Families of Earth–Moon trajectories with applications to transfers towards Sun–Earth libration point orbits

Abstract

We studied Earth–Moon transfer trajectories in the circular restricted three-body problem (CRTBP) from the viewpoint of families and considered their applications in transferring a spacecraft from the Earth to periodic orbits around Sun–Earth libration point $L_{2}$ (SE–L2). Initially, twelve families of trajectories with transfer time shorter than fifty days are identified in the Earth–Moon system. By connecting these transfers with stable manifolds of the target orbit, low-energy transfers from the low Earth orbit to a small-amplitude periodic orbit around SE–L2 are determined in two separate CRTBPs (Earth–Moon and Sun–Earth CRTBPs). Then, taking the patched trajectories as initial guesses and introducing a small maneuver at the perilune, we optimize the whole transfer trajectories in the Sun–Earth–Moon–Spacecraft system. Results indicate that it is possible to realize low-energy transfers to small-amplitude orbits around SE–L2 by patching the Earth–Moon transfers with stable manifolds of the target orbits.