Stability of prograde and retrograde planets in circular binary systems

TL;DR

This study compares the stability of prograde and retrograde planets in circular binary systems, revealing that retrograde planets are stable closer to the perturber due to differences in resonance structures.

Contribution

The paper introduces an analytical model for resonance locations and stability analysis, highlighting the fundamental differences in phase-space topology between prograde and retrograde resonances.

Findings

Retrograde planets are stable at closer distances than prograde planets.

Instability arises from resonance overlap or single resonance forcing.

Retrograde resonance order differs from prograde, affecting stability.

Abstract

We investigate the stability of prograde versus retrograde planets in circular binary systems using numerical simulations. We show that retrograde planets are stable up to distances closer to the perturber than prograde planets. We develop an analytical model to compute the prograde and retrograde mean motion resonances' locations and separatrices. We show that instability is due to single resonance forcing, or caused by nearby resonances' overlap. We validate our results regarding the role of single resonances and resonances' overlap on orbit stability, by computing surfaces of section of the CR3BP. We conclude that the observed enhanced stability of retrograde planets with respect to prograde planets is due to essential differences between the phase-space topology of retrograde versus prograde resonances (at p/q mean motion ratio, prograde resonance is of order p - q while retrograde resonance is of order p + q).