Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-Body Problem

TL;DR

This paper computes and analyzes resonant periodic orbits and invariant tori in a four-body celestial system, extending known three-body resonances to a more complex model, with implications for understanding orbital dynamics near Jupiter's moons.

Contribution

It introduces a method to compute and continue resonant orbits from a four-body problem into a three-body problem, revealing potential KAM tori near known resonances.

Findings

Identification of invariant tori corresponding to Jupiter-Europa and Jupiter-Ganymede resonances.

Successful continuation of a Jupiter-Europa 3:4 resonant orbit into the Jupiter-Ganymede PCRTBP.

Evidence suggesting the existence of a KAM torus near the 3:2 Jupiter-Ganymede resonance.

Abstract

Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. In this study, we compute tori corresponding to exterior Jupiter-Europa and interior Jupiter-Ganymede PCRTBP resonant periodic orbits in a concentric circular restricted 4-body problem (CCR4BP). Motivated by the 2:1 Laplace resonance between Europa and Ganymede's orbits, we then attempt the continuation of a Jupiter-Europa 3:4 resonant orbit from the CCR4BP into the Jupiter-Ganymede PCRTBP. We strongly believe that the resulting dynamical object is a KAM torus lying near but not on the 3:2 Jupiter-Ganymede resonance.