Volume 3 Issue 3
Authors: Gerassimos Manoussakis
Abstract: The vertical derivative of normal gravity at a specific point P is given by the Bruns formula. The Bruns formula contains the mean curvature of a chosen normal equipotential surface. To use the Bruns formula for a chosen point above the ellipsoid, the mean curvature of the normal equipotential surface passing through this point needs to be known. In this work a simple approach is presented to deal with this problem, by deriving a formula to express the mean curvature of the normal equipotential surfaces using three variables: geodetic latitude, geodetic longitude and geometric height. With this formula which is valid for points on the Earth’s surface, a more general form of the Bruns formula has been constructed which allows the determination of the vertical derivative of normal gravity. The general form of the Bruns formula can be extended for any point above the reference ellipsoid of revolution.
Keywords: Normal Gravity Field / Equipotential Surfaces / Normal Gravity Vector / Vertical Gradient