Skip to main content
SpringerLink
Log in

Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

To design a free-return orbit for manned lunar mission based on low earth orbit (LEO) rendezvous, an adaptive LEO-phase free-return orbit design method based on high-precision dynamics model is proposed. First, the radius of perilune and the absolute value of perilune velocity are decoupled using a coordinate system rotation, which is derived from moon-centric local vertical and local horizontal instantaneous coordinate system at the time of perilune. The two Euler rotation angles and the absolute value of perilune velocity are used as independent design variables because their initial values are easy to guess. Next, a two-segment numerical integration strategy is proposed to calculate orbital elements at the moments of trans-lunar injection and free-return vacuum perigee. Subsequently, an optimization algorithm software package for solving large-scale nonlinear sequential quadratic programming problems (SQP_snopt) is employed to search the objective free-return orbit with a fixed trans-lunar injection inclination and the other two constraints on radiuses of perigee at the times of trans-lunar injection and vacuum perigee. After that, an iteration algorithm is devised to adjust trans-lunar injection window for adaptive LEO-phase. Finally, numerical results show a fast and accurate performance of the direct optimization method, which can provide valuable references to manned lunar missions based on LEO rendezvous.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Lunney G. Discussion of several problem areas during the Apollo 13 operation [C]. AIAA 7th Annual Meeting and Technical Display, Houston, Texas. 1970

  2. Miele, A.: Theorem of image trajectories in earth moon space [J]. Acta Astronautica. 6(51), 225–232 (1960)

    MATH  Google Scholar 

  3. Schwaniger, A.J.: Trajectories in the earth-moon space with symmetric free-return properties [R]. In: NASA Technical Note D-1833 (1963)

    Google Scholar 

  4. Jesick, M., Ocampo, C.: Automated generation of symmetric lunar free-return trajectories [J]. J. Guid. Control. Dyn. 34(1), 98–106 (2011)

    Article  Google Scholar 

  5. Egorov V A. Three-dimensional lunar trajectories [R]. NASA Technical Translation, F-504,1969

  6. Farquhar, R.W.: Dunham D W. a new trajectory concept for exploration the earth’s geomagnetic tail [J]. J. Guid. Control. Dyn. 4(2), 192–196 (1980)

    Article  Google Scholar 

  7. He, B.Y., Li, H.Y., Zhou, J.P.: Solution domain analysis of earth-moon quasi-symmetric free-return orbits [J]. Trans. Japan Soc. Aero. Space Sci. 60(4), 195–201 (2017)

    Article  Google Scholar 

  8. Egorov, V.A.: Certain problems of moon flight dynamics [M]. International Physical Index Inc, New York (1958)

    Google Scholar 

  9. Tolson, R.H.: Geometrical characteristic of lunar orbits established from earth-moon trajectories [R]. NASA Technical Note D-1780, Washington DC (1963)

    Google Scholar 

  10. Penzo A P. An analysis of free-flight circumlunar trajectories [C]. AIAA Astrodynamicss conference, new haven, Connecticut, USA, August, 19–21. 1963

  11. Dallas, S.S.: Moon-to-earth trajectories [C]. AIAA Astrodynamics Conference, New Haven (1963)

    Book  Google Scholar 

  12. Gibson F T. Application of the matched conic model in the study of circumlunar trajectories [R]. NASA Project Apollo Working Paper No.1066. 1963

  13. Peng, Q.B., Shen, H.X., Li, H.Y.: Free return orbit design and characteristics analysis for manned lunar mission [J]. Sci. China Technol. Sci. 54(12), 3243–3250 (2011)

    Article  Google Scholar 

  14. Li, J.Y., Gong, S.P., Baoyin, H.X.: Generation of multi-segment lunar free-return trajectories [J]. J. Guid. Control. Dyn. 36(3), 765–775 (2013)

    Article  Google Scholar 

  15. Wilson S W. A pseudostate theory for the approximation of three-body trajectories [C]. AAS/AIAA Astrodynamics Conference, AAS/AIAA Astrodynamics Conference, Santa Barbaba, 1970

  16. Wilson, R.S., Howell, K.C.: Trajectory design in the sun-earth-moon system using lunar gravity assists. J. Spacecr. Rocket. 35(2), 191–198 (1998)

    Article  Google Scholar 

  17. Byrnes, D.: Application of the pseudostate theory to the three body lambert problem [J]. J. Astronaut. Sci. 37, 221–232 (1989)

    MathSciNet  Google Scholar 

  18. Ramanan, R.: Integrate algorithm for lunar transfer trajectories using a pseudo state technical[J]. J. Guid. Control. Dyn. 25(2), 946~952 (2002)

    Google Scholar 

  19. Luo, Q.Q., Yin, J.F., Han, C.: Design of earth-moon free-return trajectories [J]. J. Guid. Control. Dyn. 36(1), 263–271 (2013)

    Article  Google Scholar 

  20. Zhang, H.L., Luo, Q.Q., Han, C.: Accurate and fast design algorithm for free-return lunar flyby trajectories [J]. Acta Astronautica. 102(5), 14–26 (2014)

    Article  Google Scholar 

  21. Stanley, D., Cook, S., Connolly, J., et al.: NASA’s exploration system architecture study [R]. NASA-TM-2005-214062. In: November (2005)

    Google Scholar 

  22. Yan, H., Gong, Q.: High-accuracy trajectory optimization for a trans-earth-lunar mission [J]. J. Guid. Control. Dyn. 34(4), 1219–1227 (2011)

    Article  Google Scholar 

  23. He, B.Y., Li, H.Y., Zhang, B.: Analysis of transfer orbit deviation propagation mechanism and robust design for manned lunar landing [J]. Acta Phys. Sin. 62(19), 91–98 (2013)

    Google Scholar 

  24. Yim, S.Y., Baoyin, H.X.: High latitude landing circumlunar free return trajectory design [J]. Aircraft. Engin. and Aeros. Techn. 87(4), 380–391 (2015)

  25. Berry, R.L.: Launch window and trans-lunar orbit, lunar orbit, and trans-earth orbit planning and control for the Apollo 11 lunar landing mission [R]. AIAA 8th Aerospace Sciences Meeting, AIAA 70–0024, New York (1970)

    Google Scholar 

  26. Topputo, F.: On optimal two-impulse earth-moon transfers in a four-body model [J]. Celestial Mech. Dyn. Astr. 117(3), 279–313 (2013)

    Article  MathSciNet  Google Scholar 

  27. Shen, H.X., Zhou, J.P., Peng, Q.B., et al.: Point return orbit design and characteristics analysis for manned lunar mission [J]. Sci. China Technol. Sci. 55(9), 2561–2569 (2012)

    Article  Google Scholar 

  28. Gill, P.E., Murray, W., Saunder, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization [J]. Siam J. Optim. 12(4), 979–1006 (2002)

    Article  MathSciNet  Google Scholar 

  29. Garn M, Qu M, and Chrone J, et al. NASA’s planned return to the moon: global access and anytime return requirement implications on the lunar orbit insertion burns [C]. AAS/AIAA Astrodynamicss Specialist Conference and Exhibit, August. 2008

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11702330) and National Defense Science and Technology Innovation Special Zone Project.

Author information

Authors and Affiliations

  1. State Key Laboratory of Astronautic Dynamics (ADL), Xi’an Satellite Control Center, Xi’an, China

    Bo-yong He & Heng-nian Li

  2. Beijing Aerospace Flight and Control Center, Beijing, China

    Ai-wu Zheng

Authors
  1. Bo-yong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heng-nian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ai-wu Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bo-yong He.

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

He, By., Li, Hn. & Zheng, Aw. Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous. J Astronaut Sci 66, 446–459 (2019). https://doi.org/10.1007/s40295-019-00182-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-019-00182-3

Keywords

Search

Navigation