VARIATIONAL-METHODS TO CALCULATE THE HYDROSTATIC STRUCTURE OF ROTATING PLANETS

Two variational strategies to calculate the internal flattening induce d in the structure of slowly rotating hydrostatic planets are discusse d. In the first procedure, the minimization of energy fixes the physic al coefficients of a polynomial that describes the dependence of the f lattening on depth. In the second, the planet is assumed to be divided into thin equidensity shells, and the condition of minimum energy lea ds to an algebraic method that can compete with the usual one based on Clairaut's equation. These methods are applied to the Earth. The diff erences between them and other previous variational strategies are dis cussed.