Transfers to distant periodic orbits around the Moon via their invariant manifolds

This paper presents two ways to transfer a spacecraft to distant periodic orbits in the Earth–Moon system. These unstable periodic orbits of the restricted three-body problem reveal a rich phase-portrait structure that can be used by space missions. Through the perspective of dynamical system theory, distant periodic orbits’ invariant manifolds can be exploited to design novel low-energy trajectories in the Earth–Moon framework. Interior and exterior transfers are presented. The latter use impulsive, high-thrust propulsion to target the stable manifold from the exterior. Interior transfers are instead formulated with continuous, low-thrust propulsion. The attainable sets are used in both cases to handle families of either coast arcs or low-thrust orbits. First guess solutions are optimized in the framework of the Sun–Earth-Moon–Spacecraft restricted four-body problem through direct transcription and multiple shooting. The novelty of the presented solutions, as well as their efficiency, is demonstrated through examples