Skip to main content
Log in

Families of Earth–Moon trajectories with applications to transfers towards Sun–Earth libration point orbits

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

We studied Earth–Moon transfer trajectories in the circular restricted three-body problem (CRTBP) from the viewpoint of families and considered their applications in transferring a spacecraft from the Earth to periodic orbits around Sun–Earth libration point \(L_{2}\) (SE–L2). Initially, twelve families of trajectories with transfer time shorter than fifty days are identified in the Earth–Moon system. By connecting these transfers with stable manifolds of the target orbit, low-energy transfers from the low Earth orbit to a small-amplitude periodic orbit around SE–L2 are determined in two separate CRTBPs (Earth–Moon and Sun–Earth CRTBPs). Then, taking the patched trajectories as initial guesses and introducing a small maneuver at the perilune, we optimize the whole transfer trajectories in the Sun–Earth–Moon–Spacecraft system. Results indicate that it is possible to realize low-energy transfers to small-amplitude orbits around SE–L2 by patching the Earth–Moon transfers with stable manifolds of the target orbits.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Barden, B., Howell, K., Lo, M.: Astrodynamics Conference, 3602 (1996)

  • Belbruno, E.A., Miller, J.K.: J. Guid. Control Dyn. 16(4), 770 (1993)

    Article  ADS  Google Scholar 

  • Belló, M., Gómez, G., Masdemont, J.J.: Space Manifold Dynamics. Springer, Berlin (2010)

    MATH  Google Scholar 

  • Capuzzo-Dolcetta, R., Giancotti, M.: Celest. Mech. Dyn. Astron. 115(3), 215 (2013)

    Article  ADS  Google Scholar 

  • Cuevas, O., Kraft-Newman, L., Mesarch, M., et al.: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 4425 (2002)

  • Deprit, A., Henrard, J.: Astron. J. 172, 158 (1967)

    Article  ADS  Google Scholar 

  • Doedel, E.J., Paffenroth, R.C., Keller, H.B., et al.: Int. J. Bifurc. Chaos 13(06), 1353 (2003)

    Article  Google Scholar 

  • Dunham, D.W., Farquhar, R.W.: Libration Point Orbits and Applications. World Scientific, Singapore (2003)

    Google Scholar 

  • Farquhar, R.W.: The control and use of libration-point satellites (1968)

  • Fehlberg, E.: Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control (1968)

  • Gómez, G., Jorba, A., Masdemont, J., et al.: Celest. Mech. Dyn. Astron. 56(4), 541 (1993)

    Article  ADS  Google Scholar 

  • Gómez, G., Marcote, M., Masdemont, J.J.: Acta Astronaut. 56(7), 652 (2005)

    Article  ADS  Google Scholar 

  • Howell, K.C.: Celest. Mech. 32(1), 53 (1984)

    Article  ADS  Google Scholar 

  • Koon, W.S., Lo, M.W., Marsden, J.E., et al.: Dynamical Systems, the Three Body Problem and Space Mission Design. Springer, New York (2006)

    MATH  Google Scholar 

  • Lei, H., Xu, B., Sun, Y.: Adv. Space Res. 51(5), 917 (2013)

    Article  ADS  Google Scholar 

  • Li, M., Zheng, J.: Acta Astronaut. 66(9–10), 1481 (2010)

    Google Scholar 

  • Liu, C.B., Hou, X.Y., Liu, L.: Adv. Space Res. 40(1), 76 (2007)

    Article  ADS  Google Scholar 

  • Marson, R., Pontani, M., Perozzi, E., et al.: Celest. Mech. Dyn. Astron. 106(2), 117 (2010)

    Article  ADS  Google Scholar 

  • Mengali, G., Quarta, A.A.: J. Guid. Control Dyn. 28(2), 209 (2005)

    Article  ADS  Google Scholar 

  • Onozaki, K., Yoshimura, H., Ross, S.D.: Adv. Space Res. 60(10), 2117 (2017)

    Article  ADS  Google Scholar 

  • Oshima, K., Yanao, T.: AAS/AIAA Space Flight Mechanics Meeting, AAS. 14 (2014)

  • Ozimek, M.T., Howell, K.C.: J. Guid. Control Dyn. 33(2), 533 (2010)

    Article  ADS  Google Scholar 

  • Peng, H., Gao, Q., Wu, Z., et al.: Adv. Space Res. 51(11), 2093 (2013)

    Article  ADS  Google Scholar 

  • Qi, Y., Xu, S.: Aerosp. Sci. Technol. 55, 282 (2016a)

    Article  Google Scholar 

  • Qi, Y., Xu, S.: Celest. Mech. Dyn. Astron. 125(3), 333 (2016b)

    Article  ADS  Google Scholar 

  • Qi, Y., Xu, S., Qi, R.: Acta Astronaut. 133, 145 (2017)

    Article  ADS  Google Scholar 

  • Salmani, M., Büskens, C.: Acta Astronaut. 69(9–10), 882 (2011)

    Article  ADS  Google Scholar 

  • Sousa-Silva, P., Terra, M.O., Ceriotti, M.: Astrophys. Space Sci. 363(10), 210 (2018)

    Article  ADS  Google Scholar 

  • Szebehely, V.: Theory of Orbits: the Restricted Problem of Three Bodies. Academic Press, New York (2006)

    MATH  Google Scholar 

  • Tantardini, M., Fantino, E.M., Ren, Y.: Celest. Mech. Dyn. Astron. 108(3), 215 (2010)

    Article  ADS  Google Scholar 

  • Topputo, F.: Celest. Mech. Dyn. Astron. 117(3), 279 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  • Uphoff, C.W.: Adv. Astronaut. Sci. 69, 333 (1989)

    Google Scholar 

  • Wilson, R.S., Howell, K.C.: J. Spacecr. Rockets 35(2), 191 (1998)

    Article  ADS  Google Scholar 

  • Yagasaki, K.: Physica D 197(3–4), 313 (2004)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is carried out with the financial support of the National Natural Science Foundation of China (No. 11603011) and the National Basic Research Program 973 of China (2015CB857100), and the National Defense Scientific Research Fund (No. 2016110C019).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hanlun Lei.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, Q., Lei, H. Families of Earth–Moon trajectories with applications to transfers towards Sun–Earth libration point orbits. Astrophys Space Sci 364, 43 (2019). https://doi.org/10.1007/s10509-019-3532-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-019-3532-1

Keywords

Navigation