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

Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 107-81, Pasadena, CA 91125, USA. E-mail:

(with G Gomez, W S Koon, M W Lo, J E Marsden and J J Masdemont)


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 manoeuvre 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 missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.

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