and park around two high-cost far-away libration points in a single journey. Eliminating most of the loops around EM L3, the quickest one among the example transfers requests about 175 days. Furthermore, it is presented how to utilize the stable manifolds of the planar QPLO alone to design faster transfers to the EM L4 vicinity. By this construction, the lowest time of flight is about 61 days. The advantages of these two constructions are discussed.