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K. Ohtsuki (U. Colorado), H. Tanaka (SWRI), S. Ida (Tokyo Inst. Tech.)
We investigate gap formation in planetary rings due to gravitational scattering by an embedded moonlet. Using three-body orbital integrations including effects of gravitational interactions and inelastic collisions, we estimate the viscosity of self-gravitating planetary rings with low optical depth. We find that the effect of gravitational encounters between ring particles greatly enhances the viscosity compared to non-gravitating cases, unless the sum of the radii of the two interacting particles is much larger than their mutual Hill radius. Using this numerical value of the viscosity based on three-body orbital integrations, minimum mass of a moonlet for gap formation is obtained as a function of the surface number density and the mass of ring particles as well as the distance from the primary. We also carry out N-body simulations for a system of ring particles and an embedded moonlet, where mutual gravity and inelastic collisions are taken into account, and find that the above estimate for the minimum mass of the moonlet for gap formation agrees with the results of N-body simulations.