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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

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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.

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  1. Department of Geodesy and Geoinformatics, Stuttgart University, 70174, Stuttgart, Germany

    Erik W. Grafarend

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  1. Erik W. Grafarend
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Correspondence to Erik W. Grafarend.

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Dedicated to Willi Freeden’s 65th Birthday.

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Grafarend, E.W. 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. Int J Geomath 6, 101–140 (2015). https://doi.org/10.1007/s13137-014-0068-y

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