Density distortion within a rotating body

This paper ascertains the distortion of the density distribution within a self-gravitating body in hydrostatic equilibrium under the influence of rotation.For this purpose, the Poisson equation has been solved by using the undistorted density profile _o(a) within the Laplacian to obtain the distorted density (a, ). The Laplacian has been expressed in terms of a system of curvilinear coordinates for which the equipotential surfaces constitute a family of fundamental surfaces.In performing the requisite algebraic manipulations, the Clairaut and Radau equations developed in a previous paper (Lanzano, 1974) were utilized to eliminate the derivatives of the elements pertaining to the equipotential surfaces.The density distortion has been obtained up to third-order terms in a small rotational parameter.