Exploiting Distant Periodic Orbits and Their Invariant Manifolds to Design Novel Space Trajectories to the Moon

This paper analyzes distant periodic orbits in the Earth-Moon system. Unstable periodic orbits in the restricted three-body problem reveal a rich phase-portrait structure useful for many space mission opportunities. Through the perspective of dynamical system theory, their invariant manifolds can be deterministically exploited to design novel low-energy trajectories in the Earth Moon scenario. Indeed, transfers to distant periodic orbits, both interior (through the L1 gateway) as well as exterior (through the L2 gateway after traveling along the Sun Earth invariant pathways) are designed. Low-thrust propulsion is also taken into account to define efficient trajectories in terms of propellant consumption and flight time. Special attainable sets are defined to incorporate the low-thrust term in the invariant-manifold technique. In the framework of the Sun Earth Moon Spacecraft restricted four-body problem, accurate first guess solutions are then optimized, through a direct method approach and multiple shooting technique.