We give a simple linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. A full analysis requires the possibility of perturbing all bodies. If the massive body is sufficiently dominant, then one can ignore perturbations to it. In this paper, we give a linear stability analysis based on perturbations to just one of the small ring bodies. Such an analysis could be justified by assuming that this one body has mass zero. But, we do not make this assumption. Therefore, it is surprising that the result we obtain agrees to within a factor of 2 with the result one obtains by considering perturbations to all ring bodies. We also give a simple back-of-the-envelope computation that shows that our stability mass threshold is consistent with the observed optical density of Saturn's rings.