Abstract Spiral density waves and spiral bending waves have been observed at dozens of locations within Saturn's rings. These waves are excited by resonant gravitational perturbations from moons orbiting outside the ring system. Modelling of spiral waves yields the best available estimates for the mass and the thickness of Saturn's ring system. Angular momentum transport due to spiral density waves may cause significant orbital evolution of Saturn's rings and inner moons. Similar angular momentum transfer may occur in other astrophysical systems such as protoplanetary discs, binary star systems with discs and spiral galaxies with satellites.

Introduction

Saturn's ring system was the first astrophysical disc to be discovered. When Galileo observed the rings in 1610, he believed them to be two giant moons in orbit about the planet. However, these “moons” appeared fixed in position, unlike the four satellites of Jupiter which he had previously observed. Moreover, Saturn's “moons” had disappeared completely by the time Galileo resumed his observations of the planet in 1612. Many explanations were put forth to explain Saturn's “strange appendages”, which grew, shrank and disappeared every 15 years. In 1655, Huygens finally deduced the correct explanation, that Saturn's strange appendages are a flattened disc of material in Saturn's equatorial plane, which appear to vanish when the Earth passes through the plane of the disc (Figure 1). The length of time between Galileo's first observations of Saturn's rings and Huygens' correct explanation was due in part to the poor resolution of early telescopes. However, a greater difficulty was recognition of the possibility and plausibility of astrophysical disc systems.