Characterization of Low-Energy Quasiperiodic Orbits in the Elliptic Restricted 4-Body Problem with Orbital Resonance

In this work, we investigate the behavior of low-energy trajectories in the dynamical framework of the spatial elliptic restricted 4-body problem, developed using the Hamiltonian formalism. Introducing canonical transformations, the Hamiltonian function in the neighborhood of the collinear libration point L1 (or L2 ), can be expressed as a sum of three second order local integrals of motion, which provide a compact topological description of low-energy transits, captures and quasiperiodic libration point orbits, plus higher order terms that represent perturbations. The problem of small denominators is then applied to the order three of the transformed Hamiltonian function, to identify the effects of orbital resonance of the primaries onto quasiperiodic orbits. Stationary solutions for these resonant terms are determined, corresponding to quasiperiodic orbits existing in the presence of orbital resonance. The proposed model is applied to the Jupiter-Europa-Io system, determining quasiperiodic orbits in the surrounding of Jupiter-Europa L1 considering the 2:1 orbital resonance between Europa and Io.