We consider a dilute axisymmetric planetary ring consisting of identic
al smooth inelastic spheres. We first obtain approximate analytic expr
essions relating the components of the second moment of the velocity d
istribution to the coefficient of restitution of a particle collision.
Then we employ a form of the energy flux appropriate for inelastic pa
rticles and calculate the variation of density and mean kinetic energy
(i.e., the granular temperature) normal to the ring plane. We find th
at the density distribution differs only slightly from that correspond
ing to a uniform temperature. Finally, we use these results together w
ith a boundary condition obtained from the 6/7 Lindblad resonance at t
he outer edge of Saturn's A-ring to relate the midplane value of the g
ranular temperature, the midplane value of the solid volume fraction,
and the particle diameter to either the coefficient of restitution or
the optical depth. (C) 1994 Academic Press, Inc.