ON THE VERTICAL STRUCTURE OF DILUTE PLANETARY RINGS

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.