Computing natural transfers between Sun–Earth and Earth–Moon Lissajous libration point orbits

The four body problem Sun–Earth–Moon–spacecraft can be decoupled, in a raw first approximation, in two restricted three body problems (RTBPs): the Sun–Earth+MoonSun–Earth+Moon (SE) and the Earth–Moon (EM). Using the hyperbolic manifolds of the libration orbits of both problems and intersecting them in an adequate way, trajectories joining the solar and lunar libration regions can be found. Unfortunately, however, the coupling of two different RTBPs does not correspond to the physical reality of the Sun, Earth and Moon relative motions. Therefore, the initial trajectories obtained in the simplified model have to be refined to more realistic models. The present work introduces a way to compute connecting trajectories between EM and SE L2L2 Lissajous type orbits, starting from a simple model which couples two RTBP and refining them to JPL ephemeris. Furthermore, the refinement of the trajectories is tackled in such a way that the cost of the coupling is iteratively reduced, while the trajectory is kept similar to the original one in the coupled RTBPs. As a result, zero cost or natural connecting trajectories are obtained when possible. For less favourable cases, the outcome of the method are connecting trajectories which need a maneuver at the coupling point, always below 100 m/s of total ΔvΔv.