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Current Estimation of the Earth’s Mechanical and Geometrical Parameters

  • Conference paper

Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA,volume 133)

Abstract

The Earth’s mechanical and geometrical parameters were estimated from the simultaneous adjustment of the 2nd-degree harmonic coefficients of six gravity field models and seven values of the dynamical ellipticity H_D all reduced to the common MHB2000 precession constant at epoch J2000. The transformation of 2nd-degree harmonic coefficients in the case of a finite commutative rotation was developed to avoid uncertainty in the deviatoric part of inertia tensor. This transformation and the exact solution of eigenvalue-eigenvector problem are applied to determine (a) the static components and accuracy of the Earth’s tensor of inertia at epoch 2000 and (b) the time-dependent constituents of the inertia tensor. Special attention was given to the computation of temporally varying components of the Earth’s inertia tensor, which are based on the time series of 2nd-degree coefficients through GRACE observations. A remarkable stability in time of the position of the axis Ā of inertia as the parameter of the Earth’s triaxiality is discussed

Keywords

  • Principal axes and moments of inertia
  • Dynamical ellipticity
  • GRACE
  • Precession constant

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References

  • Bretagnon, P., G. Francou, P. Rocher, and J.L. Simon (1998) SMART97: A new solution for the rotation of the rigid Earth. Astronomy and Astrophysics, 329, pp. 329–338

    Google Scholar 

  • Bursa, M. (1995) Primary and derived parameters of common relevance of astronomy, geodesy, and geodynamics. Earth, Moon and Planets, 69, pp. 51–63

    CrossRef  Google Scholar 

  • Dehant, V. et al. (1999) Considerations concerning the non-rigid Earth nutation theory. Celestial Mechanics and Dynamical Astronomy, 72, pp. 245–309

    CrossRef  Google Scholar 

  • Groten E. (2000) Parameters of common relevance of astronomy, geodesy, and geodynamics. Journal of Geodesy, 74, pp. 134–140

    Google Scholar 

  • Hartmann, T., M. Soffel, and C. Ron (1999) The geophysical approach towards the nutation of a rigid Earth, Supplement Series, Astronomy & Astrophysics, 134, pp. 271–286

    Google Scholar 

  • Lambeck K. (1971) Determination of the Earth’s pole of rotation from laser range observations to satellites. Bulletin Géodésique, 101, pp. 263–281

    CrossRef  Google Scholar 

  • Madelund E. (1957) Die Mathematischen Hilfsmittel des Physikers, Berlin, Gottingen, Heidelberg, Springer-Verlag,

    Google Scholar 

  • Marchenko A.N. (1998) Parameterization of the Earth’s Gravity Field. Point and Line Singularities. Lviv Astronomical and Geodetic Society, Lviv

    Google Scholar 

  • Marchenko A., 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

    CrossRef  Google Scholar 

  • Mathews, P.M. (2000) Improved models for precession and nutation. In: Proceedings of IAU Colloquium 180 “Towards Models and Constants for Sub-Microarcsecond Astrometry”, Naval Observatory, Washington, pp. 212–222

    Google Scholar 

  • Mathews, P.M., Herring T.A., and Buffet, B.A. (2002) Modeling of nutation-precession: new nutation series for nonrigid Earth, and insights into the Earth’s interior, Journal of Geophysical Research, Vol. 107, No. B4, 10.1029/2001JB000390

    Google Scholar 

  • McCarthy D. and Petit G. (2004) IERS Conventions (2003), IERS Technical Note, No. 32, Verlag des Bundesamts fur Kartographie und Geodasie, Frankfurt am Main

    Google Scholar 

  • Melchior P. (1978) The Tides of the Planet Earth. Pergamon, Oxford

    Google Scholar 

  • Reigber Ch., Jochmann H., Wünsch J., Neumayer K.-H., Schwintzer. P (2003) First insight into temporal gravity variability from CHAMP. In: Reigber Ch., Lühr, H., Schwintzer, P. (eds.), In: “First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies”. Springer-Verlag Berlin-Heidelberg, pp. 128–133

    Google Scholar 

  • Rochester, M.G., and D.E. Smylie (1974) On changes in the trace of the Earth’s inertial tensor. Journal of Geophysical Research, 79 (32), pp. 4948–4951

    CrossRef  Google Scholar 

  • Roosbeek, F., and V. Dehant (1998) RDAN97: An analytical development of rigid Earth nutation series using the torque approach. Celestial Mechanics, 70, pp. 215–253

    CrossRef  Google Scholar 

  • Souchay, J., and H. Kinoshita (1996) Corrections and new developments in rigid Earth nutation theory: I. Luni-solar influence including indirect planetary effects, Astronomy and Astrophysics, 312, pp. 1017–1030

    Google Scholar 

  • Williams, J.G. (1994) Contributions to the Earth’s obliquity rate, precession and nutation, Astronomical Journal, 108, pp. 711–724

    CrossRef  Google Scholar 

  • Yoder, C.F., J.G. Williams, J.O. Dickey, B.E. Schutz, R.J. Eanes, and B.D. Tapley (1983) Secular variation of earth’s gravitational harmonic J2 coefficient from Lageos and nontidal acceleration of earth rotation. Nature, 303, pp. 757–762

    CrossRef  Google Scholar 

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Marchenko, A. (2009). Current Estimation of the Earth’s Mechanical and Geometrical Parameters. In: Sideris, M.G. (eds) Observing our Changing Earth. International Association of Geodesy Symposia, vol 133. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85426-5_57

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