Bombardment of planetary rings by meteoroids: General formulation and effects of Oort cloud projectiles

Abstract

We present a general solution for the angular distribution of the intensity and velocity of interplanetary projectiles as they impinge on a planetary ring system, given the original distribution in inertial space. Our solution lends itself immediately to three results of importance. First, we demonstrate a variation with orbital longitude of an impact-velocity-weighted impact rate of cometary meteoroids in planetary rings. The largest rate of energetic impacts occurs at orbital longitudes near solar midnight, consistent in location and form with observed creation rates of “spokes” in Saturn's rings. This provides support for spoke formation hypotheses which rely on meteroid impact. Second, we determine the angular distribution of the intensity of ejecta which result from the bombardment of a planetary ring composed of centimeter- to meter-sized particles by interplanetary meteroids in the subcentimeter-size range. We do this using a radiative transfer formalism. The angular distribution of ejecta resulting from the bombardment of a single target particle is first obtained as a function of angle from a single incident direction. In this step, we incorporate results from laboratory studies of nondisruptive hypervelocity impacts into granular and powdery surfaces. This single particle “phase function” is part of a standard expression for the net scattering function of the layer as a whole, which accounts for the escape probabilities of ejecta emerging from impacts occurring at different depths within the ring layer. We assume that multiple scattering terms resulting from impacts into nearby particles by the more slowly moving ejecta are negligible. Finally, the net scattering function of the layer is integrated over the angular distribution of the incoming meteoroids, which is determined in the frame of an orbiting ring particle by accounting for aberration effects arising from the orbital motion of the ring particle and its parent planet. Our calculated ejecta distributions are incorporated into evolutions of ring mass density and radial structure in a companion paper (Durisen et al. 1989, Icarus, 80 136–166). Third, we calculate the radial drift velocity of a planetary ring of arbitrary optical depth which results from two factors: simple mass loading, and aberration-induced asymmetry in the impact rate. Bombardment of ring systems at the currently accepted rate of interplanetary meteoroid flux leads to an inward radial drift of several cm yr −1 in regions of moderate optical depth. This rate is large enough for the Uranian α and β rings, and the entire C ring of Saturn, to fall into the atmosphere of the parent planet in about 10 8 years under only the known flux of projectiles on Oort cloud orbits. These effects can vary significantly with the orbital distribution of the projectile population. In this paper, we present results for projectiles with “Oort cloud” orbits. In a subsequent paper, we will present the results anticipated for projectiles in “local family” prograde, low inclination orbits.