On the rotation of co-orbital bodies in eccentric orbits

TL;DR

This paper presents an analytical study of how eccentricity and orbital perturbations influence the spin dynamics of co-orbital bodies, revealing multiple resonance families and conditions for chaotic rotation.

Contribution

It introduces a simple analytical model for co-orbital bodies' spin dynamics, identifying three families of spin-orbit resonances and their dependence on orbital parameters.

Findings

Three families of spin-orbit resonances identified.

Resonance widths and locations can be estimated.

Chaotic rotation occurs when resonant islands overlap.

Abstract

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.