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Some space gravity formulas and the dimensions and the mass of the Earth

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Summary

Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×1020 cm3 sec−2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.

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Authors and Affiliations

  1. Institute of Geophysics and Planetary Physics, of University of California, Los Angeles

    Michele Caputo

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  1. Michele Caputo
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Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste.

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Caputo, M. Some space gravity formulas and the dimensions and the mass of the Earth. PAGEOPH 57, 66–82 (1964). https://doi.org/10.1007/BF00879710

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