Dynamic Planet pp 280-287 | Cite as

A Validation Procedure for Satellite Orbits and Force Function Models Based on a New Balance Equation Approach

  • A. Löcher
  • K. H. Ilk
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 130)


Since the availability of CHAMP and GRACE data, the energy approach has become an important tool for the recovery of the gravity field based on continuously observed satellite orbits. Up to now, only the total energy of the satellite’s three-dimensional motion has been considered which is known as the Jacobi integral if formulated in a constantly rotating Earth-fixed reference frame. Beside this, additional energy integrals can be found for the components of the satellite’s motion and various combinations hereof, starting from the three scalar components of Newton’s equation of motion. Furthermore, integrals of motion based on the linear momentum and the angular momentum can be formulated which show even better mathematical characteristics than the Jacobi integral for the determination of the gravity field. Therefore, this new approach seems to be appropriate to validate the consistency of gravity field models and precisely observed satellite orbits and to improve, subsequently, these gravity field models. The advantages and critical aspects of this approach are investigated in this paper. First results with real data were presented using kinematic CHAMP orbits.


CHAMP GRACE integrals of motion energy integral Jacobi integral balance equations gravity field recovery validation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ilk KH, Löcher A (2003) The Use of Energy Balance Relations for Validation of Gravity Field Models and Orbit Determination Results, F. Sansò (ed.) A Window on the Future of Geodesy, IUGG General Assembly 2003, Sapporo, Japan, International Association of Geodesy Symposia, Vol. 128, pp. 494–499, SpringerGoogle Scholar
  2. Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96, NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, MDGoogle Scholar
  3. Löcher A, Ilk KH (2005) Energy Balance Relations for Validation of Gravity Field Models and Orbit Determinations Applied to the Results of the CHAMP Mission, in C. Reigber, H. Liihr, P. Schwintzer, J. Wickert (Eds.): Earth Observation with CHAMP, Results from Three Years in Orbit, pp. 53–58, SpringerGoogle Scholar
  4. Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (2005) ITG-CHAMP01: A CHAMP Gravity Field Model from Short Kinematic Arcs of a One-Year Observation Period, Journal of Geodesy (2005) 78:462–480CrossRefGoogle Scholar
  5. Reigber C, Schmidt R, Flechtner F, Konig R, Meyer U, Neumayer KH, Schwintzer P, Zhu SY (2003) First EI-GEN Gravity Field Model based on GRACE Mission Data Only, in preparation for GRLGoogle Scholar
  6. Schneider M (2002) Zur Methodik der Gravitationsfeldbe-stimmung mit Erdsatelliten, Schriftenreihe IAPG/FESG, 15, Institut fur Astronomische und Physikalische Geodäsie, München, 3-934205-14-3Google Scholar
  7. Schneider M (2005) Beiträge zur Gravitationsfeldbestim-mung mit Erdsatelliten, Schriftenreihe IAPG/ FESG, 21, Institut für Astronomische und Physikalische Geodäsie, München, 3-934205-20-8Google Scholar
  8. Švehla D, Rothacher M (2003) Kinematic and reduced dynamic precise orbit determination of low-Earth orbiters, Adv. Geosciences 1:47–56CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

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

Personalised recommendations