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Optimization of a Low-Thrust Heliocentric Trajectory between the Collinear Libration Points of Different Planets

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Abstract

The aim of this study is to optimize a low-thrust interplanetary trajectory using collinear libration points L1 and L2 as the junction points of the geocentric or planetocentric segments of the trajectory with the heliocentric segment. The problem of optimizing the heliocentric segment of perturbed low-thrust interplanetary transfer is considered in the four-body ephemeris model, which includes the Sun, Earth, target planet, and spacecraft. To optimize the trajectories, an indirect approach is used based on Pontryagin’s maximum principles and the continuation method. The possibility of reducing the characteristic velocity in comparison with the estimates obtained through the method of zero sphere of influence is shown.

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REFERENCES

  1. Topputo, F. and Belbruno, E., Earth–Mars transfers with ballistic capture, Celestial Mech. Dyn. Astron., 2015, vol. 121, no. 4, pp. 329–346. https://doi.org/10.1007/s10569-015-9605-8

    Article  ADS  MathSciNet  Google Scholar 

  2. Mingotti, G., Topputo, F., and Bernelli-Zazzera, F., Earth–Mars transfers with ballistic escape and low-thrust capture, Celestial Mech. Dyn. Astron., 2011, vol. 110, no. 2, pp. 169–188. https://doi.org/10.1007/s10569-011-9343-5

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Mingotti, G. and Gurfil, P., Mixed low-thrust invariant-manifold transfers to distant prograde orbits around Mars, J. Guid., Control, Dyn., 2010, vol. 33, no. 6, pp. 1753–1764. https://doi.org/10.2514/1.49810

    Article  ADS  Google Scholar 

  4. Topputo, F., Vasile, M., and Bernelli-Zazzera, F., Low energy interplanetary transfers exploiting invariant manifolds of the restricted three-body problem, Astronaut. Sci., 2005, vol. 53, no. 4, pp. 353–372. https://doi.org/10.1007/BF03546358

    Article  MathSciNet  Google Scholar 

  5. Ovchinnikov, M., Interplanetary small-satellite missions: Ballistic problems and their solutions, Gyrosc. Navig., 2021, vol. 12, no. 4, pp. 281–293. https://doi.org/10.1134/S2075108721040064

    Article  Google Scholar 

  6. Lo, M. and Ross, S., The lunar L 1 gateway: Portal to the stars and beyond, AIAA Space 2001 Conference, Albuquerque, NM, August 28–30, 2001. https://doi.org/10.2514/6.2001-4768

  7. Ross, S., Koon, W., Lo, M.W., et al., Design of a multi-moon orbiter, 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico, February 9–13, 2003, p. AAS 03-143.

  8. Loeb, H., Petukhov, V., Popov, G.A., et al., A realistic concept of a manned Mars mission with nuclear-electric propulsion, Acta Astronaut., 2015, vol. 116, pp. 299–306. https://doi.org/10.1016/j.actaastro.2015.07.019

    Article  Google Scholar 

  9. Petukhov, V. and Yoon, S.W., End-to-end optimization of power-limited Earth–Moon trajectories, Aerospace, 2023, vol. 10, no. 3, p. 231. https://doi.org/10.3390/aerospace10030231

    Article  Google Scholar 

  10. Petukhov, V.G., One numerical method to calculate optimal power-limited trajectories, Int. Electric Propulsion Conf. IEPC-95-221, Moscow, 1995, pp. 1474–1480.

  11. Petukhov, V.G., Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method, Cosmic Res., 2008, vol. 46, no. 3, pp. 219–232. https://doi.org/10.1134/S0010952508030052

    Article  ADS  Google Scholar 

  12. Petukhov, V.G., Method of continuation for optimization of interplanetary low-thrust trajectories, Cosmic Res., 2012, vol. 50, no. 3, pp. 249–261. https://doi.org/10.2514/1.4022

    Article  ADS  Google Scholar 

  13. Haberkorn, T., Martinon, P., and Gergaud, J., Low thrust minimum-fuel orbital transfer: A homotopic approach, J. Guid., Control, Dyn., 2004, vol. 27, no. 6, pp. 1046–1060. https://doi.org/10.2514/1.4022

    Article  ADS  Google Scholar 

  14. Jiang, F., Baoyin, H., and Li, J., Practical techniques for low-thrust trajectory optimization with homotopic approach, J. Guid., Control, Dyn., 2012, vol. 35, no. 1, pp. 245–258. https://doi.org/10.2514/1.52476

    Article  ADS  Google Scholar 

  15. Petukhov, V., Ivanyukhin, A., Popov, G., et al., Optimization of finite-thrust trajectories with fixed angular distance, Acta Astronaut., 2022, vol. 197, pp. 354–367. https://doi.org/10.1016/j.actaastro.2021.03.012

    Article  ADS  Google Scholar 

  16. Petukhov, V.G. and Yoon, S.W., Optimization of perturbed spacecraft trajectories using complex dual numbers. Part. 1: Theory and method, Cosmic Res., 2021, vol. 59, no. 5, pp. 401–413. https://doi.org/10.1134/S0010952521050099

    Article  ADS  Google Scholar 

  17. Dargent, T., Automatic minimum principle formulation for low thrust optimal control in orbit transfers using complex numbers, Proc. 21st Int. Symp. Space Flights Dynamics, Toulouse, France, September 28–October 2, 2009.

  18. Dargent, T., An integrated tool for low thrust optimal control orbit transfers in interplanetary trajectories, Proc. 18th Int. Symp. Space Flight Dynamics, Munich, Germany, October 11–15, 2004, ESA SP-548, p. 143.

  19. Bertrand, R. and Epenoy, R., CNES Technical note no. 147, December 2002, p. 36.

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Funding

This study was supported by the grant of the Russian Science Foundation “Development of the Theory and Methods for Designing the Trajectories of Spacecraft with High- and Low-Thrust Propulsion Systems,” no. 22-19-00329, https://rscf.ru/project/22-19-00329/.

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Authors and Affiliations

  1. Research Institute of Applied Mechanics and Electrodynamics, Moscow Aviation Institute, 125080, Moscow, Russia

    V. G. Petukhov

  2. Moscow Aviation Institute, 125080, Moscow, Russia

    S. W. Yoon

Authors
  1. V. G. Petukhov
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  2. S. W. Yoon
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Corresponding authors

Correspondence to V. G. Petukhov or S. W. Yoon.

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The authors declare that they have no conflicts of interest.

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Translated by M. Chubarova

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Petukhov, V.G., Yoon, S.W. Optimization of a Low-Thrust Heliocentric Trajectory between the Collinear Libration Points of Different Planets. Cosmic Res 61, 418–430 (2023). https://doi.org/10.1134/S0010952523700351

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  • DOI: https://doi.org/10.1134/S0010952523700351

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