Least Square Approximation by Linear Combinations of Multi(Poles).
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEYING
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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 non-spherical 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 earths surface in the outer space. In addition, for each compact subset of the outer space with positive distance to the earths surface, the convergence is uniform. A numerical method of computing the external gravitational potential by truncated series expansions concludes the paper. Author
- Statistics and Probability