Computer Simulations of Planetary Rings

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Contribution to Book

Publication Date



The local dynamics of planetary rings is governed by the orbital motion, the frequent impacts between ring particles, their mutual self-gravity, and the perturbations exerted by external satellites and embedded moonlets. In Saturn's dense A and B rings the particles collide ~100 times per orbital revolution. Although the orbital velocities are ~20 km/s, the random velocities related to orbital eccentricities and inclinations are small, of the order of few mm/s (this corresponds to a ring vertical thickness of few tens of meters, excluding strongly perturbed regions). Such gentle impacts do not lead to fragmentation, but still dissipate a significant fraction of random kinetic energy in each collision. This loss is balanced by the viscous gain of energy from the orbital motion around the planet, resulting in a local steady-state in a timescale of few tens of impacts per particle. Characteristics of this energy balance (such as velocity dispersion, geometric thickness, and viscosity) are determined by the frequency and elasticity of impacts, and by the internal density and size distribution of particles. In much longer timescales the ring radial evolution is governed by viscous evolution. Depending on the viscosity–density relation following from the energy balance, the ring can be either stable or unstable against the viscous growth of local perturbations. For example, dense rings composed of quite inelastic particles can become viscously overstable, while less dissipative particles may be prone to viscous instability.

Document Object Identifier (DOI)



Matthew S. Tiscareno, Carl D. Murray


Cambridge University Press





Publication Information

Planetary Ring Systems: Properties, Structure, and Evolution

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