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

This paper is devoted to a new approach to construct the transfers from the Earth to the Earth-Moon (EM) $L_{4}$ using stable and unstable manifolds of planar quasiperiodic Lyapunov orbits (QPLOs) of the EM $L_{3}$ in the planar bicircular SunEarth-Moon system. Some planar QPLOs have stable manifolds intersecting the Earth parking orbits and unstable manifolds passing through the EM $L_{4}$ 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 $\mathrm{L}_{4}$ vicinity, respectively. The trajectories near the stable manifolds spent some time moving around $L_{3}$ and then approach the unstable manifolds towards $L_{4}$. To reduce the multi-revolution behavior around EM $L_{3}$, 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 $L_{3}$ 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 $L_{3}$, 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 $L_{4}$ vicinity. By this construction, the lowest time of flight is about 61 days. The advantages of these two constructions are discussed.