Transfer Orbits Guided by the Unstable/Stable Manifolds of the Lagrangian Points

A.A. Correa, G. Gomez and T.J. Stuchi

Abstract. The unstable and stable manifolds of the Lagrangian point orbits
provide a natural mechanism to transfer natural and artificial bodies in the
Solar System. In the case of spacecrafts, low energy transfer trajectories can
be attained using the complex dynamics described by the unstable/stable
manifolds which coalesce in those orbits. However, these manifold tubes do not
approach the larger primary, so that is not possible to determine a transfer
orbit from the Earth to the Moon vicinity in the Earth-Moon system. This fact
can be overcome by decoupling the restricted four body problem into two planar
restricted three body systems with a common primary body
(Sun-Earth-spacecraft+Earth-Moon-spacecraft). The spacecraft leaves the Earth
parking orbit through the stable/unstable manifold structure in the Sun-Earth
problem and it is then connected to a transit orbit related to the stable
manifold of the Earth-Moon problem. A Poincare map located on a plane through
the Earth is used to find  the appropriate connections which depend on the
Jacobi's constant of each model.