Influence of a second satellite on the rotational dynamics of an oblate moon

TL;DR

This study investigates how a second satellite affects the rotational dynamics of an oblate moon, revealing that it can induce chaos and disrupt regular motion patterns, especially in low-eccentricity orbital systems.

Contribution

It introduces a simplified model to analyze the gravitational influence of a second satellite on an oblate moon's rotation, highlighting the transition to chaos and loss of structured bifurcation patterns.

Findings

Presence of a second satellite causes some regular trajectories to become chaotic.

Bifurcation diagrams lose their structured dependence on eccentricity when the second satellite is considered.

Periodicities and critical curves are destroyed by the gravitational influence of the second satellite.

Abstract

The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined. A simplified model, assuming the axis of rotation perpendicular to the (Keplerian) orbit plane, is derived. The differences between the two models, i.e. in the absence and presence of the second satellite, are investigated via bifurcation diagrams and by evolving compact sets of initial conditions in the phase space. It turns out that the presence of another satellite causes some trajectories, that were regular in its absence, to become chaotic. Moreover, the highly structured picture revealed by the bifurcation diagrams in dependence on the eccentricity of the oblate body's orbit is destroyed when the gravitational influence is included, and the periodicities and critical curves are destroyed as well. For demonstrative purposes, focus is laid on parameters of the Saturn-Titan-Hyperion system, and on oblate satellites on low-eccentric orbits, i.e. $e\approx 0.005$.