Topology of lunar capture orbits: a numerical study

Abstract

This paper is concerned with the topological study of low-energy trajectories to the Moon, with emphasis to long-term lunar capture orbits, in the context of the classical circular restricted three-body problem. An original cylindrical representation of the phase space, associated with the third body dynamics, is proposed. Periodic orbits, transit orbits, and trajectories asymptotic to the periodic orbit around the Lagrange point 1 L are mapped through this cylindrical representation. Conley's theorem on the topology of lunar capture trajectories is employed to locate the initial conditions of potential interest, i.e. those generating long-term capture lunar orbits. This approach allows finding a number of long-term capture trajectories. One of these trajectories exhibits special features, in terms both of capture duration and of geometric distribution. A simple strategy - that nevertheless minimizes propellant consumption - to transform low-energy trajectories into the final (supposedly desired) circular orbit around the Moon is then proposed.