where

and

Here, , , are spherical coordinates whose symmetry axis coincides with the axis of rotation. Moreover, is the fluid pressure, the mass density, the gravitational potential, the centrifugal potential, and the angular rotation velocity. Taking the curl of Equation (D.1), we deduce that , and, hence, that

Let us assume that the contours of are spheroidal, so that

where

Here, and are the mean radius and ellipticity of the density contour , respectively. Furthermore, it is assumed that . (See Section 3.6). It follows from Equations (D.4) and (D.5) that

The aim of this appendix is to deduce the relationship between the degree of flattening of the body, its rotational angular velocity, and its moment of inertia about its rotation axis.