Characterization of asteroid shapes and stability on their surface using super-ellipsoids

Abstract In this paper, the shapes of asteroids and the stability on their surfaces are characterized using super-ellipsoids, i.e. geometric shapes defined from the tri-axial ellipsoid equation replacing the exponent 2 by any positive exponent. The concept of dynamically equivalent equal-mass super-ellipsoid (DEEMSE) of a body is introduced as a homogeneous super-ellipsoid with equal principal moments of inertia and mass as the body. The overall shapes of high-resolution polyhedral shape models of Bennu, Ryugu, Vesta, Ceres and Eros are suitably described by their DEEMSE adjusting the exponent to best fit their surface. Next, for a spinning super-ellipsoid with a test-mass m on its surface, the minimum spin period to avoid detachment is computed along with the corresponding slope angle, which is the minimum friction angle to avoid sliding of m . The surface stability of different super-ellipsoidal bodies is analysed considering that the smaller the slope angle is, the less friction is required to avoid sliding, so the more stable the surface is. For fast rotation relative to the limit detachment rate, top-shaped bodies have more stable surfaces than ellipsoidal ones. For slower rotation, ellipsoids have more stable surfaces, even with zero slope angle (unconditional stability) under given conditions that nearly hold for Ceres and Vesta equivalent ellipsoids at their current spin rates. Those outcomes are compatible with rubble-pile outer asteroid structures reshaping to minimize surface tensions depending on the spin rate. Finally, the surface stability of Didymos is discussed as related to its bulk density and shape.