An integrable model for first-order three-planet mean motion resonances

TL;DR

This paper introduces the first general integrable model for first-order three-planet mean motion resonances, enhancing understanding of their dynamics and implications for planetary system stability.

Contribution

It develops a novel one degree of freedom Hamiltonian model for first-order three-planet MMRs, extending previous two-planet models to three-body resonances.

Findings

The model accurately matches numerical simulations.

Applicable to any mass ratio and first-order resonance.

Provides insights into planetary system stability.

Abstract

Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one degree of freedom Hamiltonian, little is known of the exact dynamics of three-bodies resonances besides the cases of zeroth-order MMRs or when one of the body is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one degree of freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application I show how this model could improve our understanding of the capture into MMRs as well as their role on the stability of planetary systems.