ORBITAL STABILITY OF THE URANIAN SATELLITE SYSTEM

We have numerically integrated approximately 500 systems of mutually g ravitating bodies which were based on subsets of the uranian satellite system. In each run within a set, the satellite masses were initially multiplied by a common mass enhancement factor m(f). The simulations were terminated at the ''crossing time,'' t(c), when mutual perturbati ons excited eccentricities sufficiently large for orbits of a pair of bodies to cross. For a given set, t(c) is well represented as a power law function of m(f) of the form t(c) = beta m(f)(alpha), where the va lues of the constants alpha and beta depend on the system; values of a lpha ranging from -13 to -3 are found here. This mass-scaling relation ship may have wider implications as a diagnostic for the stability of many orbital configurations. We find that satellite systems which orbi t around a significantly oblate planet are slightly more stable than i dentical systems in orbit about a spherically symmetric planet, presum ably because the precession induced by planetary oblateness precludes secular resonances between the moons. Extrapolation of our results sug gests that the five classical satellites of Uranus are stable over the age of the solar system (in the absence of tidal torques from the pla net). Uranus' inner moons appear far less stable, with Desdemona conce ivably colliding with either Cressida or Juliet sometime within the ne xt 4-100 million years (provided the satellite masses adopted here are within a factor of 2 of the correct values). Thus, at least some of U ranus' inner moons are probably ''young'' by geological standards. Imp lications for the origin and evolution of these satellites are discuss ed. (C) 1997 Academic Press