Resonance Effects in Planetary Rings II Narrow Ringlets and Satellites

Abstract

The discovery on 1977 March 10 of the Uranian rings caused enormous interest amongst researchers. Indeed, the origin and stability of narrow elliptical rings turned out to be very problematic. First of all, a narrow ring must spread out because of the exchange of angular momentum between colliding particles — after a number of centuries, with a characteristic “viscous” time t v ~ (vk 2)−1 — increasing its width and diminishing the steepness of its edges. Secondly, the asphericity of the Uranian field causes a precession of elliptical orbits at a rate which depends on the major semi-axis. The difference in the precession of particles at the outer and the inner edges of the ring — differential precession — must after a few hundred years separate the lines of apsides of the particles, destroy an elliptical narrow ring and form a circular, wider ring. Nonetheless, the rings have not spread out and have clearly defined boundaries, and precess as a whole.