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The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold tubes associated to libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. 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. The current 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, the paper shows 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 maneuver is needed to perform the transfer from one libration point orbit to the other. The knowledge of these orbits can be very useful in the design of missions such as Genesis, and may provide the backbone for other interesting orbits in the future. 1
Gómez et al. (Fri,) studied this question.