Celestial Mechanics and Dynamical Astronomy

, Volume 121, Issue 4, pp 415–429 | Cite as

On the energy integral formulation of gravitational potential differences from satellite-to-satellite tracking

  • J. Y. Guo
  • K. Shang
  • C. Jekeli
  • C. K. Shum
Original Article


Two approaches have been formulated to compute the gravitational potential difference using low–low satellite-to-satellite tracking data based on energy integral: one in the geocentric inertial reference system, and the other in the terrestrial reference system. The focus of this work is on the approach in the geocentric inertial reference system, where a potential rotation term appears in addition to the potential term. In former formulations, the contribution of the time-variable components of the gravitational potential to the potential term was included, but their contribution to the potential rotation term was neglected. In this work, an improvement to the former formulations is made by reformulating the potential rotation term to include the contribution of the time-variable components of the gravitational potential. A simulation shows that our more accurate formulation of the potential rotation term is necessary to achieve the accuracy for recovering the temporal variation of the Earth’s gravity field, such as for use to the Gravity Recovery And Climate Experiment GRACE observation data based on this approach.


Gravity Satellite-satellite tracking GRACE Energy integral method Potential difference Potential rotation term Jekeli formulation 



This research is supported by grants from NASA’s GRACE Science Team Program (NNX12AJ95G), Concept in Advanced Geodesy Program (NNX12AK28G), Cryosphere Program (NNX11AR47G), and the State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of geodesy and Geophysics, Chinese Academy of Sciences (SKLGED2015-5-3-E). GRACE data product is from Univ. of Texas Center for Space Research via JPL/PODAAC. The figures in this paper were generated using Generic Mapping Tools (GMT) (Wessel and Smith 1991).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • J. Y. Guo
    • 1
  • K. Shang
    • 1
    • 2
  • C. Jekeli
    • 1
  • C. K. Shum
    • 1
    • 3
  1. 1.Division of Geodetic Science, School of Earth SciencesOhio State UniversityColumbusUSA
  2. 2.State Key Laboratary of Geodesy and Earth’s DynamaicsInstitute of Geodesy and Geophysics, Chinese Academy of SciencesWuhanChina
  3. 3.Institute of Geodesy and Geophysics, Chinese Academy of SciencesWuhanChina

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