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Analytical Theories of the Motion of Artificial Satellites

  • Gen-Ichiro Hori
  • Yoshihide Kozai
Part of the COSPAR-IAU-IUTAM book series (IUTAM)

Abstract

The present paper gives a general review of various analytical theories of the motion of artificial satellites presented for these fifteen years or so. Most theories treat the main problem (i.e. problem of the oblateness perturbations), and they are classified according to a) intermediaries adopted, b) perturbation techniques used, and c) orders of approximations carried out. We next review the theories that treat of other sources of perturbations such as tesseral harmonics of the earth’s potential, luni-solar attraction, drag of the earth’s atmosphere, solar radiation, and so on. All of them are of the second order in magnitude, but are still very important especially in view of secular and long-period perturbations. The resonance cases (i.e. problem of the critical inclination and motion of 24-hours satellites) are also treated by many authors. The orders of perturbations needed for analytical theories to attain an accuracy of 10−6 and 10−8 are shown in concluding the review.

Keywords

Earth Satellite Force Function Solar Radiation Pressure Artificial Satellite Kepler Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aksnes, K.: Astrophys. Norvegica X, n. 4 (1965) 69; Aksnes, K.: Dissertation, Yale University, 1969.Google Scholar
  2. 2.
    Allan, R.R.: Celes. Mech. 2 (1970) 121.CrossRefGoogle Scholar
  3. 3.
    Aoki, S.: Astron. J. 68 (1963) 355.CrossRefGoogle Scholar
  4. 4.
    Berger, X.: Bulletin G.R.G.S. n. 5 (1972)Google Scholar
  5. Berger, X.: Bulletin G.R.G.S. n. 8 (1973).Google Scholar
  6. 5.
    Brouwer, D.: Astron. J. 64 (1959) 378.MathSciNetCrossRefGoogle Scholar
  7. 6.
    Deprit, A.: Celes. Mech. 1 (1969) 12.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 7.
    Deprit, A.; Rom, A.: Celes. Mech. 2 (1970) 166.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 8.
    Giacaglia, G.E.O.: Celes. Mech. 9 (1974) 239.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 9.
    Gaposhkin, E.: not published (1970).Google Scholar
  11. 10.
    Garfinkel, B.: Astron. J. 63 (1958) 88CrossRefGoogle Scholar
  12. Garfinkel, B.: Astron. J. 65 (1960) 624MathSciNetCrossRefGoogle Scholar
  13. Garfinkel, B.: Celes. Mech. 7 (1973) 205.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 11.
    Garfinkel, B.; Aksnes, K.: Astron. J. 75 (1970) 85.MathSciNetCrossRefGoogle Scholar
  15. 12.
    Hagihara, Y.: S.A.O. n. 5, 5 (1961) 39.Google Scholar
  16. 13.
    Hori, G.: Astron. J. 65 (1960) 291MathSciNetCrossRefGoogle Scholar
  17. Hori, G.: Astron. J. 66 (1961) 258MathSciNetCrossRefGoogle Scholar
  18. Hori, G.: Publ. Astron. Soc. Japan 18 (1966) 287; An article in Recent Advances in Dynamical Astronomy, ed. by B.D. Tapley and V. Szebehely. Dordrecht-Holland: D. Reidel Pub. Co. 1973, 231–249.Google Scholar
  19. 14.
    Iszak, I.: S. A.O. Special Report 90 (1962); Astron. J. 68 (1963) 559.Google Scholar
  20. 15.
    Kaula, W.M.: Theory of Satellite Geodesy. Waltham, U.S.: Blaisdell Pub. Co. 1960.Google Scholar
  21. 16.
    Kozai, Y.: Astron. J. 66 (1961) 132MathSciNetCrossRefGoogle Scholar
  22. Kozai, Y.: S.A.O. n. 5, 5 (1961) 53Google Scholar
  23. Kozai, Y.: Astron. J. 67 (1962) 446.MathSciNetCrossRefGoogle Scholar
  24. 17.
    Lyddane, R.H.: Astron. J. 68 (1963) 555.MathSciNetCrossRefGoogle Scholar
  25. 18.
    Message, P.J., et al.: The Observatory 168 (1962).Google Scholar
  26. 19.
    Peters, C.F.: An article in Periodic Orbits, Stability and Resonances, ed. by G.E.O. Giacaglia. Dordrecht-Holland: D. Reidel Pub. Co. 1970, 469–473.Google Scholar
  27. 20.
    Poritsky, H.: Astron. J. 67 (1962) 212.MathSciNetCrossRefGoogle Scholar
  28. 21.
    Scheifele, G.; Stiefel, E.: Canonical Satellite Theory. Report to ESRO. 1972.Google Scholar
  29. 22.
    Smith, O.K.: Astron. J. 66 (1963) 359.CrossRefGoogle Scholar
  30. 23.
    Stern, T.E.: Astron. J. 63 (1958) 28.CrossRefGoogle Scholar
  31. 24.
    Vinti, J.P.: J. Res. NBS n. 2, 63B (1959) 105Google Scholar
  32. Vinti, J.P.: J. Res. NBS n. 1, 70B (1966) 1.Google Scholar
  33. 25.
    Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, New York: Dover Pub. 1944, 152.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • Gen-Ichiro Hori
    • 1
  • Yoshihide Kozai
    • 1
  1. 1.University of TokyoTokyoJapan

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