Low-Energy Transfers in the Earth–Moon System

Abstract

The aim of this work is to compute low-energy trajectories in the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. It is known that this model admits five equilibrium points, in a proper reference system. We look for connection paths between the neighbourhood of a given collinear libration point and one of the primaries. We focus on the point L ₁ and on the point L ₂, whose linear behaviour is of type center × center × saddle. We consider Lindstedt–Poincaré series expansion as main procedure to compute invariant stable manifolds associated with periodic and quasi-periodic orbits around L ₁ and L ₂. It turns out that direct lunar transfers are allowed only from certain regions on the Moon’s surface and that the most advantageous connections between the Earth and a libration point orbit take place at the local maxima of the function distance between the Earth and a given stable manifold.