Dynamic portrait of the retrograde 1:1 mean motion resonance

TL;DR

This paper explores the detailed phase-space structure of the retrograde 1:1 mean motion resonance in the solar system, revealing new libration modes and orbital behaviors through analytical and numerical methods.

Contribution

It introduces a simple integrable approximation for the retrograde 1:1 resonance and uncovers a new apocentric libration mode within the resonance.

Findings

Discovered a new apocentric libration mode inside the planet's orbit.

Analyzed the phase portrait of the retrograde 1:1 resonance.

Observed significant orbital jumps caused by close encounters.

Abstract

Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planet's orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.