A Method for Calculating the Trajectory of a Single-Impulse Flight to a Halo Orbit around the L2 Libration Point of the Earth–Moon

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Abstract

The problem of calculation of low-energy impulse trajectories to halo orbits in the vicinity of the L2 point of the Earth–Moon system is considered. A new method for calculating the trajectories of a single-impulse low-energy flight to a halo orbit is presented. The limited problem of four bodies is analyzed, within which the attraction of the Earth, Moon, and Sun is taken into account, and their position and speed are calculated using high-precision ephemeris support. Particular attention in the development of the method is paid to ensuring its computational stability for calculating trajectories with a long stay of a spacecraft (SC) in the zone of weak stability near the boundary of the Hill sphere of the Earth. The results of the calculation of single-impulse transfer trajectories from low Earth orbit to halo orbit around the L2 point of the Earth–Moon system are given. The analysis of the dependence of the main characteristics of single-impulse trajectories from the date of approach to the halo orbit is carried out.

About the authors

Zhou Rui

Moscow Aviation Institute, 125080, Moscow, Russia

Author for correspondence.
Email: 420790076@qq.com
Россия, Москва

References

  1. Себехей В. Теория орбит: ограниченная задача трех тел / пер. с англ.; под ред. Г.Н. Дубошина. М.: Наука, 1982. 657 с.
  2. Маркеев А.П. Точки либрации в небесной механике и космодинамике. М.: Наука, 1978. 312 с.
  3. Folta D.C., Pavlak T.A., Haapala A.F. et al. Earth–Moon libration point orbit stationkeeping: Theory, modeling, and operations // Acta Astronaut. 2014. V. 94. Iss. 1. P. 421–433. https://doi.org/10.1016/j.actaastro.2013.01.022
  4. Shan G., Wenyan Z., Weiguang L. et al. Trajectory analysis and design for relay satellite at Lagrange L2 point of Earth-Moon system // J. Deep Space Exploration. 2017. V. 4. Iss. 2. P. 122–129.https://doi.org/10.15982/j.issn.2095-7777.2017.02.004
  5. Folta D.C., Pavlak T.A., Haapala A.F. et al. Earth–Moon libration point orbit stationkeeping: Theory, modeling, and operations // Acta Astronaut. 2014. V. 94. Iss. 1. P. 421–433. https://doi.org/10.1016/j.actaastro.2013.01.022
  6. Gordon D.P. Transfers to earth-moon L2 halo orbits: Master Thesis of Science in Aeronautics and Astronautics. Purdue University West Lafayette, Indiana, 2008. 182 p.
  7. Wu W., Tang Y., Zhang L., Qiao D. Design of communication relay mission for supporting lunar-farside soft landing // J. Science China Information Sciences. 2018. V. 61. Iss. 4. 14 p. https://doi.org/10.1007/s11432-017-9202-1
  8. Davis D., Bhatt S., Howell K. et al. Orbit maintenance and navigation of human spacecraft at cislunar near rectilinear halo orbits // 27th AAS/AIAA Space Flight Mechanics Meeting. 5–9 Feb. 2017, San Antonio, Texas. 2017. Art. ID. JSC-CN-38626. 21 p.
  9. Starchville T.F., Melton R.G. Optimal low-thrust trajectories to Earth–Moon L2 Halo orbits (circular problem). // Advances in the Astronautical Sciences. 1997. V. 97. P. 1741–1756.
  10. Parrish N.L., Parker J.S., Hughes S.P. et al. Low-thrust transfers from distant retrograde orbits to L2 halo orbits in the Earth-Moon system // 6th Intern. Conf. Astrodynamics Tools and Techniques. 14–17 March 2016, Darmstadt. 2016. Art. ID. GSFC-E-DAA-TN30224. 10 p.
  11. An R., Wang M., Liang X.G. Transfer trajectory optimal design for Earth-Moon L2 based on invariant manifolds // J. Deep Space Exploration. 2017. V. 4. Iss. 3. P. 252–257.
  12. Ivanyukhin A.V., Petukhov V.G. Low-Energy Sub-Optimal Low-Thrust Trajectories to Libration Points and Halo-Orbits // Cosmic Research. 2019. V. 57. Iss. 5. P. 378–388. https://doi.org/10.1134/S0010952519050022
  13. Lei H., Xu B., Sun Y. Earth–Moon low energy trajectory optimization in the real system // Advances in Space Research. 2013. V. 51. Iss. 5. P. 917–929. https://doi.org/10.1016/j.asr.2012.10.011
  14. Parker J.S., Born G.H. Modeling a low-energy ballistic lunar transfer using dynamical systems theory // J. Spacecraft and Rockets. 2008. V. 45. Iss. 6. P. 1269–1281. https://doi.org/10.2514/1.35262
  15. Qi Y., Xu S. Earth–Moon transfer with near-optimal lunar capture in the restricted four-body problem // Aerospace Science and Technology. 2016. V. 55. P. 282–291.
  16. Richardson D.L. Halo orbit formulation for the ISEE-3 mission // J. Guidance and Control. 1980. V. 3. Iss. 6. P. 543–548.
  17. Richardson D.L. Analytic construction of periodic orbits about the collinear points // Celestial mechanics. 1980. V. 22. Iss. 3. P. 241–253.
  18. Петухов В.Г., Чжоу Ж. Расчет возмущенной импульсной траектории перелета между околоземной и окололунной орбитами методом продолжения по параметру // Вестник Московского авиац. ин-та. 2019. Т. 26. Iss. 2. P. 155–165.
  19. Kokou P., Le Bihan B., Receveur J.B. et al. Computing an optimized trajectory between Earth and an EML2 halo orbit // Proc. 2014 IEEE Chinese Guidance, Navigation and Control Conf. (CGNCC). Yantai, China, 8–10 Aug. 2014. Art. ID. 0450.
  20. Belbruno E., Carrico J. Calculation of weak stability boundary ballistic lunar transfer trajectories // Astrodynamics Specialist Conf. 2000. Art. ID. AIAA 2000-4142. 11 p. https://doi.org/10.2514/6.2000-4142
  21. Petukhov V.G., Ivanyukhin A.V. Low-energy trajectories to the Earth–Moon libration points and to halo-orbits // IAA/AAS SciTech Forum 2019 on Space Flight Mechanics and Space Structures and Materials. Moscow. V. 174: Advances in the Astronautical Sciences Series. 2021. P. 81–94.
  22. Guzzetti D., Zimovan E.M., Howell K.C. et al. Stationkeeping analysis for spacecraft in lunar near rectilinear halo orbits // 27th AAS/AIAA Space Flight Mechanics Meeting. American Astronautical Society. 5–9 Feb. 2017, San Antonio, TX, USA. 2017. 20 p.
  23. Zimovan E.M., Howell K.C., Davis D.C. Near rectilinear halo orbits and their application in cis-lunar space // 3rd IAA Conf. Dynamics and Control of Space Systems. Moscow, Russia. 2017. P. 20–40.
  24. Whitley R.J., Davis D.C., Burke L.M. et al. Earth-Moon near rectilinear halo and butterfly orbits for lunar surface exploration // Proc. AAS/AIAA Astrodynamics Specialist Conf. 19–23 Aug. 2018, Snowbird, UT, USA.
  25. Zimovan-Spreen E.M., Howell K.C., Davis D.C. Near rectilinear halo orbits and nearby higher-period dynamical structures: orbital stability and resonance properties // Celestial Mechanics and Dynamical Astronomy. 2020. V. 132. Iss. 5. Art. ID. 28. 25 p. https://doi.org/10.1007/s10569-020-09968-2
  26. Smith M., Craig D., Herrmann N. et al. The Artemis program: an overview of NASA’s activities to return humans to the Moon // Proc. 2020 IEEE Aerospace Conf. Big Sky, MT, USA. 7–14 Mar. 2020. 10 p.

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