Connecting orbits and invariant manifolds in the spatial restricted three-body problem

Gomez, G., W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont and S. D. Ross

Nonlinearity, 17, 1571-1606

Abstract:

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a Petit Grand Tour of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case.

Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L₁ and the other around L₂. Since these connections are asymptotic orbits, no maneuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.