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Bulletin géodésique

, Volume 52, Issue 2, pp 159–164 | Cite as

Direct gravity formula for the Geodetic Reference System 1967

  • Dezsö Nagy
Article

Abstract

A Direct Gravity Formula, polynomial in latitude, has been obtained from the series expansion of the closed gravity formula of Somigliana by a telescoping procedure. The use of the 7 coefficient formula gives a result as accurate as the closed expression. With 6 coefficients it gives an order of magnitude better accuracy than that of the widely used Chebyshev approximation and with 5 coefficients a result that is accurate to better than that of the conventional form of computing theoretical gravity. The derived approximation is not only simpler than other forms, but also at least 11 and 17 times faster on the CDC CYBER 74 computer than the Chebyshev approximation and the closed gravity formula respectively.

Keywords

Power Series Chebyshev Polynomial Require Accuracy Conventional Form Economical Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. P.J. DAVIS, 1965: Interpolation and approximation. Blaisdell Publishing Company, New York.Google Scholar
  2. Geodetic Reference System 1967, International Association of Geodesy, Publication Speciale No. 3, ParisGoogle Scholar
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  4. C. LANCZOS, 1956: Applied Analysis, Prentice-Hall, Inc, Englewood Cliffs, New Jersey.Google Scholar
  5. E. MITTERMAYER, 1969: Numerical Formulas for the Geodetic Reference System 1967. Bulletino di Geofisica, Vol. XI, pp. 96–107.Google Scholar
  6. NBS, 1952: Tables of Chebyshev Polynomials Sn (x) and Cn (x). National Bureau of Standards, Applied Mathematics Series, No. 9. Washington, D.C.Google Scholar
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Copyright information

© Bureau Central de L'Association Internationale de Géodésie 1978

Authors and Affiliations

  • Dezsö Nagy
    • 1
  1. 1.Gravity and Geodynamics DivisionEarth Physics Branch Energy, Mines and ResourcesOttawaCanada

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