Stability maps for the 5/3 mean motion resonance between Ariel and Umbriel with inclination

TL;DR

This paper constructs stability maps for Uranus's satellites during the 5/3 mean motion resonance crossing, revealing how chaos develops with increasing energy and affecting orbital stability.

Contribution

It introduces a frequency analysis method to quantify chaos in the phase-space of the Uranian satellite system during resonance crossing.

Findings

Low-energy phase-space is mostly stable.

Chaotic regions expand with increasing energy.

Stable libration regions become localized at higher energies.

Abstract

The evolution of the five largest satellites of Uranus during the crossing of the 5/3 mean motion resonance between Ariel and Umbriel is strongly affected by chaotic motion. Studies with numerical integrations of the equations of motion and analysis of Poincar\'e surface sections provided helpful insights to the role of chaos on the system. However, they lack of a quantification of this chaos in the phase-space. Here, we construct stability maps using the frequency analysis method. We determine that for low energies (small eccentricity and/or inclinations), the phase-space is mainly stable. As the energy increases, the chaotic regions replace the stable motion, until only small, localized libration regions remain stable.