Major satellites cause wavy deformation of Saturn's rings

Abstract

THE rings of Saturn consist of many solid particles, each revolving around Saturn as an independent satellite. Typical particle size or, more exactly, mean particle radius, ρ, has been estimated from radio interferometry and radar observations to be 2–15 cm (refs 1, 2)—consistent with a ring thickness of just over 10 m. However, the ring thickness z_o as determined photometrically is at least 4 orders of magnitude greater, at 1–3 km (refs 3, 4). The generally-accepted explanation for this difference is that the particle orbits are not fully coplanar, but inclined to the mean ring plane at appreciable angles i_p. However, such a model would be unstable. Indeed, particle collisions must be frequent as each particle crosses the mean plane twice for one revolution and the probability of meeting another particle is high. As a result of collisions, the energy of particle movement normal to the mean plane is dissipated, and so very soon the particle orbits must become coplanar, that is z_o→2ρ_max where ρ_max is very likely much less than 1 km. I show here that allowing for gravitational perturbations of particle orbits by satellites and the oblateness of Saturn one may obtain a model satisfying the observational data. The main features of the model are: (1) specific wavy deformation of the rings which thus appear twisted—this is the consequence of differential precession of particle orbits with i_p ≠ 0; (2) particle collisions are rare (and there is therefore only slow energy dissipation) because the neighbouring particles move in nearly the same phase.