In contrast, the orbits of these moons are fairly well known, and they present an interesting dynamical system. The
We have numerically integrated approximately 500 systems of mutually gravitating bodies which were based on subsets of orbits are nearly coplanar and circular, as is common for the uranian satellite system. In each run within a set, the satel-''regular'' planetary satellites. However, several of the orlite masses were initially multiplied by a common mass enbits are quite closely spaced, with the 6 middle moons hancement factor m f . The simulations were terminated at the being concentrated within a range of less than 20% in ''crossing time,'' t c , when mutual perturbations excited eccensemimajor axis. Although these moons are quite tiny, the tricities sufficiently large for orbits of a pair of bodies to cross. separations between their orbits are so small that dynami-For a given set, t c is well represented as a power law function cal scaling arguments suggest that the current configuration of m f of the form t c โซุโฌ โคm f โฃ , where the values of the constants may not be stable over the age of the solar system (Lissauer โฃ and โค depend on the system; values of โฃ ranging from ุ13 1995). Moreover, from the cratering records observed on to ุ3 are found here. This mass-scaling relationship may have Uranus' classical moons, Smith et al. (1986) estimate that wider implications as a diagnostic for the stability of many orbital configurations. some of these small inner moons have lifetimes against We find that satellite systems which orbit around a significatastrophic disruption by impacts of only 1-2 Gyr. In cantly oblate planet are slightly more stable than identical addition to being of interest in their own right, the inner systems in orbit about a spherically symmetric planet, presumuranian moons can serve as a natural prototype for a class ably because the precession induced by planetary oblateness of orbital configurations which may currently exist in extraprecludes secular resonances between the moons. Extrapolation solar planetary and satellite systems and which may have of our results suggests that the five classical satellites of Uranus existed during the late stages of planetary growth in our are stable over the age of the solar system (in the absence of own system.
tidal torques from the planet). Uranus' inner moons appear far Uranus also has five ''classical'' moons (discovered prior less stable, with Desdemona conceivably colliding with either Cressida or Juliet sometime within the next 4-100 million years to Voyager), whose orbits lie exterior to the 10 newly (provided the satellite masses adopted here are within a factor discovered satellites. Dynamical mass estimates are availof 2 of the correct values). Thus, at least some of Uranus' able for all 5 classical moons. The classical satellites are inner moons are probably ''young'' by geological standards. significantly larger and more distant from one another than Implications for the origin and evolution of these satellites are are the new moons. Moreover, as they orbit farther from discussed.