Dynamical evolution of the Uranian satellite system I. From the 5/3 Ariel-Umbriel mean motion resonance to the present

Abstract

Mutual gravitational interactions between the five major Uranian satellites raise small quasi-periodic fluctuations on their orbital elements. At the same time, tidal interactions between the satellites and the planet induce a slow outward drift of the orbits, while damping the eccentricities and the inclinations. In this paper, we revisit the current and near past evolution of this system using a $N-$body integrator, including spin evolution and tidal dissipation with the weak friction model. We update the secular eigenmodes of the system and show that it is unlikely that any of the main satellites were recently captured into a high obliquity Cassini state. We rather expect that the Uranian satellites are in a low obliquity Cassini state and compute their values. We also estimate the current variations in the eccentricities and inclinations, and show that they are not fully damped. We constrain the modified quality factor of Uranus to be $Q_U^{\prime }=(1.2\pm 0.4)\times 10^5$, and that of Ariel to be $Q_A^{\prime }=(7\pm 3)\times 10^4$. We find that the system most likely encountered the 5/3 mean motion resonance between Ariel and Umbriel in the past, at about $(0.7\pm 0.2)$ Gyr ago. We additionally determine the eccentricities and inclinations of all satellites just after the resonance passage that comply with the current system. We finally show that, from the crossing of the 5/3 MMR to the present, the evolution of the system is mostly peaceful and dominated by tides raised on Uranus by the satellites.

Published at Icarus

References in corpus (16)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• Long-term tidal evolution of short-period planets with companions
• Six transiting planets and a chain of Laplace resonances in TOI-178
• Irregular Satellites of the Planets: Products of Capture in the Early Solar System
• Tidal evolution of hierarchical and inclined systems
• Tidal dissipation within hot Jupiters: a new appraisal
• TOI-1136 is a Young, Coplanar, Aligned Planetary System in a Pristine Resonant Chain
• On the equilibrium figure of close-in planets and satellites
• Secular and tidal evolution of circumbinary systems
• Stellar and planetary Cassini states
• Co-accretion + giant impact origin of the Uranus system: Tilting Impact
• Tidal evolution for any rheological model using a vectorial approach expressed in Hansen coefficients
• Can the Uranian Satellites Form from a Debris Disk Generated by a Giant Impact?
• A direct N-body integrator for modelling the chaotic, tidal dynamics of multi-body extrasolar systems: TIDYMESS
• Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel-Umbriel mean motion resonance
• Effect of the inclination in the passage through the 5/3 mean motion resonance between Ariel and Umbriel

Cited by in corpus (1)

• Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel-Umbriel mean motion resonance