The Dynamics of Planetary Rings

The discovery of ring systems around Uranus and Jupiter, and the Pioneer and Voyager spacecraft observations of Saturn, have shown that planetary rings are both more common and more complex than previously suspected. These ring systems, interesting in their own right, also serve as prototypes for more massive disk systems such as accretion disks and spiral galaxies occurring elsewhere in astronomy. Disks and rings are a natural consequence of dissipation in rotating systems. A cloud of debris surrounding a spherical planet settles into a flat circular ring because interparticle collisions dissipate energy but conserve total angular momentum. Since planets are oblate, only the component of angular momentum along the spin axis is conserved, and the flat ring lies in the equatorial plane. Collisions redistribute angular momentum among the particles and the ring spreads, transferring mass inward and angular momentum outward (Lynden-Bell & Pringle 1974). However, the spreading process occurs on a much longer timescale than the flattening process since the collision speeds in a flat ring are much lower than the orbital speeds (see Sections 2.2 and 5. 3). Spreading can be slowed by gravitational interactions with satellites; nevertheless, a ring cannot live forever and an important constraint on possible ring models is that they yield survival times at least comparable to the age of the solar system (cf. Sections 5, 6). This review was written in October 1981, shortly after the Voyager 2 encounter with Saturn. Analysis of the data from the Voyager encounters is not yet complete. Therefore the emphasis in this review is on the basic physical processes that occur in planetary rings, rather than on a detailed confrontation of theoretical predictions with observation. Table 1 lists some of the important properties of the planets with known ring systems. For the sake of brevity we shall refer to a series of papers we have written on rings (Goldreich & Tremaine 1978a, b, c, 1979a, b, c, 1980, 1981) as GT 1, . . . , GT 8.