On the gravitational potential energy of the Earth

: pp. 34 – 42
Department of Higher Geodesy and Astronomy, Lviv Polytechnic National University

To estimate the gravitational potential energy of Earth E, the 3D distribution of the density of the ellipsoidal planet together with its accuracy estimate is used. It was the use of the latter that allowed E to be evaluated on the basis of only the radial distribution of density in the form of its continuous and piecewise continuous models: Legendre-Laplace, Rosh, Bullard, and Gauss. The result is an inequality for E with an upper bound EH for a homogeneous distribution and the lower edge of EGauss, which corresponds to the Gaussian distribution for Earth's density. The main E ratings give a good agreement with EGauss: as in the case of E, based on the Rosh model with the 6 main drops of bounce, and the E estimates corresponding to the 4 most simple models with one jump of density at the boundary of the kernel-mantle.

  1. Dziewonski A.M. and Anderson D.L. (1981) Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, Vol. 25, pp. 297-356.
  2. Grafarend E., Engels J., and Varga P. (2000) The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation. Journal of Geodesy, Vol. 74, pp. 519-530.
  3. Groten E. (2004) Fundamental parameters and current (2004) best estimates of the parameters of common relevance to astronomy, geodesy and geodynamics. Journal of Geodesy, Vol. 77, pp. 724-731.
  4. Marchenko A.N. (2000) Earth’s radial density profiles based on Gauss’ and Roche’s distributions. Bolletino di Geodesia e Scienze Affini, Anno LIX, No.3, pp. 201-220.
  5. Marchenko A.N. and Schwintzer P. (2003) Estimation of the Earth's tensor of inertia from recent global gravity field solutions. Journal of Geodesy, Vol. 76, p. 495-509.
  6. McCarthy D. and Petit G. (2004) IERS Conventions (2003), IERS Technical Note, No.32, Verlag des Bundesamts fur Kartographie und Geodasie, Frankfurt am Main, 2004.
  7. Mescheryakov G.A. (1973) On the estimation of some values characterizing the internal gravity field of the Earth. Geodesy, cartography and aerophotosurveying, Lvov, No. 17, pp. 34-40 (in Russian).
  8. Mescheryakov G.A. (1977) On the unique solution of the inverse problem of the potential theory. Reports of the Ukrainian Academy of Sciences, Kiev, Series A, No. 6, pp. 492-495 (in Ukrainian).
  9. Mescheryakov G.A. (1991) Problems of the potential theory and generalized Earth. “Nauka”, Moscow, 1991. 203 p. (in Russian).
  10. Mescheryakov G.A., Shopjak I.N., and Dejneka Yu.P. (1977) Function’s representation inside the Earth’s ellipsoid by means of the partial sum of a generalized Fourier series. Geodesy, cartography and aerophotosurveying, No 21, pp. 55-62, Lvov (in Russian).
  11. Moritz, H. (1990) The Figure of the Earth. Theoretical Geodesy and Earth’s Interior. Wichmann, Karlsruhe.
  12. Rubincam D.P. (1979) Gravitational potential energy of the Earth: A spherical harmonic approach. Journal of Geophysical Research, Vol. 84, No. B11, pp. 6219-6225.