Investigating the combined effects of shape, density, and rotation on small body surface slopes and erosion rates

Based upon observational evidence and the derived shape-models from seven small Solar System bodies (Comets 103P Hartley 2 and 9P Tempel 1; Asteroids 433 Eros, 243 Ida, 951 Gaspra, and 25143 Itokawa; and the martian moon Phobos) we explore the existence of a self-correcting (negative-feedback) system in which disturbance-triggered downslope regolith flow is constantly working to erode the local surface topography of rotating, irregularly shaped, small bodies towards that of a flat, equipotential surface. This process is driven by the fact that erosion rates are very non-linear with respect to slope: becoming quite high as slopes approach the angle-of-repose, but also quite low when slopes are small. Four conditions are required for this system: (1) the mean rotational force is a significant fraction of the mean gravitational force; (2) a sufficiently thick, low cohesion, mobile regolith layer exists over most of the body's surface; (3) a downslope flow disturbance source is present, such as volatile activity on comets or impact-induced seismic shaking; and (4) a sufficient amount of time has occurred since the body's last major surface alteration. When these conditions are met, then the magnitude of the gravitational force for the body (and hence its bulk density) can be estimated by assuming that the body has reached an erosional 'saddle-point' in which either increasing or decreasing the body's rotation rate will increase erosion rates and drive the surface topography back towards a low-slope state. This technique yields bulk density estimates of 220 (140-520) kg m−3 for Comet 103P Hartley 2, and 1400 (930-2800) kg m−3 for Asteroid 951 Gaspra, neither of which have accurate density measurements via other means.