Chaining periodic three-body orbits in the Earth–Moon system

Abstract

In this paper, we describe methods to construct complex chains of orbit transfers in the planar circular restricted Earth–Moon three-body system using the invariant manifolds of unstable three-body orbits. It is shown that the Poincaré map is a useful tool to identify and construct transfer trajectories from one orbit to another, i.e., homoclinic and heteroclinic orbit connections, with applications to practical spacecraft mission design. A multiple-shooting differential corrector is used to construct complex orbit chains and complex periodic orbits. The resulting complex periodic orbits are shown to be members of continuous families of such orbits, where the characteristics of each orbit in the family vary continuously from one end of the family to the other. Finally, we characterize the cost of constructing an orbit transfer between any two points along two libration orbits using a single maneuver. It is shown that a spacecraft requires substantially less Δ V to perform such single-maneuver transfers if the transfers are near heteroclinic connections in the corresponding phase space.