Arches of chaos, heteroclinic connections of first-order MMRs and the chaotic transport of small bodies in the Sun-Jupiter system

TL;DR

This study explores heteroclinic connections in the Sun-Jupiter system's restricted three-body problem, revealing complex chaotic structures and pathways for small bodies' transport across resonances.

Contribution

It explicitly computes manifolds of periodic orbits related to key MMRs and uncovers new heteroclinic connections influencing chaotic transport in the system.

Findings

Identifies heteroclinic channels allowing particle transits across Jupiter's orbit.

Reveals new heteroclinic connections involving L3 and MMR periodic orbits.

Shows the persistence of chaotic structures in both circular and elliptic RTBP.

Abstract

We investigate the heteroclinic connections between stable and unstable manifolds of unstable periodic orbits associated with the most important mean motion resonances (MMRs) in the Sun-Jupiter planar restricted three-body problem. We explicitly compute the stable and unstable manifolds of the unstable periodic orbits associated with the first order interior MMRs 2:1, 3:2, and the exterior MMR 2:3. We also compute short-time FLI maps showing the chaotic saddle structure created by the manifolds of several interior or exterior MMRs other than the 1:1 (co-orbital) resonance. Transits of particles from the exterior to the interior of Jupiter's orbit and vice versa are allowed for Tisserand parameter lesser than 3, and are shown to exist through a variety of heteroclinic channels. Besides the classical ones by Koon et al., we find heteroclinic connections between manifolds of short-period orbits around L3 and periodic orbits of interior or exterior first order MMRs, as well as direct connections between interior and exterior MMR manifolds not involving co-orbital periodic orbits. Through these manifolds and the corresponding FLI ridges, we explain the 'arches-of-chaos' in the asteroid orbital plane (a,e). Chaotic orbits shadowing heteroclinic trajectories exhibit resonance hopping, suggesting links to quasi-Hildas and Jupiter-family comets. Results are obtained in the circular RTBP but persist in the elliptic problem.