Definition
In geodesy, by a global model we mean a global gravity field model of the Earth. It is a mathematical function which describes the gravity field of the Earth in the three-dimensional space. The determination of the Earth’s global gravity field is one of the main tasks of geodesy: it serves as a reference for geodesy itself, and it provides important information about the Earth, its interior, and its fluid envelope for all geosciences.
Gravitation Versus Gravity
According to Newton’s law of gravitation (Newton, 1687), the magnitude of the attracting force F between two point-shaped masses m1 and m2 is
where l is the distance between the two masses and G is the gravitational constant. The vector of the attracting force of a body with the density ρ in the volume v acting onto a point-shaped sample mass m at the point P is given by the volume integral:
References and Reading
Barthelmes, F., 2013. Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models: Theory and Formulas Used by the Calculation Service of the International Centre for Global Earth Models (ICGEM). http://icgem.gfz-potsdam.de/ICGEM/, Scientific Technical Report STR09/02, Revised Edition, Jan 2013, GeoForschungZentrum Potsdam.
Barthelmes, F., and Köhler, W., 2012. International Centre for Global Earth Models (ICGEM). Journal of Geodesy, The Geodesists Handbook 2012, 86(10), 932–934.
Bronshtein, I., Semendyayev, K., Musiol, G., and Mühlig, H., 2007. Handbook of Mathematics. Berlin: Springer.
Förste, C., Bruinsma, S., Flechtner, F., Marty, J.-C., Lemoine, J.-M., Dahle, C., Abrikosov, O., Neumayer, K.-H., Biancale, R., Barthelmes, F., and Balmino, G., 2012. A preliminary update of the Direct approach GOCE Processing and a new release of EIGEN-6C. Paper presented at the AGU Fall Meeting 2012, San Francisco, 3–7 Dec, Abstract No. G31B-0923.
Heiskanen, W. A., and Moritz, H., 1967. Physical Geodesy. San Francisco: Freeman. A Series of Books in Geology [et al.].
Hobson, E. W., 1931. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge: Cambridge University Press.
Kaula, W., 1966. Theory of Satellite Geodesy: Applications of Satellites to Geodesy. Waltham: Blaisdell Pub. Co. (Special series of brief books covering selected topics in the Pure and applied sciences).
Merson, R. H., and King-Hele, D. G., 1958. Use of artificial satellites to explore the earth’s gravitational field: results from sputnik 2 (1957β). Nature, 182, 640–641.
Moritz, H., 1980. Geodetic reference system 1980. Bulletin Géodésique, 54, 395–405.
Newton, I., 1687. Philosophiae naturalis principia mathematica. J. Societatis Regiae ac Typis J. Streater.
Pick, M., Picha, J., and Vyskocil, V., 1973. Theory of the Earth’s Gravity Field. Praha: Academia.
Smith, J., 1997. Introduction to Geodesy: The History and Concepts of Modern Geodesy. New York: Wiley.
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Vaníček, P., and Krakiwsky, E. J., 1982. Geodesy: The Concepts. Amsterdam: North-Holland [et al.].
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Barthelmes, F. (2018). Global Models. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_43-2
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Global Gravity Field Models- Published:
- 11 March 2023
DOI: https://doi.org/10.1007/978-3-319-02370-0_43-3
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Global Models
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- 24 April 2018
DOI: https://doi.org/10.1007/978-3-319-02370-0_43-2
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Global Models- Published:
- 05 June 2015
DOI: https://doi.org/10.1007/978-3-319-02370-0_43-1