Resonant Satellite Geodesy by High Speed Analysis of Mean Kepler Elements

  • C. A. Wagner
  • B. C. Douglas
Part of the COSPAR-IAU-IAG/IUGG-IUTAM book series (IUTAM)

Abstract

A general resonant orbit and gravity constant determining program has been developed accepting short arc mean Kepler elements as data. The evolution of these elements is calculated by numerical integration of their long period and secular variations.

With only slowly-changing mean element coordinates being integrated, a step size of the order of an orbit revolution or more is achieved. Satellite ephemerides over 5000 revolutions are calculated in about a minute on an IBM/360 computer. Partial derivatives of the evolved mean elements with respect to initial values and gravity constants are readily evaluated from numerically generated variant trajectories.

To test the method, simulated and actual orbit data from long resonant twelve-hour trajectories have been processed for gravity information by a least-squares technique. The gravity recovery is in excellent agreement with the model for the simulated data, and with previous analytic results from the actual data on Cosmos 41.

Extensive data from many resonant 12 and 24 h satellites is currently being processed by the mean element program. Preliminary determinations from this data are given. The final result should be definitive information on more than a quarter of the longitude harmonics through 8,8.

Keywords

Resid Lution Geophysics 

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References

  1. 1.
    Cook, A. H.: Resonant Orbits of Artificial Satellites and Longitude Terms in the Earth’s External Gravitational Potential. Geophys. J. 4 (1961) 53–72.MATHCrossRefGoogle Scholar
  2. 2.
    Wagner, C. A.: Resonant Perturbations of Earth Satellites in 2 Day Commensurable Orbits. NASA-Goddard Space Flight Center Document X-643-68-373, Greenbelt, Md. 1968.Google Scholar
  3. 3.
    Gaposchkin, E. M.: Tesseral Harmonic Coefficients and Station Coordinates from the Dynamic Method. In: Geodetic Parameters for a 1966 Smithsonian Institution Standard Earth, Vol.2; Smithsonian Astrophysical Observatory, Cambridge, Mass. 1966.Google Scholar
  4. 4.
    Anderle, R. J.: Observations of Resonance Effects on Satellite Orbits Arising from the Thirteenth and Fourteenth Order Tesseral Gravitational Coefficients, J. Geophys. Res. 70/10 (1965) 2453.CrossRefGoogle Scholar
  5. 5.
    Yionoulis, S. M.: A Study of the Resonance Effects Due to the Earth’s Potential function, J. Geophys. Res. 70 (1965) 5991–5996.CrossRefGoogle Scholar
  6. 6.
    Kaula, W. M.: Analysis of Geodetic Satellite Tracking to Determine Tesseral Harmonics of the Earth’s Gravitational Field. Publication No. 656, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Calif. 1968.Google Scholar
  7. 7.
    Wagner, C. A., Douglas, B. C: Perturbations of Existing Resonant Satellites. Planetary Space Sc. 17 (1969) 1507–1517.Google Scholar
  8. 8.
    Kozai, Y.: The Zonal Harmonic Coefficients. In: Geodetic Parameters for a 1966 Smithsonian Institution Standard Earth, Vol. 2, Smithsonian Astrophysical Observatory, Cambridge, Mass. 1966.Google Scholar
  9. 9.
    King-Hele, D. G., Cook, G. E., Scott, D. W.: Even Zonal Harmonics in the Earth’s Gravitational Potential — A Comparison of Recent Determinations. Planetary Space Sc. 14 (1966) 42–52.Google Scholar
  10. 10.
    King-Hele, D. G., Cook, G. E., Scott, D. W.: Odd Zonal Harmonics in the Geopotential, Determined from 14 Well Distributed Satellite Orbits. Planetary Space Sc. 15 (April 1967) 741.CrossRefGoogle Scholar
  11. 11.
    Kaula, W. M.: Theory of Satellite Geodesy, Waltham, Mass.: Blaisdell Press 1966.Google Scholar
  12. 12.
    Brouwer, D.: Solution of the Problem of Artificial Satellite Theory without Drag. Astron. J. 64 (1959) 378.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Brown, E. W., Shook, C. A.: Planetary Theory, New York City: Dover Press 1964.Google Scholar
  14. 14.
    Kaula, W. M.: Development of the Lunar and Solar Disturbing Functions for a Close Earth Satellite. Astron. J. 67 (1962) 300CrossRefGoogle Scholar
  15. 15.
    King-Hele, D. G.: Theory of Satellite Orbits in an Atmosphere, London: Butterworth’s Press 1964.MATHGoogle Scholar
  16. 16.
    Kozai, Y.: The Motion of a Close Earth Satellite. Astron. J. 64 (1959) 367.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wagner, CA.: Determination of Low Order Resonant Gravity Harmonics from the Drift of two Russian 12-Hour Satellites. J. Geophys. Res. 73, No. 14, July 1968.Google Scholar

Copyright information

© Springer Verlag, Berlin/Heidelberg 1970

Authors and Affiliations

  • C. A. Wagner
    • 1
  • B. C. Douglas
    • 2
  1. 1.Goddard Space Flight CenterNational Aeronautics and Space AdministrationGreenbeltUSA
  2. 2.Wolf Research and Development CorporationRiverdaleUSA

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