Planetary rings — nonequilibrium systems in space

Abstract

Planetary rings consist of myriads of granular particles in nearly circular orbits around the giant planets. Unlike assemblies of dense packed granules under terrestrial conditions, the equilibrium of the centrifugal and the gravitational force of the central body (planet) causes the particle ensemble to move almost freely like molecules in gases or fluids. Although this force balance is crucial for the dynamics of planetary rings, their unique wealth of structures is mainly determined by the dissipative character of inter-particle collisions. E. g. the extreme flatness of the rings - the ratio between the thickness and the tangential extend is about 10⁻⁶ ... 10⁻⁷ (for comparison, that of a razor blade is 1000 ... 10,000 larger) - is the consequence of a “quasi” equilibrium between viscous heating and the collisional “cooling” both caused by imperfect elastic collisions. In the same context, the very existence of stationary density waves, wakes, which are generated by the gravity of the numerous satellites of the “Giants”, as well as granular clustering as transient phenomenon are the result of the nonelastic collisions. Using new models of the collisional dynamics, we demonstrate the dynamical evolution of these structures by numerical N-body “experiments”. The main results of these computations are: granular clustering is not stable under conditions in a gravitational field of a planet, and structures generated by the gravity of satellites are only stationary if dissipation in the rings is taken into account.