Celestial Mechanics and Dynamical Astronomy

, Volume 128, Issue 4, pp 409–433 | Cite as

Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system

  • Yu ChengEmail author
  • Gerard Gómez
  • Josep J. Masdemont
  • Jianping Yuan
Original Article


This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.


Transfer orbits Libration point orbits Invariant manifolds Lunar orbits 



Y. C. thanks the support of Doctorate Foundation of Northwestern Polytechnical University and the Chinese Scholarship Council during her stay in Barcelona. G. G. thanks the Catalan Grant Government for the Grant 2014SGR1145, and MINECO-FEDER for the Grant MTM2013-41168-P. J. J. M. thanks MINECO-FEDER for the Grant MTM2015-65715-P and the Catalan Government for the Grant 2014SGR504. The authors would like to thank the referees for a careful reading of the manuscript and their valuable and useful comments.


  1. Alessi, E.M., Gómez, G., Masdemont, J.J.: Two-manoeuvres transfers between LEOs and lissajous orbits in the Earth–Moon system. Adv. Space Res. 45(10), 1276–1291 (2010)ADSCrossRefGoogle Scholar
  2. Anderson, R.L., Parker, J.S.: Comparison of low-energy lunar transfer trajectories to invariant manifolds. Celest. Mech. Dyn. Astron. 115(3), 311–331 (2013)ADSCrossRefzbMATHGoogle Scholar
  3. Archinal, B.A., et al.: Report of the IAU working group on cartographic coordinates and rotational elements: 2009. Celest. Mech. Dyn. Astron. 109(2), 101–135 (2011)ADSCrossRefzbMATHGoogle Scholar
  4. Born, G.H., Parker, J.S.: Direct halo lunar transfers. J. Astronautical. Sci. 56(4), 441–476 (2008)ADSCrossRefGoogle Scholar
  5. Cao, J., Hu, S., Huang, Y.: Orbit determination and analysis for chang’E-2 extended mission. Geomat. Inf. Sci. Wuhan Universe 38(9), 1029–1033 (2013)Google Scholar
  6. Escobal, P.R.: Methods of Astrodynamics. Wiley, London (1969)Google Scholar
  7. Folta, D.C., Woodard, M., Howell, K.C., Patterson, C., Schlei, W.: Applications of multi-body dynamical environments: the ARTEMIS transfer trajectory design. Acta Astronaut. 73, 237–249 (2012)ADSCrossRefGoogle Scholar
  8. Gómez, G., Llibre, J., Martínez, R., Simó, C.: Dynamics and Mission Design Near Libration Points. Vol. I Fundamentals: The Case of Collinear Libration Points. World Scientific, Singapore (2001)zbMATHGoogle Scholar
  9. Gómez, G., Mondelo, J.-M.: The dynamics around the collinear equilibrium points of the RTBP. Phys. D Nonlinear Phenom. 157(4), 283–321 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. Gómez, G., Masdemont, J.J., Mondelo, J.-M.: Libration point orbits: a survey from the dynamical point of view. In: Gómez, G., Lo, M.W., Masdemont, J.J. (eds.) Proceedings of the Conference Libration Point Orbits and Applications, pp. 311–372. World Scientific (2003)Google Scholar
  11. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos 10, 427–469 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Low energy transfer to the Moon. Celest. Mech. Dyn. Astron. 81, 63–73 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Dynamical Systems, the Three-Body Problem and Space Mission Design. Marsden Books, Wellington (2011). (ISBN 978-0-615-24095-4)zbMATHGoogle Scholar
  14. Liu, L., Liu, Y., Cao, J., Hu, S., Tang, G., Xie, J.: CHANGE-2 lunar escape maneuvers to the Sun Earth \(L_2\) libration point mission. Acta Astronaut. 93, 390–399 (2014)ADSCrossRefGoogle Scholar
  15. Miller, J.K.: Lunar Transfer Trajectory Design and the Four Body Problem. 13th AAS/AIAA Space Flight Mechanics Meeting, Paper No. AAS 03-144 (2002)Google Scholar
  16. NASA: A Standardised Lunar Coordinate System for the Lunar Reconnaissance Orbiter and Lunar Datasets, LRO Project and LGCWG White Paper, Version 5. (2008)
  17. Parker, J.S., Anderson, R.L.: Low-Energy Lunar Trajectory Design. Deep Space Communications and Navigation Series (DESCANSO) (2013)Google Scholar
  18. Peng, H., Wang, Y., Masdemont, J.J., Gómez, G.: Design and Analysis of Transfers from Lunar Polar Orbits to Sun–Earth Libration Point Orbit (2017)Google Scholar
  19. Ren, Y., Shan, J.: Low-energy lunar transfers using spatial transit orbits. Commun. Nonlinear Sci. Numer. Simul. 19(3), 554–569 (2014)ADSMathSciNetCrossRefGoogle Scholar
  20. Rincón, Á., Rojo, P., Lacruz, E., Abellán, G., Díaz, S.: On non-coplanar Hohmann transfer using angles as parameters. Astrophys. Space Sci. 359, 1–6 (2015)ADSCrossRefGoogle Scholar
  21. Roberts, C.E.: The SOHO mission \(L_1\) halo orbit recovery from the attitude control anomalies of 1998. In: Gómez, G., Lo, M.W., Masdemont, J.J. (eds.) Proceedings of the Conference Libration Point Orbits and Applications, pp. 171–218. World Scientific (2003)Google Scholar
  22. Szebehely, V.: Theory of Orbits. Academic Press, London (1967)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.National Key Laboratory of Aerospace Flight DynamicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.IEEC and Department de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain
  3. 3.IEEC and Department de MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain

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