A Note on Ellipsoidal Shape and Gravitational Potential First Order Relationships in Planetary Geodesy

We generalize the basic first order Clairaut formula to the case of a triaxial ellipsoid subject to rotational and tidal deformations from another body. We also prove and put together some relationships involving the gravitational static harmonics and the secular Love number of degree two, which are of wide use in planetary geodesy though difficult to find in textbooks.