On retrograde orbits, resonances and stability

TL;DR

This paper investigates the stability of retrograde orbits, demonstrating their enhanced stability over prograde ones in certain regimes, and explores their resonance behavior with implications for small Solar System bodies.

Contribution

It provides new stability maps for retrograde resonances in the planar circular restricted 3-body problem, extending understanding of their geometric and dynamical properties.

Findings

Retrograde configurations show increased stability compared to prograde in low mass ratio regimes.

New stability maps for 2/1 and 1/2 retrograde resonances are presented.

The stability borders are linked to the geometry of resonant orbits.

Abstract

We start by reviewing our previous work on retrograde orbital configurations and on modeling and identifying retrograde resonances. Then, we present new results regarding the enhanced stability of retrograde configurations with respect to prograde configurations in the low mass ratio regime of the planar circular restricted 3-body problem. Motivated by the recent discovery of small bodies which are in retrograde resonance with the Solar System's giant planets we then explore the case with mass ratio 0.001 and show new stability maps in a grid of semi-major axis versus eccentricity for the 2/1 and 1/2 retrograde resonances. Finally, we explain how the stability borders of the 2/1 and 1/2 retrograde resonances are related to the resonant orbits' geometry.