Thermal forces on planetary ring particles: application to the main system of Saturn ,

Context. The motion of small particles in planetary rings is affected in the long-term by radiation forces. While the Poynting-Robertson effect has been extensively discussed and applied to the dynamics of micron-sized ring particles, studies of thermal self-acceleration of particles are only in their infancy. Aims. We extend the pioneering work of Rubincam (2006, Icarus 184, 532) by a more thorough analytical formulation of both plane-tary and solar thermal forces on ring particles. Methods. Within a sparse disk model we analytically compute both seasonal and diurnal variants of the thermal forces and we demonstrate that the diurnal effect components vanish for a sample of rapidly rotating particles with randomly oriented spin axes. For sufficiently slowly rotating ring particles, though, these diurnal components might significantly modify the expected planetocentric secular drift rates of their orbits. We also take into account the orbital effects of Poynting-Robertson drag that begin to dominate the thermal forces for particles with sizes ≤5 mm. Our formulation of the Poynting-Robertson drag is the first to account properly for the influence of the planetary shadow. Results. We critically review the previous suggestion that Saturn’s A and B ring boundaries might correlate with radiative null-torque orbits of small particles. Using the best estimates of optical and thermal parameters of Saturn’s ring particles, we show that the mil-limetre to several centimetre size particles mostly drift inward to the planet with a characteristic radial speed νr ∼ 3 × 10−6 cm/s