Transport and invariant manifolds near L3 in the Earth-Moon Bicircular model

Abstract

This paper focuses on the role of $\mathrm{L}_3$ to organise trajectories for a particle going from Earth to Moon and viceversa, and entering or leaving the Earth-Moon system. As a first model, we have considered the planar Bicircular problem to account for the gravitational effect of the Sun on the particle. The first step has been to compute a family of hyperbolic quasi-periodic orbits near $\mathrm{L}_3$. Then, the computation of their stable and unstable manifolds provides connections between Earth and Moon, and also generates trajectories that enter and leave the Earth-Moon system. Finally, by means of numerical simulations based on the JPL ephemeris we show that these connections can guide the journey of lunar ejecta towards the Earth.