Skip to main content
SpringerLink
Log in

Weak Stability Boundary Transfer into DRO Based on Numerical Continuation Method

  • Conference paper
  • First Online:
Proceedings of the International Conference on Internet of Things, Communication and Intelligent Technology (IoTCIT 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 1015))

  • 466 Accesses

Abstract

Distant retrograde orbits (DROs) are a class of periodic orbits in cislunar space, which are characterized by long-term stability and low insertion cost, can be used as a staging station for cislunar space missions. The important issue is to reduce fuel consumption. Using weak stability boundary (WSB) can effectively reduce the insertion cost for transfers from Earth to DRO, while requiring a higher launching cost. This paper aims to improve the design efficiency of WSB with lunar gravity assist (LGA) type transfer which has a lower launching cost, while finding the global optimal solution with a lower total cost. Firstly, the initial value of trajectories is obtained by the perigee Poincare map, then the multiple shooting with analytic gradient is applied to correct the trajectories, and finally using pseudo-arclength to find more WSB with LGA type transfer and obtain the global optimal solution. Using parallel computing greatly improves the computing time of the whole process, and the results show that the percentage of WSB with LGA type transfer increased by 34.1%, and for the minimum cost solution of 2:1 DRO, the flight time is 130.14 days, and the launching cost is 3.126 km/s, which is about 70 m/s lower than the WSB transfer without LGA, the DRO insertion cost only needs 52.6 m/s.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Smith, M., Craig, D., Herrmann, N., Mahoney, E., Krezel, J., McIntyre, N., Goodliff, K.: The Artemis program: An overview of NASA’s activities to return humans to the moon. In: 2020 IEEE Aerospace Conference, pp. 1–10. IEEE (2020)

    Google Scholar 

  2. Yu, D.Y., Ge, Z.J., Wang, N.D.: Supposal for structure form of lunar base. J. Astronaut. 33(12), 1840–1844 (2012)

    Google Scholar 

  3. Fan, W.W.: China and Russia signed a memorandum of understanding on cooperation in building an international lunar research station. Chin. J. Space Sci. 41(3), 1 (2021)

    Google Scholar 

  4. Condon, G.L., Williams, J.: Asteroid redirect crewed mission nominal design and performance. In: SpaceOps 2014 Conference, p. 1696 (2014)

    Google Scholar 

  5. Whitley, R., Martinez, R.: Options for staging orbits in cislunar space. In: 2016 IEEE Aerospace Conference, pp. 1–9. IEEE (2016)

    Google Scholar 

  6. Zeng, H., Li, Z.Y., Peng, K.: Research on application of Earth-Moon NRHO and DRO for lunar exploration. J. Astronaut. 41(7), 910–919 (2020)

    Google Scholar 

  7. Belbruno, E.: Lunar capture orbits, a method of constructing earth moon trajectories and the lunar GAS mission. In: 19th International Electric Propulsion Conference, p. 1054 (1987)

    Google Scholar 

  8. Belbruno, E.A., Miller, J.K.: Sun-perturbed Earth-to-Moon transfers with ballistic capture. J. Guid. Control. Dyn. 16(4), 770–775 (1993)

    Article  Google Scholar 

  9. Hatch, S., Chung, M.K., Kangas, J., Long, S., Roncoli, R., Sweetser, T.: Trans-lunar cruise trajectory design of GRAIL (Gravity Recovery and Interior Laboratory) mission. In: AIAA/AAS Astrodynamics Specialist Conference, p. 8384 (2010)

    Google Scholar 

  10. Jehn, R., Campagnola, S., Garcia, D., Kemble, S.: Low-thrust approach and gravitational capture at Mercury. In: 18th International Symposium on Space Flight Dynamics, p. 487 (2004)

    Google Scholar 

  11. Elliott, J., Alkalai, L.: Lunette: A network of lunar landers for in-situ geophysical science. Acta Astronaut. 68(7–8), 1201–1207 (2011)

    Article  Google Scholar 

  12. Vetrisano, M., Van der Weg, W., Vasile, M.: Navigating to the Moon along low-energy transfers. Celest. Mech. Dyn. Astron. 114(1), 25–53 (2012)

    Article  MathSciNet  Google Scholar 

  13. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Low energy transfer to the Moon. Celest. Mech. Dyn. Astron. 81(1), 63–73 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Topputo, F., Vasile, M., Bernelli-Zazzera, F.: Low energy interplanetary transfers exploiting invariant manifolds of the restricted three-body problem. J. Astronaut. Sci. 53(4), 353–372 (2005)

    Article  MathSciNet  Google Scholar 

  15. Hyeraci, N., Topputo, F.: Method to design ballistic capture in the elliptic restricted three-body problem. J. Guid. Control. Dyn. 33(6), 1814–1823 (2010)

    Article  Google Scholar 

  16. Topputo, F.: On optimal two-impulse Earth-Moon transfers in a four-body model. Celest. Mech. Dyn. Astron. 117(3), 279–313 (2013)

    Article  MathSciNet  Google Scholar 

  17. Sousa-Silva, P., Terra, M.O., Ceriotti, M.: Fast Earth-Moon transfers with ballistic capture. Astrophys. Space Sci. 363(10), 1–11 (2018)

    Article  MathSciNet  Google Scholar 

  18. Oshima, K., Topputo, F., Yanao, T.: Low-energy transfers to the Moon with long transfer time. Celest. Mech. Dyn. Astron. 131(1), 1–19 (2019). https://doi.org/10.1007/s10569-019-9883-7

    Article  MathSciNet  MATH  Google Scholar 

  19. Parker, J.S., Born, G.H.: Modeling a low-energy ballistic lunar transfer using dynamical systems theory. J. Spacecr. Rocket. 45(6), 1269–1281 (2008)

    Article  Google Scholar 

  20. Parker, J.S.: Targeting low-energy ballistic lunar transfers. J. Astronaut. Sci. 58(3), 311–334 (2011)

    Article  Google Scholar 

  21. Parker, J.S., Anderson, R.L., Peterson, A.: Surveying ballistic transfers to low lunar orbit. J. Guid. Control. Dyn. 36(5), 1501–1511 (2013)

    Article  Google Scholar 

  22. Parrish, N.L., Kayser, E., Udupa, S., Parker, J.S., Cheetham, B.W., Davis, D.C.: Survey of ballistic lunar transfers to near rectilinear halo orbit. In: AAS/AIAA Astrodynamics Specialists Conference, pp. 1–20 (2019)

    Google Scholar 

  23. Xu, M., Xu, S.J.: Exploration of distant retrograde orbits around Moon. Acta Astronaut. 65(5–6), 853–860 (2009)

    Google Scholar 

  24. Tan, M.H., Zhang, K., Lv, M.B., Xing, C.: Transfer to long term distant retrograde orbits around the Moon. Acta Astronaut. 98, 50–63 (2014)

    Article  Google Scholar 

  25. Scheuerle, S.T., McCarthy, B.P., Howell, K.C.: Construction of ballistic lunar transfers leveraging dynamical systems techniques. In: AAS/AIAA Astrodynamics Specialist Conference, pp. 1–20. Lake Tahoe, California (2020)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chinese Academy of Sciences, Technology and Engineering Center for Space Utilization, Beijing, 100094, China

    Yuqing Zhang & Chen Zhang

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Yuqing Zhang

Authors
  1. Yuqing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chen Zhang .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, Hunan, China

    Jian Dong

  2. School of Information Engineering, Shenzhen University, Shenzhen, Guangdong, China

    Long Zhang

Appendix

Appendix

See Table 3.

Table 3. Simulation parameters
Full size table

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhang, Y., Zhang, C. (2023). Weak Stability Boundary Transfer into DRO Based on Numerical Continuation Method. In: Dong, J., Zhang, L. (eds) Proceedings of the International Conference on Internet of Things, Communication and Intelligent Technology . IoTCIT 2022. Lecture Notes in Electrical Engineering, vol 1015. Springer, Singapore. https://doi.org/10.1007/978-981-99-0416-7_72

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-0416-7_72

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-0415-0

  • Online ISBN: 978-981-99-0416-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation