# Dynamics of the Sharp Edges of Broad Planetary Rings - Astrophysics > Earth and Planetary Astrophysics

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Abstract: Abridged The following describes a model of a broad planetary ring whosesharp edge is confined by a satellite-s m^th Lindblad resonance LR. Thismodel uses a streamline formalism to calculate the ring-s internal forces,namely, ring gravity, pressure, viscosity, as well as a hypothetical dragforce. The model calculates the streamlines- forced orbit elements and surfacedensity throughout the perturbed ring. The model is then applied to the outeredge of Saturn-s B ring, which is maintained by an m=2 inner LR with thesatellite Mimas. Ring models are used to illustrate how a ring-s perturbedstate depends on the ring-s physical properties: surface density, viscosity,dispersion velocity, and the hypothetical drag force. A comparison of models tothe observed outer B ring suggests that the ring-s surface density there isbetween 10 and 280 gm-cm^2. The ring-s edge also indicates where the viscoustorque counterbalances the perturbing satellite-s gravitational torque on thering. But an examination of seemingly conventional viscous B ring models showsthat they all fail to balance these torques at the ring-s edge. This is duering self-gravity and the fact that a viscous ring tends to be nearlyperi-aligned with the satellite, which reduces the satellite-s torque on thering and makes the ring-s edge more difficult to maintain. Nonetheless, thefollowing shows that a torque balance can still be achieved in a viscous Bring, but only in an extreme case where the ratio of the ring-s bulk-shearviscosities satisfy ~10^4. However, if the dissipation of the ring-s forcedmotions is instead dominated by a weak drag force, then the satellite can exerta much stronger torque that can counterbalance the ring-s viscous torque.

Author: ** Joseph M. Hahn, Joseph N. Spitale, Carolyn C. Porco**

Source: https://arxiv.org/