Dynamics around the Earth–Moon triangular points in the Hill restricted 4-body problem

Abstract

In this talk, we give a review of the motion of a small particle moving near the triangular points (L4,5) of the Earth-Moon system subject to periodic forcing of the Sun modelled by the Hill restricted 4-body problem. We do this in several steps. First, we continue equilibria into periodic solutions in the perturbed problem, as well as resonant periodic solutions via subharmonic Melnikov methods. Then, we apply a center manifold reduction to limited effect. Given the limitations of the center manifold reduction, we apply a flow map method to compute five families of quasi-periodic invariant 2-tori around the two periodic orbits (one replacing L4 and a 2:1 resonant orbit) in the region. We compute their linear normal behavior and identify bifurcations. Mechanisms for transport between Earth, L4, and the Moon will be discussed.