The External Gravity Field of a Rotating Spheroid to the order of e³

Abstract

The theory of the external gravity field of a rotating body bounded by a spheroidal equipotential surface is carried to terms of the order of e3. The potential is expanded in functions that are orthogonal in the space outside an oblate spheroid. It is found that terms of order e3 in the gravity formula and in the relation between J, e and m are mostly very small.