A numerical study of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in planetary systems

TL;DR

This study numerically investigates the stability and phase space topology of retrograde mean motion resonances in planetary systems, revealing the existence of periodic orbit families and comparing different three-body problem models.

Contribution

It provides a comprehensive numerical analysis of retrograde resonances across various three-body problem configurations, highlighting the structure of stable orbits and phase space differences.

Findings

Existence of periodic orbit families in all configurations

Stable resonant librations identified via MEGNO analysis

Comparison of phase space topology across models

Abstract

We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted 3-body problem) or masses corresponding to either Neptune, Saturn or Jupiter (planetary 3-body problem). For each system we obtain stability maps using the n-body numerical integrator REBOUND and computing the chaos indicator mean exponential growth factor of nearby orbits (MEGNO). We show that families of periodic orbits exist in all configurations and they correspond to the libration of either a single resonant argument or all resonant arguments (fixed points). We compare the results obtained in the elliptic restricted 3-body problem with previous results in the literature and we show the differences and similarities between the phase space topology for these retrograde resonances in the circular restricted, elliptic restricted and planetary 3-body problems.