Dynamics of the Uranian and Saturnian satelite systems: A chaotic route to melting Miranda?

We argue that the anomalously large inclination of Miranda, the postaccretional resurfacing of both Miranda and Ariel, and the anomalously large eccentricities of the inner Uranian satellites indicate that resonant configurations once existed in the Uranian satellite system that have been since disrupted. Similar anomalies that cannot be accounted for by the present resonant configurations also exist in the Saturnian satellite system, and we suggest that temporary resonances existed in the past in that system as well. Using classical methods of analyzing the dynamics of resonance, we show how temporary capture into a second- or higher-order resonance can produce large increases in e and I on comparatively short time scales. However, these methods may not provide a complete description of resonances in the Uranian satellite system. Since values of J₂( R_p a)² for the inner Uranian satellites are small while their mass ratios, m M, are large, resonances in the Uranian system are not always well separated. For resonances that are not well separated, it is not possible to analyzed the dynamics using a disturbing function that is truncated to the extent that it contains only a single resonant argument. We have made some progress with this problem using the Cornell National Supercomputer to simulate the dynamics numerically. We find that capture into resonance may result in chaotic motion. We discuss two mechanisms that can be invoked to disrupt high-order resonances: the "spontaneous" disruption of chaotic resonances and the disruption of resonances due to the tidal damping of a satellite's eccentricity while the satellite is in a nonsynchronous spin state.