Torques exerted by a shallow fluid on a non-spherical, rotating planet

A general derivation is given for the torque exerted on a non-spherical planet by a shallow fluid, presenting in a unified form a number of results which are currently scattered through the literature, and deriving those results in a new way. This shows how the sum of gravitational and pressure torques can be rewritten as a “centrifugal” torque plus a topographic torque due to pressure acting on topography measured relative to the geoid. This clarifies the physics behind the use of spherical coordinate atmosphere and ocean models for calculating torques on the earth. It also shows why the total torque due to the earth’s equatorial bulge can be calculated as if it were a pressure torque on an “effective bulge” of approximately 11 km, the gravitational torque partially offsetting the actual pressure torque on the earth’s 21 km bulge.