Transfers to Earth-Moon triangular libration points by Sun-perturbed dynamics

Abstract

This paper is devoted to the construction of transfers to Earth-Moon triangular libration points based on their Sun-perturbed dynamics in the Sun-Earth-Moon system. In this bi-circular problem (BCP), the solar gravity perturbation breaks the stability of the Earth-Moon triangular libration points with three remaining periodic orbits (two stable and one unstable) around them as their dynamical substitutions. As the stable region, the invariant tori full of quasi-periodic orbits around the two stable periodic orbits can be used as the destination of triangular libration point transfers for a low station-keeping cost. However, the instability of the unstable periodic orbit is so mild that its stable and unstable manifolds are folded around the invariant tori surrounding the other two stable orbits. Thus, the authors approximate the stable and unstable manifolds of the unstable orbit through the parameterization method, which emerge from the Sun-perturbed Earth-Moon triangular libration points vicinity. They act as a bridge between outer space and the stable region around triangular libration points. First, the transfers connecting the Earth’s vicinity are constructed using the manifolds. Subsequently, a new connection mechanism near L4 and L5 based on the N:M multi-loop transfers is developed by extending the conventional patching skill to time-dependent situations. The quickest one is achieved by a 1:1 L4-L5 heteroclinic-based connection with a TOF of less than 26.9 days at a fuel cost of 117.88 m/s. Note that such Sun-perturbed transfers cannot be produced by continuing any trajectory in the Earth-Moon circular restricted three-body problem but they can generate two-impulsive transfers in the ephemeris model by continuation.