Advertisement

Celestial Mechanics and Dynamical Astronomy

, Volume 115, Issue 2, pp 185–211 | Cite as

A note on the dynamics around the Lagrange collinear points of the Earth–Moon system in a complete Solar System model

  • Yijun LianEmail author
  • Gerard Gómez
  • Josep J. Masdemont
  • Guojian Tang
Original Article

Abstract

In this paper we study the dynamics of a massless particle around the L 1,2 libration points of the Earth–Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the two collinear equilibrium points. For the analysis and computation of the quasi-periodic orbits, a new iterative algorithm is introduced which is a combination of a multiple shooting method with a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds for the algorithm the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in the Solar System force-field model for large time-spans, that cover most of the relevant Sun–Earth–Moon periods.

Keywords

Collinear libration point Quasi-periodic orbit Fourier analysis Multiple shooting Solar System restricted n-body problem Earth–Moon system 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andreu, M.A.: The quasi-bicircular problem. PhD Thesis, Department of Matemàtica Aplicada i Anàlisi, Universitat de Barcelona (1998)Google Scholar
  2. 2.
    Carpenter, R.J., Folta, D.C., Moreau, M.C., Quinn, D.A.: Libration point navigation concepts supporting the vision for Space exploration. AIAA/AAS Astrodynamics Specialist Conference, Providence, Rhode Island, August 2004, Paper No. AIAA 2004–4747Google Scholar
  3. 3.
    Colombo, G.: The stabilization of an artificial satellite at the inferior conjunction point of the Earth–Moon system. Smithsonian Astrophysical Observatory Special Report, 80 (1961)Google Scholar
  4. 4.
    Conley C.: Low energy transit orbits in the restricted three–body problem. SIAM J. Appl. Math. 16, 732–746 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Escobal P.: Methods of Astrodynamics. Wiley, New Jersey (1968)Google Scholar
  6. 6.
    Farquhar, R.W.: The control and use of libration point satellites. NASA Technical Report NASA TR R-346 (1970)Google Scholar
  7. 7.
    Folta, D.C., Woodard, M., Pavlak, T., Haapala, A., Howell, K.: Earth–Moon libration stationkeeping: theory, modeling, and operations. 1st IAA Conference on Dynamics and Control of Space Systems, Porto, Portugal, 19–21 March 2012. Paper No. IAA-AAS-DyCoSS1-05-10Google Scholar
  8. 8.
    Gómez G., Mondelo J.M.: The dynamics around the collinear equilibrium points of the RTBP. Phys. D 157(4), 283–321 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Gómez G., Masdemont J.J., C. Simó C.: Quasihalo orbits associated with libration points. J. Astron. Sci. 42(2), 135–176 (1998)Google Scholar
  10. 10.
    Gómez G., Mondelo J.M., Simó C.: A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: numerical tests and examples. DCDS-B 14(1), 41–74 (2010)zbMATHCrossRefGoogle Scholar
  11. 11.
    Gómez G., Mondelo J.M., Simó C.: A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: analytical error estimates. DCDS-B 14(1), 75–109 (2010)zbMATHCrossRefGoogle Scholar
  12. 12.
    Gómez G., Masdemont J.J., Mondelo J.M.: Solar system models with a selected set of frequencies. Astron. Astrophys. 390(2), 733–749 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Hill, K., Parker, J.S., Born, G.H., Lo, M.W.: Low–cost lunar communication and navigation. CCAR White Paper, 5 May 2006Google Scholar
  14. 14.
    Hou X.Y., Liu L.: On quasi-periodic motions around the triangular libration points of the real Earth–Moon system. Celest. Mech. Dyn. Astron. 108(3), 301–313 (2010)MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Hou X.Y., Liu L.: On quasi-periodic motions around the collinear libration points of the real Earth–Moon system. Celest. Mech. Dyn. Astron. 110(1), 71–98 (2011)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Howell, K., Ozimek, M.: Low-thrust transfers in the Earth–Moon system including applications to libration point orbits. AAS/AIAA Astrodynamics Specialist Conference, Mackinac Island, Michigan, August 2007, Paper No. AAS 07-343Google Scholar
  17. 17.
    Jorba À, Masdemont J.J.: Dynamics in the center manifold of the restricted three-body problem. Phys. D 132, 189–213 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Lo, M.W., Ross,S.D.: The lunar L 1 gateway: portal to the stars and beyond. AIAA Space Conference, Albuquerque, New Mexico, USA, 28–30 August 2001. Paper No. 2001-4768Google Scholar
  19. 19.
    Masdemont J.J.: High order expansions of invariant manifolds of libration point orbits with applications to mission design. Dyn. Syst. 20, 59–113 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Siegel C.L., Moser J.K.: Lectures on Celestial Mechanics. Springer, Heidelberg (1971)zbMATHCrossRefGoogle Scholar
  21. 21.
    Standish, E.M.: JPL Planetary and Lunar Ephemerides, DE405/LE405. JPL IOM 312. F-98-048 (1998)Google Scholar
  22. 22.
    Szebehely V.: Theory of Orbits. Academic Press, New York (1967)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Yijun Lian
    • 1
    • 2
    Email author
  • Gerard Gómez
    • 3
  • Josep J. Masdemont
    • 4
  • Guojian Tang
    • 1
  1. 1.College of Aerospace and Materials EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  3. 3.IEEC and Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  4. 4.IEEC and Departament de Matemàtica Aplicada I, ETSEIBUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations