Dynamics of planets in retrograde mean motion resonance

TL;DR

This paper analytically investigates the dynamics and stability of three-body planetary systems with retrograde mean motion resonances, expanding understanding of counter-revolving planetary configurations and their orbital stability.

Contribution

It introduces a new analytical framework and canonical variables for studying retrograde resonances in three-body systems, complementing previous numerical analyses.

Findings

Analytical Hamiltonian for retrograde resonances derived

Comparison confirms analytical results align with numerical simulations

Provides insights into stability structures of counter-revolving planets

Abstract

In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are both in mean motion resonance and revolve in opposite directions. For a particular two-planet system, we have also obtained a new orbital fit involving such a counter-revolving configuration and consistent with the observational data. In the present paper, we analytically investigate the three-body problem in this particular case of retrograde resonances. We therefore define a new set of canonical variables allowing to express correctly the resonance angles and obtain the Hamiltonian of a system harboring planets revolving in opposite directions. The acquiring of an analytical "rail" may notably contribute to a deeper understanding of our numerical investigation and provides the major structures related to the stability properties. A comparison between our analytical and numerical results is also carried out.