Dynamical evolution of the Uranian satellite system III. The passage through the7/4 MMR between Miranda and Ariel

Abstract

The passage through the $5/3$ mean-motion resonance between Ariel and Umbriel, two of Uranus's largest moons, still raises several open questions. Previous studies suggest that, in order to reproduce the current orbital configuration, Ariel must have had an eccentricity of approximately $\sim 0.01$ before the resonance encounter, which would prevent resonant capture. However, the rapid tidal circularization of Ariel's orbit implies that some prior mechanism must have excited its eccentricity before the resonance encounter. In this work, we performed a large number of simulations using an N-body integrator to assess whether the earlier $7/4$ mean-motion resonance between Miranda and Ariel could serve as a mechanism to increase Ariel's eccentricity. Our results show that, due to divergent migration, resonance capture does not occur. As the satellites cross the nominal resonance, Ariel's eccentricity is only excited to $3.4 \times 10^{-4}$, substantially smaller than the required value. Therefore, the $7/4$ mean-motion resonance is not a viable mechanism for increasing Ariel's eccentricity.