Celestial Mechanics and Dynamical Astronomy

, Volume 75, Issue 2, pp 85–101 | Cite as

The determination of gravitational potential differences from satellite-to-satellite tracking

  • Christopher Jekeli


A new, rigorous model is developed for the difference of gravitational potential between two close earth-orbiting satellites in terms of measured range-rates, velocities and velocity differences, and specific forces. It is particularly suited to regional geopotential determination from a satellite-to-satellite tracking mission. Based on energy considerations, the model specifically accounts for the time variability of the potential in inertial space, principally due to earth’s rotation. Analysis shows the latter to be a significant (±1 m2/s2) effect that overshadows by many orders of magnitude other time dependencies caused by solar and lunar tidal potentials. Also, variations in earth rotation with respect to terrestrial and celestial coordinate frames are inconsequential. Results of simulations contrast the new model to the simplified linear model (relating potential difference to range-rate) and delineate accuracy requirements in velocity vector measurements needed to supplement the range-rate measurements. The numerical analysis is oriented toward the scheduled Gravity Recovery and Climate Experiment (GRACE) mission and shows that an accuracy in the velocity difference vector of 2×10−5 m/s would be commensurate within the model to the anticipated accuracy of 10−6 m/s in range-rate.

gravitational potential satellite-to-satellite tracking range-rate measurements earth rotation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bernard, A. and Touboul, P.: 1989, A spaceborne gravity gradiometer for the nineties. Paper presented at the General Meeting of the International Association of Geodesy, 3–12 August 1989, Edinburgh, Scotland.Google Scholar
  2. Colombo, O. L.: 1984, The global mapping of gravity with two satellites, Report of the Netherlands Geodetic Commission, 7(3), Delft.Google Scholar
  3. Danby, J. M. A.: 1988, Fundamentals of Celestial Mechanics, Willman-Bell Inc., Richmond, Virginia.Google Scholar
  4. Dickey, J. O. (ed.): 1997, Satellite gravity and the geosphere, Report from the committee on earth gravity from space, National Research Council, National Academy Press.Google Scholar
  5. Fischell, R. E. and Pisacane, V. L.: 1978, A drag-free lo-lo satellite system for improved gravity field measurements, Proc. Ninth GEOP Conference, Report no. 280, Department of Geodetic Science, Ohio State University, Columbus.Google Scholar
  6. Goldstein, H.: 1950, Classical Mechanics, Addison-Wesley Publ. Co., Reading, Massachusetts.Google Scholar
  7. Ilk, K. H.: 1986, On the regional mapping of gravitation with two satellites, Proc. First Hotine-Marussi Symposium on Mathematical Geodesy, 3–6 June 1985, Rome.Google Scholar
  8. Jekeli, C. and Rapp, R. H.: 1980, Accuracy of the determination of mean anomalies and mean geoid undulations from a satellite gravity mapping mission. Report No. 307, Department of Geodetic Science, The Ohio State University.Google Scholar
  9. Jekeli, C. and Upadhyay, T. N.: 1990, 'Gravity estimation from STAGE, a satellite-to-satellite tracking mission', J. Geophys. Res. 95(B7), 10973-10985.ADSGoogle Scholar
  10. Keating, T., Taylor, P., Kahn, W., Lerch, F.: 1986, Geopotential Research Mission, Science, Engineering, and Program Summary, NASA Tech. Memo. 86240.Google Scholar
  11. Lambeck, K.: 1988, Geophysical Geodesy, Clarendon Press, Oxford.Google Scholar
  12. Lemoine, F.G. et al.: 1998, The development of the joint NASA GSFC and the National Imagery Mapping Agency (NIMA) geopotential model EGM96, NASA Technical Report NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, Maryland.Google Scholar
  13. Martin, J. L.: 1988, General Relativity, A Guide to Its Consequences for Gravity and Cosmology, Ellis Horwood Ltd, Chichester.Google Scholar
  14. McCarthy, D. D.: 1996, IERS Conventions (1996), IERS Technical Note 21, Observatoire de Paris, Paris.Google Scholar
  15. Morgan, S. H. and Paik, H. J. (eds): 1988, Superconducting gravity gradiometer mission, Vol. II, Study Team Technical Report, NASA Tech. Memo. 4091.Google Scholar
  16. Mueller, I. I.: 1969, Spherical and Practical Astronomy, Frederick Ungar Publ. Co., New York.Google Scholar
  17. Rummel, R.: 1980, Geoid heights, geoid height differences, and mean gravity anomalies from 'low-low’ satellite-to-satellite tracking — an error analysis. Report No. 306, Department of Geodetic Science, Ohio State University, Columbus.Google Scholar
  18. Rummel, R. and Sneeuw, N.: 1997, Toward dedicated satellite gravity field missions, Paper presented at the Scientific Assembly of the IAG, Rio de Janeiro, Brazil, 3–9 September 1997.Google Scholar
  19. Seeber, G.: 1993, Satellite Geodesy, Walter de Gruyter, Berlin.Google Scholar
  20. Seidelmann, P. K.: 1992, Explanatory Supplement to the Astronomical Almanac, Prepared by U.S. Naval Observatory. University Science Books, Mill Valley, California.Google Scholar
  21. Tapley, B. D. and Reigber, C.: 1998, GRACE: A satellite-to-satellite tracking geopotential mapping mission, Proc. Second Joint Meeting of the Int. Gravity Commission and the Int. Geoid Commission, 7–12 September 1998, Trieste.Google Scholar
  22. Torge, W.: 1991, Geodesy, Walter de Gruyter, Berlin.Google Scholar
  23. Wagner, C. A.: 1983, 'Direct determination of gravitational harmonics from low-low GRAVSAT data', J. Geophy. Res. 88(B12), 10309-10321.ADSGoogle Scholar
  24. Wolff, M.: 1969, 'Direct measurement of the earth's gravitational potential using a satellite pair', J. Geophy. Res. 74(22), 5295-5300.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Christopher Jekeli
    • 1
  1. 1.Department of Civil and Environmental Engineering and Geodetic ScienceThe Ohio State UniversityColumbusU.S.A., e-mail

Personalised recommendations