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Celestial Mechanics and Dynamical Astronomy

, Volume 60, Issue 4, pp 455–470 | Cite as

Balanced earth satellite orbits

  • V. Kudielka
Article

Abstract

An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (“balanced” orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 105 revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.

Key words

Artificial satellite theory luni-solar perturbations near polar inclinations 

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References

  1. Allan, R.R. and Cook, G.E.: 1964,Proc. R. Soc. Lond. A 280, 97–109.Google Scholar
  2. Cook, G.E.: 1962,Geophys. J. R. Astr. Soc. 6, 271–291.Google Scholar
  3. Hough, M.E.: 1981,Celest. Mech. 25, 111–136.Google Scholar
  4. Hughes, S.: 1980,Proc. R. Soc. Lond. A 372, 243–264.Google Scholar
  5. King-Hele, D.G.: 1958,Proc. R. Soc. Lond. A 247, 49–72.Google Scholar
  6. Kozai, Y.: 1959, ‘The Earth's Gravitational Potential Derived from the Motion of Satellite 1958 Beta Two’,Smithsonian Inst. Astrophys. Observ. Spec. Rep. 22, 03/1959, 1–6.Google Scholar
  7. Lidov, M.L.: 1961,Planet. Space Sci. 9, 719–759.Google Scholar
  8. Lidov, M.L.: 1962, ‘On the Approximated Analysis of the Orbit Evolution of Artificial Satellites’, inDynamics of Satellites, pp. 168–179.Google Scholar
  9. Lorell, J.: 1965,J. Astronaut. Sci. 12, 142–152.Google Scholar
  10. Meeus, J.: 1980, ‘Astronomical Formulae for Calculators’,Monografieën over Astronomie en Astrofysica 4.Google Scholar
  11. Montenbruck, O.: 1984, ‘Grundlagen der Ephemeridenrechnung’,Sterne und Weltraum Taschenbuch 10.Google Scholar
  12. Orlov, A.A.: 1954,Tr. Gos. Astron. Inst. Mosk. Gos. Univ. 24, 139–153.Google Scholar
  13. Roy, A.E.: 1969,Astrophysics and Space Science 4, 375–386.Google Scholar
  14. Shapiro, I.I.: 1962, ‘The Prediction of Satellite Orbits’, in M. Roy (ed.),Dynamics of Satellites, pp. 257–312.Google Scholar
  15. Solari G. and Viola R.: 1992, ‘M-HEO: The Optimal Satellite System for the Most Highly-Populated Regions of the Northern Hemisphere’,ESA Bull. 70, 05/1992, 81–88.Google Scholar
  16. Stumpff, K. and Weiss, E.H.: 1968a, ‘A Fast Method of Orbit Computation’,NASA TN D-4470, 04/1968, 37 p.Google Scholar
  17. Stumpff, K. and Weiss, E.H.: 1968b, ‘Application of an N-body Reference Orbit’,The J. Astronaut. Sci. XV, No. 5, pp. 257–261.Google Scholar
  18. Stumpff, K.: 1974, ‘Himmelsmechanik’,Vol. III, Chap. XXXI, Sect. 258, pp. 322–327.Google Scholar
  19. Wolfram, S.: 1988, ‘Mathematica: A System for Doing Mathematics by Computer’, 2nd ed.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • V. Kudielka
    • 1
  1. 1.ViennaAustria

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