Horsing around on Saturn.

On the basis of simple statistical mechanical models, the prevailing view of the rings of Saturn is that they are unstable and must therefore have been formed rather recently. In this paper, we argue that the Saturn rings and inner moons are in much more stable orbits than previously thought and, therefore, that they likely formed together as part of the initial formation of the solar system. To make this argument, we give a detailed description of so-called horseshoe orbits and show that this horseshoeing phenomenon greatly stabilizes the rings of Saturn. This paper is part of a collaborative effort with E. Belbruno and J.R. Gott III. For a description of their part of the work, see their papers in these proceedings.