Lunar capture trajectories in the four-body problem

In this paper, we develop the low energy trajectory design of a spacecraft from the Earth to the Moon in the context of the Planar Restricted Four Body Problem, which may be approximately modeled by coupling two Planar Restricted Three Body Problems, i.e., the Sun-(Earth+Moon)-Spacecraft and the Earth-Moon-Spacecraft systems. The principal idea lies in the so-called tube dynamics, which may patch invariant manifolds of the two PR3BPs to obtain the required lunar capture trajectories. We first model the S-E-M-S/C system by the coupled Planar Restricted Circular Three Body Problem (PRC3BP) and we also analyze the case, in particular, where the E-M-S/C system is modeled by the Planar Restricted Elliptic Three Body Problem (PRE3BP), since the E-M system has the nonnegligible eccentricity. Finally, we develop the low energy lunar capture trajectory in the coupled PRC3B-PRE3BP in comparison with the case of the coupled PRC3BP.