Planetary and satellite three body mean motion resonances

TL;DR

This paper introduces a semi-analytical method to evaluate the strengths of three-body mean motion resonances in planetary systems, analyzing their dependence on orbital parameters and exploring their dynamical significance through numerical simulations.

Contribution

The paper presents a novel semi-analytical approach to compute three-body resonance strengths and applies it to planetary systems, including the Galilean satellites, highlighting the relevance of higher order resonances.

Findings

Zero order resonances are strongest at low eccentricity and inclination.

Higher order 3BRs become relevant in excited orbits.

Capture in a chain of two-body resonances is more probable than in a pure 3BR.

Abstract

We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the orbital parameters and the order of the resonance and we compare with previous studies. We confirm that for low eccentricity low inclination orbits zero order resonances are the strongest ones; but for excited orbits higher order 3BRs become also dynamically relevant. By means of numerical integrations and the construction of dynamical maps we check some of the predictions of the method. We numerically explore the possibility of a planetary system to be trapped in a 3BR due to a migrating scenario. Our results suggest that capture in a chain of two body resonances is more probable than a capture in a pure 3BR. When a system is locked in a 3BR and one of the planets is forced to migrate the other two can react migrating in different directions. We exemplify studying the case of the Galilean satellites where we show the relevance of the different resonances acting on the three innermost satellites.