Advertisement

Evolution of space tethered system’s orbit during space debris towing taking into account the atmosphere influence

  • Alexander LedkovEmail author
  • Vladimir Aslanov
Original Paper
  • 32 Downloads

Abstract

Space debris removal by a low thrust tethered spacecraft is considered in this paper. The objective of the work is the development of a simplified mathematical model describing the perturbed motion of the space tethered system under the influence of the aerodynamic drag forces and low thrust of the spacecraft’s engines and study the evolution of the space tethered system’s center of mass orbital parameters on large time intervals. The mathematical model describing the plane motion of a space tethered system with inextensible massless tether is constructed. Linearization and averaging of the mathematical model over the angle of the tether deflection are carried out. Separation of fast and slow variables is performed using Van der Pol approach. The obtained system is averaged over a fast variable. It is used to study the evolution of the center of mass orbit during space debris removal. The effect of the space tethered system attitude motion on the center of mass motion is analyzed. It is concluded that the greatest influence of the relative motion is observed in the case when the tether oscillates near the local vertical so that the space tug is located above the space debris.

Keywords

Space debris Space tether Orbit evolution Low thrust Averaged equations 

Notes

Acknowledgements

This study was supported by the Russian Science Foundation (Project No. 19-19-00085).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Bonnal, C., Ruault, J.M., Desjean, M.C.: Active debris removal: recent progress and current trends. Acta Astron. 85, 51–60 (2013)CrossRefGoogle Scholar
  2. 2.
    Shan, M., Guo, J., Gill, E.: Review and comparison of active space debris capturing and removal methods. Prog. Aerosp. Sci. 80, 18–32 (2016)CrossRefGoogle Scholar
  3. 3.
    Hakima, H., Emami, M.R.: Assessment of active methods for removal of LEO debris. Acta Astron. 144, 225–243 (2018)CrossRefGoogle Scholar
  4. 4.
    Botta, E.M., Sharf, I., Misra, A.K.: Contact dynamics modeling and simulation of tether nets for space-debris capture. J. Guid. Control Dyn. 40(1), 110–123 (2017)CrossRefGoogle Scholar
  5. 5.
    Dudziak, R., Tuttle, S., Barraclough, S.: Harpoon technology development for the active removal of space debris. Adv. Space Res. 56(3), 509–527 (2015)CrossRefGoogle Scholar
  6. 6.
    Trushlyakov, V.I., Yudintsev, V.V., Pikalov, R.S.: Dynamic control of tug-debris tethered system after the capturing of the debris. J. Phys. Conf. Ser. 1050(1), 012092 (2018)CrossRefGoogle Scholar
  7. 7.
    Jaworski, P., Lappas, V., Tsourdos, A., Gray, I., Schaub, H.: Debris rotation analysis during tethered towing for active debris removal. J. Guid. Control Dyn. 40(7), 1769–1778 (2017)CrossRefGoogle Scholar
  8. 8.
    Aslanov, V.S., Misra, A.K., Yudintsev, V.V.: Chaotic attitude motion of a low-thrust tug-debris tethered system in a Keplerian orbit. Acta Astron. 139, 419–427 (2017)CrossRefGoogle Scholar
  9. 9.
    Aslanov, V.S., Ledkov, A.S.: Dynamics of towed large space debris taking into account atmospheric disturbance. Acta Mech. 225(9), 2685–2697 (2014)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jasper, L., Schaub, H.: Tethered towing using open-loop input-shaping and discrete thrust levels. Acta Astron. 105(1), 373–384 (2014)CrossRefGoogle Scholar
  11. 11.
    Beletskii, V.V., Levin, E.M.: Dynamics of Space Tether Systems, vol. 83. Univelt Incorporated, San Diego (1993)Google Scholar
  12. 12.
    Cartmell, M.P., McKenzie, D.J.: A review of space tether research. Prog. Aerosp. Sci. 44(1), 1–21 (2008)CrossRefGoogle Scholar
  13. 13.
    Williams, P.: A review of space tether technology. Recent Pat. Space Technol. 2(1), 22–36 (2012)CrossRefGoogle Scholar
  14. 14.
    Krupa, M., Poth, W., Schagerl, M., Steindl, A., Steiner, W., Troger, H., Wiedermann, G.: Modelling, dynamics and control of tethered satellite systems. Nonlinear Dyn. 43(1–2), 73–96 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zhuk, V.I., Shakhov, E.M.: On oscillations of tethered satellite of small mass caused by aerodynamical drag and gravity. Cosm. Res. 28(6), 820–830 (1990)Google Scholar
  16. 16.
    Kokubun, K.: Resonated libration of tethered subsatellite by atmospheric density variation. J. Guid. Control Dyn. 22(6), 910–911 (1999)CrossRefGoogle Scholar
  17. 17.
    Onoda, J., Watanabe, N.: Tethered subsatellite swinging from atmospheric gradients. J. Guid. Control Dyn. 11(5), 477–479 (1988)CrossRefGoogle Scholar
  18. 18.
    Beletskii, V.V., Levin, E.M.: Dynamics of the orbital cable system. Acta Astron. 12(5), 285–291 (1985)CrossRefGoogle Scholar
  19. 19.
    Aslanov, V.S., Ledkov, A.S., Misra, A.K., Guerman, A.D.: Dynamics of space elevator after tether rupture. J. Guid. Control Dyn. 36(4), 986–992 (2013)CrossRefGoogle Scholar
  20. 20.
    Pasca, M., Lorenzini, E.C.: Two analytical models for the analysis of a tethered satellite system in atmosphere. Meccanica 32(4), 263–277 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Jaslow, H.: Aerodynamic relationships inherent in Newtonian impact theory. AIAA J. 6(4), 608–612 (1968)CrossRefGoogle Scholar
  22. 22.
    Picone, J.M., Hedin, A.E., Drob, D.P., Aikin, A.C.: NRLMSISE-00 empirical model of the atmosphere: statistical comparisons and scientific issues. J. Geophys. Res. 107(A12), SIA 15-1–SIA 15-16 (2002)CrossRefGoogle Scholar
  23. 23.
    Korn, G., Korn, T.: Mathematical Handbook. McGraw-Hill Book Company, New York (1968)zbMATHGoogle Scholar
  24. 24.
    Aslanov, V.S., Ledkov, A.S.: Dynamics of Tethered Satellite Systems. Woodhead Publishing, Cambridge (2012)CrossRefGoogle Scholar
  25. 25.
    Troger, H., Alpatov, A.P., Beletsky, V.V., Dranovskii, V.I., Khoroshilov, V.S., Pirozhenko, A.V., Zakrzhevskii, A.E.: Dynamics of Tethered Space Systems. CRC Press, New York (2010)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Theoretical Mechanics DepartmentSamara National Research UniversitySamaraRussia

Personalised recommendations