Waves in planetary rings

The Voyager spacecraft revealed the rings of Saturn to have an unexpected richness of structure. Many of the observed features have now been identified as collective effects arising from the self-gravity of the ring material. These effects include spiral density waves and spiral bending waves, the main topics of this review. Both kinds of waves were first discussed in the astronomical literature in connection with the dynamics and structure of spiral galaxies, and the present discussion contrasts the similarities and differences between the disks of galaxies and planetary rings. After developing the theory of free and forced waves of both types, the way in which the observed waves can be used as diagnostics to obtain crucial parameters that characterize the physical state of the rings is discussed.