Derivation of Theoretical Gravity Model on the Clarke 1880 Ellipsoid for Practical Local Geoid Model Determination

Abstract

The application of gravity anomalies for gravimetric geoid model determination has necessitated the computation of normal gravity on the WGS 84 ellipsoid using the International Gravity Formula. For local gravimetric geoid model determination, the gravity anomalies are computed on the local ellipsoid adopted for geodetic computation in the area/region of study. To determine precise local gravimetric geoid model in countries where Clarke 1880 ellipsoid is adopted for geodetic computation, the theoretical gravity must be computed on the adopted geodetic computation surface. As a result, this paper derives a local theoretical gravity model on the Clarke 1880 ellipsoid for practical local geoid model determination. The model was derived using the Clarke 1880 ellipsoid parameters, angular velocity, gravitational constant and the Somiglinana's closed formula for normal gravity. The derived model was presented in two forms, model A and model B. The two forms of the derived model were compared to determine their suitability as well as agreement. The comparison results show that the two forms of the model agree. Thus, any of the model forms can be applied for accurate normal gravity computation where Clarke 1880 ellipsoid is adopted as a computation surface.