The reference figure of the rotating earth in geometry and gravity space and an attempt to generalize the celebrated Runge–Walsh approximation theorem for irregular surfaces

Original Paper

Abstract

First, we discuss the Reference Figure of the Earth of type plane, sphere, ellipsoid, regular topography, irregular topography, fractal geometry. The Standard Reference of the Earth, the Telluroid, is derived from the anharmonic Somigliana–Pizzetti gravity field, also called World Geodetic Datum, strongly influenced by the Rotation of the Earth in terms of spheroidal coordinates/spheroidal gravity field. In detail, we treat the Telluroid Mapping based on a two step procedure of type (astronomic longitude/astronomic latitude, modulus of gravity). The result is an algebraic equation of degree ten. Second, we discuss the important Runge–Walsh Approximation Theorem in the context of singularities of the Earth Geometry and Gravity Field as mentioned by Bocchio–Livieratos–Grafarend. The example by Sanso that a grain of sand blows up the series expansion of the external gravity field is of key importance.

Keywords

Singular points in the Earth topography Singular points in the Earth gravity field Equilibrium figures Anholonomity Somigliana–Pizzetti gravity field Transformation of differential manifolds Runge–Walsh approximation theorem: limits 

Mathematics Subject Classification

86A30 31A05 35J56 51H25 53A05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Geodesy and GeoinformaticsStuttgart UniversityStuttgartGermany

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