Accession Number : AD0702859

Title :   NONLINEAR SOLUTIONS OF THE GEODETIC BOUNDARY-VALUE PROBLEM,

Corporate Author : OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE

Personal Author(s) : Moritz,Helmut

Report Date : OCT 1969

Pagination or Media Count : 63

Abstract : A complete series solution of Molodensky's boundary value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient. This equivalence gives a physical explanation of the divergence of the Molodensky series. The exclusion of topographic masses to improve convergence is discussed, and computational formulas for height anomalies and deflections of the vertical are given. In the Appendix, structural similarities between the series of celestial mechanics and of physical geodesy are used to get an insight into the convergence behavior of these series. Another argument for the divergence of series of Molodensky type is given. (Author)

Descriptors :   (*EARTH(PLANET), GRAVITY), (*BOUNDARY VALUE PROBLEMS, POWER SERIES), CELESTIAL MECHANICS, GEODESICS, TERRAIN, INTEGRAL EQUATIONS, PERTURBATION THEORY, CONVERGENCE

Subject Categories : Geodesy
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE