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A spherical harmonic representation of the ellipsoidal correction to the modified Stokes formula

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Abstract.

Ellipsoidal corrections to order e2 of the original and the modified Stokes formulas are presented in series of spherical harmonics. Numerical tests show that the ellipsoidal effect can reach several decimetres for an integration cap size of 10∘ in Stokes’ formula.

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Authors and Affiliations

  1. Royal Institute of Technology, Group of Geodesy, 100 44, Stockholm, Sweden

    L. E. Sjöberg

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  1. L. E. Sjöberg
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Correspondence to L. E. Sjöberg.

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Acknowledgements. The author is in debt to three unknown reviewers for their constructive criticisms of a previous version of the manuscript. A. Ellmann is acknowledged for the numerical study.

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Sjöberg, L. A spherical harmonic representation of the ellipsoidal correction to the modified Stokes formula. Journal of Geodesy 78, 180–186 (2004). https://doi.org/10.1007/s00190-004-0378-1

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  • DOI: https://doi.org/10.1007/s00190-004-0378-1

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