Least square approximation by linear combinations of (multi)poles
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Date
1983-04
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
The purpose of the paper is to transcribe the standard procedure of expanding an external gravitational potential by trial functions (e.g., mass points, multipoles, spherical harmonics) from the classical spherical case to nonspherical models. The external gravitational potential of the earth is shown to be expandable into a series being convergent outside and on any closed surface completely surrounding the earth's surface in the outer space. In addition, for each compact subset of the outer space with positive distance to the earth's surface, the convergence is uniform. A numerical method of computing the external gravitational potential by truncated series expansions concludes the paper.