Skip to main content
Log in

Sun–Earth \(L_{1}\) and \(L_{2}\) to Moon transfers exploiting natural dynamics

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript


This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others


  • Belbruno, E.: Capture Dynamics and Chaotic Motions in Celestial Mechanics. Princeton University Press, Princeton (2004)

    MATH  Google Scholar 

  • Campagnola, S., Russell, R.P.: Endgame problem part 2: multibody technique and the tisserand-poincare graph. J. Guid. Control Dyn. 33, 476–486 (2010)

    Article  ADS  Google Scholar 

  • Canalias, E., Masdemont, J.J.: Computing natural transfers between Sun–Earth and Earth–Moon Lissajous libration point orbits. Acta Astronaut. 63, 238–248 (2008)

    Article  ADS  Google Scholar 

  • Castelli, R.: On the relation between the bicircular model and the coupled circular restricted three-body problem approximation. In: António, J., Machado, T., Baleanu, D., Luo, A. (eds.) Nonlinear and Complex Dynamics, pp. 53–68. Springer, New York (2011)

    Chapter  Google Scholar 

  • Conley, C.C.: Low energy transit orbits in the restricted three-body problems. SIAM J. Appl. Math. 16, 732–746 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  • Dachwald, B., Seboldt, W., Häusler, B.: Performance requirements for near-term interplanetary solar sailcraft missions. In: International Symposium on Propulsion for Space Transportation of the XXIst Century, Versailles (2002)

  • ESA: Herschel portal. European Space Agency. (1995). Accessed Dec 15, 2013

  • Fantino, E., Gómez, G., Masdemont, J.J., Ren, Y.: A note on libration point orbits, temporary capture and low-energy transfers. Acta Astronaut. 67, 1038–1052 (2010)

    Article  ADS  Google Scholar 

  • Felici, F.: ESA/BULLETIN 84, The SOHO project. European Space Agency. (1995). Accessed Nov 10, 2013

  • Gómez, G., Llibre, J., Martínez, R., Simó, C.: Dynamics and Mission Design Near Libration Point Orbits-Volume 1: The Case of Collinear Libration Points. World Scientific, Singapore (2000a)

    Google Scholar 

  • Gómez, G., Jorba, À., Masdemont, J.J., Simó, C.: Dynamics and Mission Design Near Libration Point Orbits-Volume 3: Advanced Methods for Collinear Points. World Scientific, Singapore (2000b)

    Google Scholar 

  • García, F., Gómez, G.: A note on weak stability boundary. Celest. Mech. Dyn. Astron. 97, 87–100 (2007)

    Article  MATH  ADS  Google Scholar 

  • Gómez, G., Koon, W.S., Lo, M.W., Marsden, J.E., Masdemont, J., Ross, S.D.: Invariant manifolds, the spatial three-body problem and space mission design. In: Astrodynamics 2001. Advances in Astronautical Sciences No.109, pp. 3–22. American Astronautical Society, San Diego (2001)

  • Haapala, A.F., Howell, K.C.: Representations of higher-dimensional Poincaré maps with applications to spacecraft trajectory design. Acta Astronaut. 96, 23–41 (2014)

    Article  ADS  Google Scholar 

  • 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 (2001a)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Constructing a low energy transfer between Jovian moons. Contemp. Math. 292, 129–146 (2001b)

    Article  MathSciNet  Google Scholar 

  • Lantoine, G., Russell, R.P., Campagnola, S.: Optimization of low-energy resonant hopping transfers between planetary moons. Acta Astronaut. 68, 1361–1378 (2011)

    Article  ADS  Google Scholar 

  • Marsden, J., Ross, S.: New methods in celestial mechanics and mission design. Bull. Am. Math. Soc. 43, 43–73 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • McGehee, R.P.: Some homoclinic orbits for the restricted three-body problem. Ph.D. thesis, University of Wisconsin (1969)

  • McInnes, C.R.: Solar Sailing: Technology, Dynamics and Mission Applications. Springer, Berlin (2004)

    Google Scholar 

  • Meyer, K.R., Hall, G.R., Offin, D.: Introduction to hamiltonian dynamical systems and the N-body problem, Springer Science + Business Media, New York (2009)

  • Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  • Silva, P.A.S., Terra, M.O.: Applicability and dynamical characterization of the associated sets of the algorithmic weak stability boundary in the lunar sphere of influence. Celest. Mech. Dyn. Astron. 113, 141–168 (2012)

    Article  ADS  Google Scholar 

  • Simo, J., McInnes, C.R.: Solar sail orbits at the Earth–Moon libration points. Commun. Nonlinear Sci. Numer. Simul. 14, 4191–4196 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967)

    Google Scholar 

  • Topputo, F., Belbruno, E., Gidea, M.: Resonant motion, ballistic escape, and their applications in astrodynamics. Adv. Space Res. 42, 1318–1329 (2008)

    Article  ADS  Google Scholar 

  • Van der Weg, W.J., Vasile, M.: High area-to-mass ratio hybrid propulsion Earth to Moon transfers in the CR3BP. In: 63rd International Astronautical Congress, Naples, Italy. IAC-12-C1.4.8 (2012)

  • Villac, B.F., Scheeres, D.J.: Escaping trajectories in the Hill three-body problem and applications. J. Guid. Control Dyn. 26, 224–232 (2003)

    Article  ADS  Google Scholar 

Download references


This work was done as part of a study for the European Space Agency named “End-Of-Life Disposal Concepts for Lagrange-Point and Highly Elliptical Orbit Missions” (Contract No. 4000107624/13/F/MOS). The authors would like to acknowledge the following team members that contributed to the ESA study: Camilla Colombo, Hugh Lewis, Francesca Letizia, Stefania Soldini, Elisa Maria Alessi, Alessandro Rossi, Linda Dimare, Massimo Vetrisano, and Markus Landgraf. The authors would like to thank Elisa Maria Alessi in particular for her provision of the orbital characteristics of SOHO’s operational orbit. This work was partially supported by the EC Marie Curie Network for Initial Training Astronet-II, Grant Agreement No. 289240.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Willem Johan van der Weg.

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1 (PDF 2920 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

van der Weg, W.J., Vasile, M. Sun–Earth \(L_{1}\) and \(L_{2}\) to Moon transfers exploiting natural dynamics. Celest Mech Dyn Astr 120, 287–308 (2014).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: