The Use of Energy Balance Relations for Validation of Gravity Field Models and Orbit Determination Results

  • K.H. Ilk
  • A. Löcher
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 128)


There is a need for a proper validation procedure of gravity field solutions, especially for those high precise ones which are derived from the dedicated gravity field missions as CHAMP, GRACE and in future GOCE. In this paper the balance equations for the energy and for the energy exchange of a satellite orbiting around the Earth are proposed as analysis tool to validate gravity field solutions together with orbits derived with precise reduced dynamic or kinematic orbit determination procedures. The theoretical foundation of the analysis tool is presented as well as simulation results and applications to real orbits of a GPS satellite and of CHAMP based on various gravity field solutions. It is shown that the validation procedure can be used to detect deficiencies in the orbit modelling and in gravity field recovery results.


Gravity field validation Orbit determination validation Energy balance relations Jacobi-Integral 


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  1. Bjerhammar, A. (1967): On the energy integral for satellites, Rep. of the R. Inst. of Techn. Sweden, Stockholm, 1967Google Scholar
  2. Falk, G., Ruppel, W. (1973): Mechanik, Relativität, Gravitation, Springer-Verlag, Berlin, Heidelberg, 1973Google Scholar
  3. Förste, Ch., Schwintzer, P., Reigber, Ch. (2001): The CHAMP Data Format, GFZ Internal Publication, CH-GFZ-FD-012Google Scholar
  4. Ilk, K.H. (2002): Energy Relations for the Motion of two Satellites within the Gravity Field of the Earth, in: M.G. Sideris (ed.), Gravity, Geoid and Geodynamics 2000, IAG Symposia Vol. 123, pp. 129–135, Springer-Verlag, Berlin, Heidelberg, 2002Google Scholar
  5. Ilk, K.H. (2003): Energy Relations for Satellite-to-Satellite Motions, in: E.W. Grafarend et al. (ed.), Geodesy — The Challenge of the Third Millenium, pp. 79–91, Springer-Verlag, Berlin, Heidelberg, 2003Google Scholar
  6. Ilk, K.H., Feuchtinger, M., Mayer-Gürr, T. (2003): Gravity Field Recovery and Validation by Analysis of Short Arcs of a Satellite-to-Satellite Tracking Experiment as CHAMP and GRACE, presented at the General Assembly of the IUGG 2003, Sapporo, Japan, 2003Google Scholar
  7. Jekeli, Ch. (1999): The determination of gravitational potential differences from satellite-to-satellite tracking, Celestial Mechanics and Dynamical Astronomy, 7582, pp. 85–100, 1999CrossRefGoogle Scholar
  8. Lijhr, H., Grunwaldt, L., Förste, Ch., Schwintzer, P., Reigber, Ch., (2001): CHAMP Reference Systems, Transformations and Standards, Internal publication, CH-GFZ-RS-002Google Scholar
  9. McCarthy, D.D. (ed.), (1996): IERS Conventions 1996, Central Bureau of IERS — Observatoire de Paris, Paris, 1996Google Scholar
  10. Montenbruck, O., Gill, E. (2000): Satellite Orbits, Models, Methods and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 2000Google Scholar
  11. O’Keefe, J.A. (1957): An application of Jacobi’s integral to the motion of an Earth satellite. The Astronomical Journal, 62(1252), 265–266CrossRefGoogle Scholar
  12. Reigber, Ch. (1969): Zur Bestimmung des Gravitationsfeldes der Erde aus Satellitenbeobachtungen, DGK, Reihe C, Heft Nr. 137, München, 1969Google Scholar
  13. Reigber, Ch., (2002): CHAMP Newsletter No. 9, GFZ Internal Publication, Newsletter_CHAMP_009Google Scholar
  14. Reigber, Ch., Balmino, G., Schwintzer, P., Biancale, R., Bode, A., Lemoine, J.-M., Koenig, R., Loyer, S., Neumayer, H., Marty, J.-C., Barthelmes, F., Perosanz, F., Zhu, S.Y., (2002): A high quality global gravity field model from CHAMP GPS tracking data and Accelerometry (EIGEN-1S), Geophysical Research Letters, 29(14), 10.1029/ 2002GL015064Google Scholar
  15. Reigber, Ch., Schwintzer, P., Neumayer, K.-H., Barthelmes, F., König, R., Förste, Ch., Balmino, G., Biancale, R., Lemoine, J.-M., Loyer, S., Bruinsma, S., Perosanz, F., Fayard, T. (2003): The CHAMP-only Earth Gravity Field Model Eigen-2, Advances in Space Research 31(8), 1883–1888, 2003CrossRefGoogle Scholar
  16. Springer, T.A., Beutler, G., Rothacher, M., (1998): A new Solar Radiation Pressure Model for the GPS satellites, IGS 1998 Analysis Center Workshop, ESOC, DarmstadtGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • K.H. Ilk
    • 1
  • A. Löcher
    • 1
  1. 1.Institute of Theoretical GeodesyUniversity of BonnBonnGermany

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