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Normal mode oscillations in Saturn excite density and bending waves in the C Ring, providing a valuable window into the planet's interior. Saturn's fundamental modes (f modes) excite the majority of the observed waves, while…
Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time scales of 10^5 - 10^7 years. The debris ejected from such impacts re-accretes on to the ring, though often at a…
The problem of dynamical heating of galactic discs by spiral density waves is discussed using the shearing sheet model. The secular evolution of the disc is described quantitatively by a diffusion equation for the distribution function of…
Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative…
The ejecta discharged by impacting meteorites can redistribute a planetary ring's mass and angular momentum. This `ballistic transport' of ring properties instigates a linear instability that could generate the 100--1000-km undulations…
We present a simplified model in which we suggest that two important galactic problems -the magnetic field configuration at large scales and the flat rotation curve- may be simultaneously explained. A highly convective disc produces a high…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume…
The Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellite's secular…
Density waves in Saturn's rings are usually tightly wrapped spiral patterns generated by resonances with either Saturn's moons or structures inside the planet. However, between the Barnard and Bessel Gaps in the Cassini Division (i.e.…
Saturn's ionosphere is produced when the otherwise neutral atmosphere is exposed to a flow of energetic charged particles or solar radiation. At low latitudes the latter should result in a weak planet-wide glow in infrared (IR),…
The origin of rings around giant planets remains elusive. Saturn's rings are massive and made of 90-95% of water ice. In contrast, the much less massive rings of Uranus and Neptune are dark and likely to have higher rock fraction. Here we…
The viscous spreading of planetary rings is believed to be counteracted by satellite torques, either through an individual resonance or through overlapping resonances. For the A ring of Saturn, it has been commonly believed that the…
Saturns rings are known to show remarkable real time variability in their structure. Many of which can be associated to interactions with nearby moons and moonlets. Possibly the most interesting and dynamic place in the rings, probably in…
Saturn's C ring contains multiple spiral patterns that appear to be density waves driven by periodic gravitational perturbations. In other parts of Saturn's rings, such waves are generated by Lindblad resonances with Saturn's various moons,…
Voyager images and Cassini occultation data have previously shown that the behavior of the outer edge of Saturn's massive B ring is determined only in part by a static response to the 2:1 inner Lindblad resonance with Mimas. In Cassini…
We demonstrate that shadows cast on a proto-planetary disk can drive it eccentric. Stellar irradiation dominates heating across much of these disks, so an uneven illumination can have interesting dynamical effects. Here, we focus on…
The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini…
We predict how a remote observer would see the brightness variations of giant planets similar to Jupiter and Saturn as they orbit their central stars. We model the geometry of Jupiter, Saturn and Saturn's rings for varying orbital and…
Time-dependent meridional circulation and differential rotation in radiative zones are central open issues in stellar evolution theory. We streamline this challenging problem using the downward control principle of atmospheric science,…