Advertisement

Celestial Mechanics and Dynamical Astronomy

, Volume 104, Issue 3, pp 227–239 | Cite as

Quasi-critical orbits for artificial lunar satellites

  • S. Tzirti
  • K. Tsiganis
  • H. Varvoglis
Original Article

Abstract

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J 2 and C 22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same time, as is the case when only the J 2 term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi-critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0°.1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J 2, C 22 and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J 2, C 22 and rotation rate.

Keywords

Lunar artificial satellite Critical inclination C22 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allan R.R.: The critical inclination problem: a simple treatment. Celest. Mech. 2, 121–122 (1970)CrossRefADSGoogle Scholar
  2. Anderson J.D., Jacobson R.A., McElrath W.B., Moore T.P., Schubert G., Thomas P.C.: Shape, mean radius, gravity field, and interior structure of Callisto. Icarus 153, 157–161 (2001)CrossRefADSGoogle Scholar
  3. Anderson J.D., Lau E.L., Sjogre W.L., Schubert G., Moore W.B.: Europa’s differentiated internal structure: inferences from two Galileo encounters. Science 276, 1236–1239 (1997)CrossRefADSGoogle Scholar
  4. Bertotti B., Farinella P., : Physics of the Solar System, pp. 42–59. Kluwer Academic Publishers, Dordrecht/Boston/London (2003)Google Scholar
  5. Delhaise F., Henrard J.: The problem of critical inclination combined with a resonance in mean motion in artificial satellite theory. Celest. Mech. Dyn. Astron. 55, 261–280 (1993)CrossRefADSMathSciNetGoogle Scholar
  6. De Saedeleer B.: Théorie analytique fermée d’un satellite artificiel lunaire pour l’analyse de mission. Presses Universitaires de Namur, Belgique (2006)Google Scholar
  7. De Saedeleer B., Henrard J.: The combined effect of J 2 and C 22 on the critical inclination of a lunar orbiter. Adv. Space Res. 37, 80–87 (2006)CrossRefADSGoogle Scholar
  8. Ferrer S., San-Juan J.F., Abad A.: A note on lower bounds for relative equilibria in the main problem of artificial satellite theory. Celest. Mech. Dyn. Astron. 99, 69–83 (2007)MATHCrossRefADSMathSciNetGoogle Scholar
  9. Hughes S.: The critical inclination: another look. Celest. Mech. 25, 235–266 (1981)MATHCrossRefADSGoogle Scholar
  10. Jefferys W.H., Moser J.: Quasi-Periodic Solutions for the Three body Problem. Astron. J. 71, 568–578 (1966)CrossRefADSMathSciNetGoogle Scholar
  11. Jupp A.H.: The Critical Inclination problem—30 years of progress. Celest. Mech. 43, 127–138 (1988)MATHADSGoogle Scholar
  12. Liu L., Innanen K.A.: Problems of critical inclination and commensurability in the motion of artificial satellites. Chin. Astron. Astrophys. 10, 245–251 (1986)CrossRefADSGoogle Scholar
  13. Morbidelli A.: Modern Celestial Mechanics, pp. 39–44. Taylor and Francis, London and New York (2002)Google Scholar
  14. Murray C., Dermott S.: Solar System Dynamics. Cambridge University Press, United Kingdom (1999)MATHGoogle Scholar
  15. Perozzi E., Di Salvo A.: Novel spaceways for reaching the Moon: an assessment for expolarion. Celest. Mech. Dyn. Astron. 102, 207–218 (2008)MATHCrossRefADSMathSciNetGoogle Scholar
  16. Palacián J.E.: Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field. Celest. Mech. Dyn. Astron. 98, 219–249 (2007)MATHCrossRefADSGoogle Scholar
  17. Roy A.E.: Orbital Motion, pp. 283–286. Adam Hilger LTD, Bristol (1982)Google Scholar
  18. Shampine L.F., Gordon M.K.: Computer Solution of Ordinary Differential Equations: The Initial Value Problem. Freeman, San Francisco (1975)MATHGoogle Scholar
  19. Sidi M.J.: Spacecraft Dynamics and Control, pp. 34–35. Cambridge University Press, USA (2002)Google Scholar
  20. Vallado D.A.: Fundamentals of Astrodynamics and Applications, pp. 509–521. Kluwer Academic Publishers, Dordrecht/Boston/London (2001)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Section of Astrophysics Astronomy & Mechanics, Department of PhysicsUniversity of ThessalonikiThessalonikiGreece

Personalised recommendations