The narrow rings of Jupiter, Saturn and Uranus

The origin of the newly discovered narrow ring systems around Jupiter, Saturn and Uranus is considered. It is pointed out that both the Uranian and Jovian ring systems have mean orbital radii of 1.8 planetary radii and lie within the Roche zones of their respective planets, and it is suggested that the Jovian ring is the product of the disintegration of a satellite that entered the Roche zone, and that large numbers of small particles are now in horseshoe orbits about the Lagrangian equilibrium points of the remnant chunks. Analysis of the path of a ring particle in a horseshoe orbit is shown to result in ring structures in agreement with those observed for the circular rings of Jupiter and the highly eccentric ring of Uranus. The stability of these ring systems is then considered, and it is suggested that the F ring of Saturn, which lies outside the Roche zone, represents primordial matter not yet accreted by small satellites just inside the Mimas first-order resonances.