LAUSR

Abstract It has long been known that the gravitational potential on the surface of a non-rotating, homogeneous tri-axial ellipsoid is lowest at the ends of its short axis, and highest at the ends of its long axis. More recently, it also has been shown that its surface gravity is strongest at the ends of its short axis, and weakest at the ends of its long axis. Here I show that the latter result is rather robust, and still holds for freely rotating homogenous ellipsoids, and for those which are tidally locked satellites, as well as for a wide range of layered structures. However, the former fact does not apply to rapidly rotating homogeneous ellipsoids and tidally locked satellites; the extrema and saddle points of their effective gravitational potential and surface slope depend on the shape and rotation rate of the ellipsoid in complicated ways. Both of the above results are illustrated herein by sample maps of the surface potential, gravity, and slope of freely rotating homogeneous elllipsoids, as well as those which are tidally locked satellites. The ends of the principal axes of an ellipsoid are equilibrium points, but their stability or instability to small displacements also depends on the shape of the ellipsoid, its rotation rate, and surface friction in complicated and unexpected ways, also illustrated herein. I use the above results to classify ellipsoids by shape alone (assuming constant densities). I classify free rotators into three classes and two one-parameter families, and use this system to classify 99 asteroids with known shapes. I also classify locked satellites into four classes and three one-parameter families; then I use this system to classify 20 small moonlets with known shapes, with a particular application to Mars’ satellite Phobos. The results of this study have implications for the geology and geodesy of small bodies throughout the Solar system.