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Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines

Abstract

This study is devoted to the possibility of creating artificial halo orbits in the circular restricted three-body problem of the Earth–Moon system due to the small acceleration from low-thrust engines acting on a spacecraft for a long time in situations, where the natural halo orbit cannot meet the mission requirements or is busy. In this paper, using collocation and parameter-continuation methods, two classes of artificial halo orbits in the Earth–Moon system are obtained. The first class is generated due to additional constant in magnitude and direction acceleration. A complete family of orbits of this class was obtained, which significantly differ from the traditional ones in terms of period and shape. The second class of orbits is generated by variable electric propulsion. This class of orbits was obtained as a solution to the problem of the optimal consumption of the working substance for orbit formation with a given period using the Pontryagin maximum principle and the method of continuation in parameter. It was shown that there are significant differences in orbital periods between artificial halo orbits—descendants of the same halo orbit. The calculation results confirm the possibility of using low-thrust engines to vary the parameters of natural halo orbits suitable for ballistic design of future lunar missions.

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REFERENCES

  1. Aksenov, S.A. and Bober, S.A., Upravlenie dvizheniem kosmicheskogo apparata na galo-orbite pri nalichii ogranichenii na napravleniya korrektiruyushchikh manevrov. Nekotorye aspekty sovremennykh problem mekhaniki i informatiki (Controlling the Spacecraft Motion in a Halo Orbit in the Presence of Restrictions on the Directions of Corrective Maneuvers. Some Aspects of Modern Problems of Mechanics and Informatics), Moscow: Inst. Kosm. Issled. Ross. Akad. Nauk, 2018.

  2. Il’in, I.S., Sazonov, V.V., and Tuchin, A.G., Transfer trajectories from low-Earth orbit to the manifold of bounded orbits in the vicinity of the libration point L_2 of the Sun–Earth system, Preprint of Keldysh Inst. of Applied Mathematics, Russ. Acad. Sci., Moscow, 2012.

    Google Scholar 

  3. Shaykhutdinov, A.R. and Kostenko, V.I., Prospects for using the halo-orbit in the vicinity of the L2 libration point of the Sun–Earth system for the ground-space millimetron radio interferometer, Cosmic Res., 2020, vol., 58, no. 5, pp. 393–401.

    ADS  Article  Google Scholar 

  4. Fain, M.K. and Starinova, O.L., Ballistic optimization of the L1–L2 and L2–L1 low thrust transfers in the Earth–Moon system, 7th Int. Conf. on Recent Advances in Space Technologies (RAST), IEEE, 2015.

  5. Farquhar, R.W. and Kamel, A.A., Quasi-periodic orbits about the translunar libration point, Celestial Mech., 1973, vol. 7, no. 4, pp. 458–473.

    ADS  Article  Google Scholar 

  6. Richardson, D.L., Analytic construction of periodic orbits about the collinear points, Celestial Mech., 1980, vol. 22, no. 3, pp. 241–253.

    ADS  MathSciNet  Article  Google Scholar 

  7. Celletti, A., Pucacco, G., and Stella, D., Lissajous and halo orbits in the restricted three-body problem, J. Nonlinear Sci., 2015, vol. 25, no. 2, pp. 343–370.

    ADS  MathSciNet  Article  Google Scholar 

  8. Shirobokov, M.G. and Trofimov, S.P., Low-thrust transfers to lunar orbits from halo orbits around lunar libration points L1 and L2, Cosmic Res., 2020, vol. 58, no. 3, pp. 181–191.

    ADS  Article  Google Scholar 

  9. Biggs, J.D., McInnes, C., and Waters, T., New periodic orbits in the solar sail restricted three-body problem, 2nd Conf. on Nonlinear Science and Complexity, 2008.

  10. Huang, J., Biggs, J.D., and Cui, N., Families of halo orbits in the elliptic restricted three-body problem for a solar sail with reflectivity control devices, Adv. Space Res., 2020, vol. 65, no. 3, pp. 1070–1082.

    ADS  Article  Google Scholar 

  11. Lukyanov, L.G., Stability of coplanar libration points in the restricted photogravitational three-body problem, Sov. Astron., 1987, vol. 31, no. 6, pp. 677–681.

    ADS  MathSciNet  MATH  Google Scholar 

  12. Kunitsyn, A.L. and Tureshbaev, A.T., On coplanar libration points of the photogravitational three-body problem, Pis’ma Astron. Zh., 1983, vol. 9, no. 7, pp. 432–435.

    ADS  Google Scholar 

  13. Chidambararaj, P. and Sharma, R.K., Halo orbits around Sun–Earth L1 in photogravitational restricted three-body problem with oblateness of smaller primary, Int. J. Astron. Astrophys., 2016, vol. 6, no. 3, pp. 293–311.

    Article  Google Scholar 

  14. Pathak, N., Thomas, V.O., and Abouelmagd, E.I., The perturbed photogravitational restricted three-body problem: analysis of resonant periodic orbits, Discrete Contin. Dyn. Syst., Ser. S, 2019, vol. 12, nos. 4–5, pp. 849–875.

    MATH  Google Scholar 

  15. Krasilnikov, P.S., Hill’s curves and libration points in the low-thrust restricted circular threebody problem, Russ. J. Nonlinear Dyn., 2017, vol. 13, no. 4, pp. 543–556.

    Google Scholar 

  16. Baig, S. and McInnes, C.R., Artificial halo orbits for low-thrust propulsion spacecraft, Celestial Mech. Dyn. Astron., 2009, vol. 104, no. 4, pp. 321–335.

    ADS  MathSciNet  Article  Google Scholar 

  17. Curtis, H.D., Orbital Mechanics for Engineering Students, Oxford: Butterworth-Heinemann, 2013.

    Google Scholar 

  18. Ivanyukhin, A.V. and Petukhov, V.G., Low-energy sub-optimal low-thrust trajectories to libration points and halo-orbits, Cosmic Res., 2019, vol. 57, no. 5, pp. 378–388.

    ADS  Article  Google Scholar 

  19. Ferrari, F. and Lavagna, M., Periodic motion around libration points in the elliptic restricted three-body problem, Nonlinear Dyn., 2018, vol. 93, no. 2, pp. 453–462.

    Article  Google Scholar 

  20. Trofimov, S., Shirobokov, M., Tselousova, A., et al., Transfers from near-rectilinear halo orbits to low-perilune orbits and the Moon’s surface, Acta Astronaut., 2020, vol. 167, pp. 260–271.

    ADS  Article  Google Scholar 

  21. Koon, W.S., Lo, M.W., Marsden, J.E., et al., Dynamical systems, the three-body problem and space mission design, Proc. Int. Conf. on Differential Equations, 2000, vol. 99, pp. 1167–1181.

  22. Aksenov, S.A. and Bober, S.A., Calculation and study of limited orbits around the L2 libration point of the Sun–Earth system, Cosmic Res., 2018, vol. 56, no. 2, pp. 144–150.

    ADS  Article  Google Scholar 

  23. Howell, K.C., Three-dimensional, periodic, ‘halo’ orbits, Celestial Mech., 1984, vol. 32, no. 1, pp. 53–71.

    ADS  MathSciNet  Article  Google Scholar 

  24. Thurman, R. and Worfolk, P.A., The geometry of halo orbits in the circular restricted three-body problem, University of Minnesota: Geometry Center Research Report GCG95, 1996.

  25. Grebow, D.J., Ozimek, M.T., Howell, K.C., et al., Multibody orbit architectures for lunar south pole, J. Spacecr. Rockets, 2008, vol. 45, no. 2, pp. 344–358.

    ADS  Article  Google Scholar 

  26. Cielaszyk, D. and Wie, B., New approach to halo orbit determination and control, J. Guid., Control, Dyn., 1996, vol. 19, no. 2, pp. 266–273.

    ADS  Article  Google Scholar 

  27. Boudad, K.K., Howell, K.C., and Davis, D.C., Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem, Adv. Space Res., 2020, vol. 66, no. 9, pp. 2194–2214.

    ADS  Article  Google Scholar 

  28. Petukhov, V.G., Method of continuation for optimization of interplanetary low-thrust trajectories, Cosmic Res., 2012, vol. 50, no. 3, pp. 249–261.

    ADS  Article  Google Scholar 

  29. Petukhov, V.G. and Chzhou, Zh., Calculation of the disturbed impulse trajectory of the flight between the near-Earth and circumlunar orbits by the method of continuation in parameter, Vestn. Mosk. Aviats. Inst., 2019, vol. 26, no. 2, pp. 155–165.

    Google Scholar 

  30. Mingotti, G., Topputo, F., and Bernelli-Zazzera, F., Combined optimal low-thrust and stable-manifold trajectories to the Earth–Moon halo orbits, AIP Conference Proceedings. American Institute of Physics, 2007, vol. 886, no. 1, pp. 100–112.

  31. Pritchett, R., Howell, K., and Grebow, D., Low-thrust transfer design based on collocation techniques: applications in the restricted three-body problem, Astrodynamics Specialists Conference, 2017.

  32. Shampine, L.F., Kierzenka, J., and Reichelt, M.W., Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, Tutorial Notes, 2000, pp. 1–27.

    Google Scholar 

  33. Higham, D.J. and Higham, N.J., MATLAB Guide, Philadelphia, PA: Society for Industrial and Applied Mathematics, 2016.

    MATH  Google Scholar 

  34. Zhang, C., Topputo, F., Bernelli-Zazzera, F., et al., Low-thrust minimum-fuel optimization in the circular restricted three-body problem, J. Guid., Control, Dyn., 2015, vol. 38, no. 8, pp. 1501–1510.

    ADS  Article  Google Scholar 

  35. Saghamanesh, M. and Baoyin, H., A robust homotopic approach for continuous variable low-thrust trajectory optimization, Adv. Space Res., 2018, vol. 62, no. 11, pp. 3095–3113.

    ADS  Article  Google Scholar 

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Correspondence to Du Chongrui.

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Du Chongrui, Starinova, O.L. Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines. Cosmic Res 60, 124–138 (2022). https://doi.org/10.1134/S0010952522020022

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  • DOI: https://doi.org/10.1134/S0010952522020022