Spacecraft Rendezvous Utilizing Invariant Manifolds for a Halo Orbit

Abstract

For spacecraft to rendezvous in a halo orbit around Earth Moon Lagrange Point 2 with an amplitude of several ten-thousand kilometers, we propose selecting a chaser's rendezvous trajectory from two different types, depending on the phase difference to the target. In the first trajectory, the chaser approaches the target from behind along the orbit, similarly to a rendezvous in a low Earth orbit. The second trajectory utilizes the homoclinic intersection of invariant manifolds of the halo orbit extended toward the Moon, where the chaser's trajectory is controlled so that it first departs from the halo orbit along an unstable manifold, is connected to a stable manifold through the intersection, and then returns to the halo orbit. We showed that this detour can adjust the time of arrival to the halo orbit with low fuel usage and the total delta-v for the rendezvous can be significantly reduced in comparison to the first trajectory if the initial phase difference is large. The strategy employed can significantly increase the flexibility of the flight plan, increase the launch window of the visiting vehicle to the target and enhance the tolerance against failure compared to the application of a traditional phasing method.