Orbital evolution of the Uranian moons in a fast-migration regime

The Uranian satellite system has recently attracted increased interest due to its complex dynamical and geological history, particularly in the context of the proposed high-priority NASA Flagship mission to Uranus. To date, Voyager 2 remains the only spacecraft to have explored the system, providing observations of the five major regular moons: Miranda, Ariel, Umbriel, Titania, and Oberon. These moons display evidence of both ancient, heavily cratered terrains and signs of more recent resurfacing events. The nature of these moons arises from differences in their formation and composition, as well as from their coupled orbital and thermal evolution – each aspect influencing the other over time. Among the various forces at play, tidal interactions are particularly significant. Tides introduce dissipation in the system through friction processes, in which orbital and rotational energy is dissipated as heat in either (or both) the surface or interior of a planet or satellite. Additionally, moons within the system gain angular momentum from their hosting planet, resulting in an outward orbital migration. Variations in orbital distance can lead to encounters with mean-motion resonances. Although the system currently lacks any mean-motion resonance, the non-negligible orbital eccentricities of the moons and Miranda’s high inclination suggest that past resonant interactions may have played a significant role in shaping their current orbits (Tittemore & Wisdom 1988, 1989, 1990; Ćuk et al. 2020; Gomes & Correia 2024).

Past studies of the orbital evolution of the Uranian moons adopted a medium-low tidal dissipation rate for Uranus, as predicted by equilibrium tide theory (Goldreich & Soter 1966). Previously proposed evolutions constrained the value of Uranus's dissipation within ranges that would prevent capture into the 2:1 mean-motion resonance between Ariel and Umbriel. The reason, as shown by Tittemore & Wisdom (1990), is that it seems not to be possible to escape such a resonance, which would be incompatible with the present configuration.

However, recent theoretical developments and measurements indicate that Uranus may exhibit a higher tidal dissipation rate than previously assumed (e.g., Nimmo 2023; Jacobson & Park 2025). This enhanced dissipation leads to a faster orbital migration of its satellites, consistent with the so-called resonance locking, as proposed by Fuller et al. (2016). Consequently, resonant interactions that were previously considered unlikely now need to be reassessed. In particular, Ariel’s fast migration implies that crossing the 2:1 mean-motion resonance with Umbriel is almost certain and may have occurred in quite recent times (within the last 1 Gyr). This fact indicates that the entire orbital history of the Uranian moon system may need to be revised.

In this presentation, we focus on the potential crossing of the 2:1 mean-motion resonance between Ariel and Umbriel, where Ariel undergoes a rapid migration. Capture into this strong resonance may have induced significant tidal heating within Ariel, potentially explaining its resurfacing. To investigate this resonant encounter, we present numerical simulations based on an ad hoc dynamical model. Assuming a resonance locking regime, we show the possible outcomes of the resonant encounter. In particular, we find that for small initial eccentricities, the moons are always captured into resonance, as already described in Tittemore & Wisdom (1990). In addition, we explore mechanisms for exiting the 2:1 resonance, possibly involving resonant perturbations from other moons of the system. We present evolution histories that depend primarily on Ariel’s tidal dissipation rate, the timing of the Ariel-Umbriel resonance capture, and the initial orbital elements of the other satellites. We propose a parametric study, dependent on tidal parameters, capable of reproducing orbital element distributions consistent with the current orbital configuration of the system.

As a product of the above analysis, we derive constraints on the tidal parameters of Uranus and its moons. This study may therefore serve as a valuable input for future space missions – such as the Uranus Orbiter and Probe space mission concept – by guiding both astronomical and geophysical measurements. A higher tidal dissipation is expected to have a more significant impact on orbital dynamics and related observational uncertainties, potentially producing detectable signatures that future missions could confirm or rule out.

 

References:

Ćuk, M., El Moutamid, M., & Tiscareno, M. S. (2020). Dynamical history of the Uranian system. The Planetary Science Journal, 1(1), 22.

Fuller, J., Luan, J., & Quataert, E. (2016). Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems. Monthly Notices of the Royal Astronomical Society, 458(4), 3867-3879.

Goldreich, P., & Soter, S. (1966). Q in the Solar System. Icarus, 5(1-6), 375-389.

Gomes, S. R., & Correia, A. C. (2024). Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel–Umbriel mean motion resonance. Icarus, 424, 116254.

Jacobson, R. A., & Park, R. S. (2025). The Orbits of Uranus, Its Satellites and Rings, the Gravity Field of the Uranian System, and the Orientation of the Poles of Uranus and Its Satellites. The Astronomical Journal, 169(2), 65.

Nimmo, F. (2023). Strong tidal dissipation at Uranus?. The Planetary Science Journal, 4(12), 241.

Tittemore, W. C., & Wisdom, J. (1988). Tidal evolution of the Uranian satellites: I. Passage of Ariel and Umbriel through the 5:3 mean-motion commensurability. Icarus, 74(2), 172-230.

Tittemore, W. C., & Wisdom, J. (1989). Tidal evolution of the Uranian satellites: II. An explanation of the anomalously high orbital inclination of Miranda. Icarus, 78(1), 63-89.

Tittemore, W. C., & Wisdom, J. (1990). Tidal evolution of the Uranian satellites: III. Evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities. Icarus, 85(2), 394-443.