Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System

TL;DR

This paper investigates the dynamics of the inner Uranian satellite system, revealing that three-body resonances play a significant role in orbital variations and system stability, with implications for understanding planetary satellite interactions.

Contribution

It demonstrates the importance of three-body resonances in the Uranian satellite system and provides a detailed analysis of their strength, frequency, and impact on orbital evolution.

Findings

Three-body Laplace angles show structured distributions near resonances.

Estimated three-body resonance libration frequencies are close to first-order two-body resonances.

Weak three-body resonances contribute to small coupled semi-major axis variations.

Abstract

Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values are distributed unevenly and have histograms showing structure, if the angle is associated with a resonant chain, with both pairs of bodies near first-order two-body resonances. Estimated three-body resonance libration frequencies can be only an order of magnitude lower than those of first-order resonances. Their strength arises from a small divisor from the distance to the first-order resonances and insensitivity to eccentricity, which make up for their dependence on moon mass. Three-body resonances associated with low-integer Laplace angles can also be comparatively strong due to the many multiples of the angle contributed from Fourier components of the interaction terms. We attribute small coupled variations in semi-major axis, seen throughout the simulation, to ubiquitous and weak three-body resonant couplings. We show that a system with two pairs of bodies in first-order mean-motion resonance can be transformed to resemble the well-studied periodically-forced pendulum with the frequency of a Laplace angle serving as a perturbation frequency. We identify trios of bodies and overlapping pairs of two-body resonances in each trio that have particularly short estimated Lyapunov timescales.