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Computing the Earth Gravity Field with Spherical Harmonics

In: From Nano to Space

Author

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  • Michael Gerstl

    (Deutsches Geodätisches Forschungsinstitut, Bayerische Akademie der Wissenschaften)

Abstract

The expensive evaluation of the spherical-harmonic series expansion of the earth gravity field is optimised by transition to 4-dimensional coordinates. That makes disappear square roots and trigonometric functions. The singularity at the poles inherent in spherical coordinates is removed by the increase of dimension. Instead of the associated Legendre functions we obtain a basis of hypergeometric Jacobi polynomials that reproduces under derivation. Thus, the calculation of their derivatives cancels in the Forsythe summation technique; for the Clenshaw summation, the recursions of function value and derivatives are decoupled.

Suggested Citation

  • Michael Gerstl, 2008. "Computing the Earth Gravity Field with Spherical Harmonics," Springer Books, in: Michael H. Breitner & Georg Denk & Peter Rentrop (ed.), From Nano to Space, pages 277-294, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74238-8_20
    DOI: 10.1007/978-3-540-74238-8_20
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