On the radial structure of planetary rings

Abstract

ABSTRACTA ring of particles in orbit about a planet experiences a viscous shear stress due to the radial gradient of orbital velocity. This stress tends to spread the ring with time. At low optical depth (τ ≲ 0.5), and again at high optical depth (τ ≳ 2), the shear stress is an increasing function of optical depth. In the intermediate range (0.5 ≲ x ≲ 2), stress may decrease with increasing τ, leading to a diffusive instability which will tend to break an Initially uniform ring into ringlets of high and low optical depths.