ANCIENT PLANETARY RINGS, VOLUME, MASS AND DENSITY

Quasi-Primitive Rings and Density Theory

Structuring eccentric-narrow planetary rings

A simple and general description of the dynamics of a narrow-eccentric ring is presented. We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global m = 1 mode, which can be seen as originating from a standing wave superposed on an axisymmetric background. We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the ...

Dense planetary rings and the viscous overstability

This paper examines the onset of the viscous overstability in dense particulate rings. First, we formulate a dense gas kinetic theory that is applicable to the Saturnian system. Our model is essentially that of Araki and Tremaine (1986), which we show can be both simplified and generalised. Second, we put this model to work computing the equilibrium properties of dense planetary rings, which we...

Apse Alignment of Narrow Eccentric Planetary Rings

The boundaries of the Uranian ǫ, α, and β rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of Uranus induces differential precession. We propose that rigid precession is maintained by a balance of forces due to ring self-gravity, planetary oblateness, and interpart...

Three-Dimensional Dynamics of Narrow Planetary Rings

Narrow planetary rings are eccentric and inclined. Particles within a given ring must therefore share the same pericenter and node. We solve for the threedimensional geometries and mass distributions that enable the Uranian α and β rings, and the Saturnian Maxwell and Colombo (Titan) rings, to maintain simultaneous apsidal and nodal lock. Ring self-gravity, interparticle collisions, and the qua...