Importance of the Coupling Effects Between Earth Potential Harmonics in the Motion of an Artificial Satellite. Computed and Checked Solution of This Coupling Problem. The Case of J7

  • X. Berger
Part of the COSPAR-IAU-IUTAM book series (IUTAM)


The “coupling” effect arising from the simultaneous presence of different harmonics can be great compared with the direct effect of the harmonics. The coupling effect J2–J7 is very significant. Theoretical, numerical and graphic studies have demonstrated this importance and given the reason for it. We have expressed literally the coupling expressions for the zonal and tesseral, nonresonant, harmonics (development of coupling equations, integration, verification by analytical-numerical comparisons, studies of the form and properties of the terms...). We indicate which coupling effects must be considered for a good representation of the motion of any satellite, and for the determination of zonal harmonics. All this has been done and has been established by computer checking.


Analytical Theory Coupling Effect Coupling Term Secular Term Artificial Satellite 
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  1. 1.
    Berger, X.: Analytical theory of the motion of a satellite under earth-moon-sun influences, computed and compared with numerical integration. Analytical developments of all the terms. First International Symposium - The use of artificial satellites for Geodesy and Geodynamics. Athens. May 1973.Google Scholar
  2. 2.
    Berger, X.: Expressions analytiques des termes seculaires en J2 et à longues periodes en J2. Bulletin G.R.G.S. n. 5 (August 1972).Google Scholar
  3. 3.
    Berger, X.: Expressions analytiques littérales des termes de couplage dans la théorie analytique du mouvement des satellites artificiels sous l’action du potentiel terrestre. Bulletin G.R.G.S. n. 8 (June 1973).Google Scholar
  4. 4.
    King Hele, D.G.; Cook, G.E.; Scott, D.W.: Evaluation of odd zonal harmonics in the Geopotential, of degree less than 33, from the analysis of 22 satellite orbits. Planet. Space Sci. 17 (1969) 629.CrossRefGoogle Scholar
  5. 5.
    Kozai, Y.: Revised zonal harmonics in the geopotential. Spec. Rep. Astrophys. Obs. n. 295 (1969).Google Scholar
  6. 6.
    Wagner, C.A.: Zonal gravity harmonics from long satellite arcs by a seminumeric method. J.G.R. n. 17 (1973).Google Scholar
  7. 7.
    Kovalevsky, J.: Géodésie Genérale 4 (1971).Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • X. Berger
    • 1
  1. 1.Meudon ObservatoryG.R.G.S.France

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