Cupid is Doomed: An Analysis of the Stability of the Inner Uranian Satellites

Abstract: We have explored the stability of the inner Uranian satellites using simulations based on the most recent observational data. We find that, across a wide range of mass assumptions, the system is unstable, resulting in the eventual crossing of orbits and probable subsequent collision of moons. Cupid and Belinda are usually the first satellites to cross orbits, and they do so on a time scale of 10^3-10^7 years. Cressida and Desdemona are generally the next pair to cross, on a time scale of 10^5-10^7 years. We show that the crossing times are highly sensitive to initial conditions and that Cupid's instability is related to its resonant interactions with Belinda. We also show that a previously discovered power law, which relates orbit crossing time to satellite mass, is valid across a wide range of masses. We generalize the power law to handle two unstable orbital pairs with overlapping lifetimes and show that it can be used to extend the time span of studies of orbital stability in a computationally efficient manner. Our results suggest that the current Uranian satellite system is in transition and that the moons will continue to collide and reaccrete for the foreseeable future.