On the density of self-graviting disks having external potentials which coincide with gravitational potentials of ellipsoids of revolution

Abstract

Cosmic bodies conform to the state of relative equilibrium and can have ellipsoidal form. Various models are used for estimation their external gravitational potentials. Some model is a system of self gravitating disks. Its necessary to determine density of the circular disk having external potential which coincides with the gravitational potential of ellipsoid of revolution. In this case we have specific inverse gravitational problem which can be solved using theory of moments. The real solution for oblate ellipsoids and the imaginary solution for prolate ellipsoids are found.