The boundary problems of physical geodesy

A method for determining the figure of the earth and its gravitational field from astrogeodetic and gravimetric data is developed, based on the solution of the linearized Molodensky problem at the geoid. In the linearized problem, an axisymmetric ellipsoid is chosen as a reference. This ellipsoid gives a good approximation of the earth and a suitable average value for the geopotential. The normal potential and the corresponding normal gravity are defined by solving an exterior Dirichlet problem. The nonlinear Molodensky problem is then treated on the basis of the linearized problem and the implicit function theorem.