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Celestial Mechanics and Dynamical Astronomy

, Volume 108, Issue 3, pp 301–313 | Cite as

On quasi-periodic motions around the triangular libration points of the real Earth–Moon system

  • X. Y. Hou
  • L. Liu
Original Article

Abstract

The two triangular libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption that the motion of the Moon is quasi-periodic, one special quasi-periodic orbit exists as dynamical substitute for each point. The way to compute the dynamical substitute was discussed before, and a planar approximation was obtained. In this paper, the problem is revisited. The three-dimensional approximation of the dynamical substitute is obtained in a different way. The linearized central flow around it is described.

Keywords

Earth–Moon Triangular libration point Dynamical substitute Quasi-periodic orbit 

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References

  1. Alfriend K.T.: The stability of the triangular Lagrangian points for commensurability of order two. Celest. Mech. 1, 351–359 (1970)MATHCrossRefADSGoogle Scholar
  2. Alfriend K.T.: Stability of the motion about L4 at three-to-one commensurability. Celest. Mech. 4, 60–67 (1971)MATHCrossRefADSGoogle Scholar
  3. Arnold V.I.: Mathematical Methods of Classical Mechanics. 2nd edn. Beijing World Publishing Corporation, Beijing (1999)Google Scholar
  4. Broucke R. Periodic orbits in the restricted three-body problem with Earth-Moon masses, JPL Techinical Report No. 32-1168 (1968)Google Scholar
  5. Brouwer D., Clemence G.M.: Methods of Celestial Mechanics. Academic press, New York (1961)Google Scholar
  6. Celletti A., Girogilli A.: On stability of the Lagrangian points in the spatial restricted problem of three bodies. Celest. Mech. Dyn. Astron. 50, 31–58 (1991)MATHCrossRefADSGoogle Scholar
  7. Danby J.M.: Stability of the triangular points in the elliptic restricted problem of three bodies. Astron. J. 69(2), 165–172 (1964)CrossRefMathSciNetADSGoogle Scholar
  8. Deprit A., Henrard J., Rom A.: Analytical lunar ephemeris. Astron. Astrophys. 100, 257–269 (1971)MathSciNetADSGoogle Scholar
  9. Deprit A., Delie A.: Trojan orbits I, d’Alembert series at L4. Icarus 4, 242–266 (1965)CrossRefMathSciNetADSGoogle Scholar
  10. Díez C., Jorba À., Simó C.: A dynamical equivalent to the equilateral libration points of the Earth-Moon system. Celest. Mech. Dyn. Astron. 50, 13–29 (1991)MATHCrossRefADSGoogle Scholar
  11. Érdi B. et al.: A parametric study of stability and resonances around L 4 in the elliptic restricted three-body problem. Celest. Mech. Dyn. Astron. 104, 145–158 (2009)MATHCrossRefADSGoogle Scholar
  12. Gómez G., Masdemont J., Simó C.: Quasi-halo orbits associated with libration points. J. Astron. Sci. 42(2), 135–176 (1998)Google Scholar
  13. Gómez G. et al.: Dynamics and Mission Design Near Libration Point Orbits, Vol. II, Fundamentals: The Case of Triangular Libration Points. World Scientific, Singapore (2001)Google Scholar
  14. Gómez G. et al.: Dynamics and Mission Design Near Libration Point Orbits, Vol. IV, Advanced Methods for Triangular Points. World Scientific, Singapore (2001)Google Scholar
  15. Gómez G., Masdemont J., Mondelo J.M.: Solar System models with a selected set of frequencies. Astron. Astrophys. 390, 733–749 (2002)CrossRefADSGoogle Scholar
  16. Jorba À., Simó C.: On quasi-periodic perturbations of elliptic equilibrium points. Siam. J. Math. Anal. 27(6), 1704–1737 (1996)MATHCrossRefMathSciNetGoogle Scholar
  17. Jorba À., Ramírez R., Villanueva J.: Effective reducibility of quasi-periodic linear equations close to constant coefficients. Siam. J. Math. Anal. 28(1), 178–188 (1997)MATHCrossRefMathSciNetGoogle Scholar
  18. Murray C.D., Dermott S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  19. Simon J.L. et al.: Numerical expressions for precession formulae and mean elements for the Moon and the planets. Astron. Astrophys. 282, 663–683 (1994)ADSGoogle Scholar
  20. Skokos C., Dokoumetzidis A.: Effective stability of the Trojan asteroids. Astron. Astrophys. 367, 729–736 (2001)CrossRefADSGoogle Scholar
  21. Szebehely V.: Theory of Orbits. Academic press, New York (1967)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Astronomy DepartmentNanjing UniversityNanjingChina
  2. 2.Institute of Space Environment and AstrodynamicsNanjing UniversityNanjingChina

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