Astronomy Reports

, Volume 63, Issue 11, pp 954–962 | Cite as

Diversion of an Asteroid Using a Transversal Thruster

  • N. BatmunkhEmail author
  • K. I. Os’kinaEmail author
  • T. N. SannikovaEmail author
  • V. B. TitovEmail author
  • K. V. KholshevnikovEmail author


The diversion of a hazardous asteroid on a collisional trajectory with the Earth using a transversal thruster is considered. The thruster could be either mounted on the asteroid or used as a “gravitational tractor”. The aim of the study is to establish the fundamental possibility (or impossibility) of diverting an asteroid to a safe distance over a time of order months or years. This is acceptable, since the impact of an asteroid with a diameter of order 100 m on the Earth just after its discovery is very improbable. A model formulation of the problem in which the thruster provides a constant transversal acceleration of the asteroid is used. The corresponding Euler-type equations are transformed using the method of previous averaging. These equations are solved using the method of “slow time” power series, and the adequacy of the solutions over time scales of decades is demonstrated. An asteroid up to 55 m in diameter can be deflected over a year using a 1 N thruster. Asteroids with diameters up to 50 m can be diverted over a month, and with diameters up to 150 m over a year, using a 20 N thruster. Moving larger asteroids requires more time or more powerful engines.


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This work was supported by the Russian Science Foundation (grant 18-12-00050).


  1. 1.
    T. N. Sannikova and K. V. Kholshevnikov, Vestn. SPbGU, Ser. 1: Mat. Mekh. Astron., No. 4, 134 (2013).Google Scholar
  2. 2.
    T. N. Sannikova and K. V. Kholshevnikov, Astron. Rep. 58, 945 (2014).ADSCrossRefGoogle Scholar
  3. 3.
    T. N. Sannikova and K. V. Kholshevnikov, Astron. Rep. 59, 806 (2015).ADSCrossRefGoogle Scholar
  4. 4.
    E. T. Lu and S. G. Love, Nature 438, 177 (2005).ADSCrossRefGoogle Scholar
  5. 5.
    Yu. D. Medvedev, M. L. Sveshnikov, A. G. Sokol’skii, E. I. Timoshkova, Yu. A. Chernetenko, N. S. Chernykh, and V. A. Shor, Asteroid-Comet Hazard, Ed. by A. G. Sokol’skii (IPA RAN, St. Petersburg, 1996) [in Russian].Google Scholar
  6. 6.
    A. M. Mikisha and M. A. Smirnov, in The Threat from the Sky: Rock or Accident?, Ed. by A. A. Boyarchuk (Kosmoinform, Moscow, 1999) [in Russian].Google Scholar
  7. 7.
    N. N. Gor’kavyi and A. E. Dudorov, The Chelyabinsk Superbolide (Chelyab. Gos. Univ., Chelyabinsk, 2016) [in Russian].Google Scholar
  8. 8.
    A. V. El’kin and L. L. Sokolov, in Proceedings of the International Conference on Asteroid Hazard-95, May 23–25, 1995, Saint Petersburg, Vol. 2, p. 41.Google Scholar
  9. 9.
    G. L. Grodzovskii, Yu. N. Ivanov, and V. V. Tokarev, Space Flight Mechanics (Optimization Problems) (Nauka, Moscow, 1975) [in Russian].Google Scholar
  10. 10.
    V. N. Lebedev, Calculation of the Motion of a Low-Impact Spacecraft (VTs AN SSSR, Moscow, 1968) [in Russian].Google Scholar
  11. 11.
    N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotical Methods in the Theory of Nonlinear Oscillations (FM, Moscow, 1963) [in Russian].zbMATHGoogle Scholar
  12. 12.
    D. Brouwer and G. M. Clemence, Methods of Celestial Mechanics (Academic, New York, 1961).zbMATHGoogle Scholar
  13. 13.
    A. Poincare, Leçons de mécanique céleste: professées a la Sorbonne (Gauthier-Villars, Paris, 1905–1910).zbMATHGoogle Scholar
  14. 14.
    M. F. Subbotin, Introduction to Theoretical Astronomy (Nauka, Moscow, 1968) [in Russian].Google Scholar
  15. 15.
    W. Gröbner, Die Lie-Reihen und ihre Anwendungen (VEB Deutscher Verlag der Wissenschaften, Berlin, 1967).zbMATHGoogle Scholar
  16. 16.
    G. E. O. Giacaglia, Perturbation Methods in Non-Linear Systems (Springer, New York, 1972).CrossRefGoogle Scholar
  17. 17.
    A. H. Nayfeh, Perturbation Methods (Wiley-VCH, Weinheim, 2000).CrossRefGoogle Scholar
  18. 18.
    K. V. Kholshevnikov, Asymptotic Methods of Celestial Mechanics (LGU, Leningrad, 1985) [in Russian].zbMATHGoogle Scholar
  19. 19.
    A. Wintner, The Analytical Foundations of Celestial Mechanics (Dover, New York, 2014).zbMATHGoogle Scholar
  20. 20.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 2000; Fizmatgiz, Moscow, 1963).Google Scholar
  21. 21.
    N. Batmunkh, T. N. Sannikova, K. V. Kholshevnikov, and V. Sh. Shaidulin, Astron. Rep. 60, 366 (2016).ADSCrossRefGoogle Scholar
  22. 22.
    NASA Solar System Dynamics.

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Astronomy and GeophysicsMongolian Academy of SciencesUlan-BatorMongolia
  3. 3.Institute of Applied AstronomyRussian Academy of SciencesSt. PetersburgRussia

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