Stokes’ Formula

Stokes’ formula is a fundamental integral equation in physical geodesy that relates gravity anomalies on the Earth’s surface to the geoid undulation with respect to a reference ellipsoid. It expresses the geoid height as a surface integral of gravity anomalies weighted by a specific kernel function (Stokes’ kernel) over the sphere.

In geodesy, Stokes’ formula provides the theoretical basis for geoid determination from terrestrial, airborne, and satellite gravity observations. It enables the transformation of gravity field information into geoid models, which are essential for converting GNSS-derived ellipsoidal heights into physically meaningful orthometric heights and for the realization of precise height systems.