Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

Abstract

Theory of the figures of equilibrium was developed actively during XIX century when causes making the form of observable massive celestial bodies (the Sun, planets, moons) almost ellipsoidal were discovered. The existence of exactly ellipsoidal figures was established. The gravitational potential of such figures can be presented as Laplace series. Its coefficients (Stoke’s constants In) are defined by a certain integral operator. The general term of the series was found in case of a homogeneous ellipsoid, and first few terms were found for several other mass distributions. Here we have found the general term of the series for an arbitrary mass distributions under condition that equidensits (surfaces of equal density) are homothetic to the outer surface of the ellipsoid of revolution. Simple estimates and asymptotics of In are also found. Refs 13.