Regularization of the expression for a gradient of Earth’s gravity potential in the local ellipsoidal coordinate system

Abstract

The results of further development of the theory of modeling the Earth’s gravitational field by series in ellipsoidal harmonics, which better approximate the Earth’s gravity potential as compared with traditional series of spherical harmonics, are presented. In the preceding study of the authors, new expansions with respect to ellipsoidal harmonics were constructed for the gravity potential and its derivatives. They depend on the hypergeometric Gauss series having the higher rate of convergence in comparison to the previously used series of other authors. In this work, the further improvement of convergence of the hypergeometric series is performed, and based on the results, the expression for the Earth’s gravity potential on the surface of the reference ellipsoid is constructed in the local north-oriented ellipsoidal coordinate system. This expression has no analytical singularities in contrast to previously known expansions that cannot be applied in polar regions on the Earth’s surface and in outer space. The new expression for the potential gradient may be used for constructing global models of the Earth’s gravitational field which take into account the data gathered in the polar regions.