The vicinity of Earth–Moon [formula omitted] and [formula omitted] in the Hill restricted 4-body problem

Abstract

The Hill restricted 4-body problem (HR4BP) is a periodic time-dependent Hamiltonian dynamical system that is both a generalization of the circular restricted 3-body problem (CR3BP) and Hill’s problem. In this work, the HR4BP is used to model the motion of an infinitesimal particle under the mutual gravitation of the Sun, Earth, and Moon. In the HR4BP, the equilibria L1 and L2 of the CR3BP are replaced by π-periodic orbits, the so-called EM L1,2 dynamical equivalents. We compute center manifold reductions about EM L1,2 to obtain a local overview of the dynamics in their vicinity. In this way, we show the existence of families of 2- and 3-dimensional quasi-periodic invariant tori around EM L1,2. Additionally, we exploit the first integral constructed in the center manifold reduction to compute hyperbolic invariant manifolds. We draw comparisons to the bicircular and quasi-bicircular restricted 4-body problems.