Top-shaped Asteroids as Lens-shaped Bodies

Several asteroids are known to be shaped like toy tops. This paper models Top-Shaped Asteroids (TSAs) as Homogeneous Symmetric Lenses (HSLs), and derives their rotational, self-gravitational, and total energies as functions of their mass, density, and angular momentum. Then we raise, test, and ultimately reject the hypothesis that TSAs take the shape of lowest total energy, subject to the constraint that they keep the same mass, density, and angular momentum, while remaining HSLs. Other processes must control the shapes of TSAs. For completeness, we also describe a Core-Mantle Model for TSAs, as well as an Inverted Core-Mantle Model, and derive their self-gravitational energies, along with their rotational energies. The gravitational potential at the center of an HSL then is derived.