Journal of Mathematical Sciences

, Volume 243, Issue 3, pp 467–492 | Cite as

Non-Keplerian Behavior and Instability of Motion of Two Bodies Caused by the Finite Velocity of Gravitation

  • V. Yu. SlyusarchukEmail author

It is shown that the motion of two bodies described with regard for the finite velocity of gravitation does not obey the Kepler laws and that this motion is unstable.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. A. Brumberg, Relativistic Celestial Mechanics [in Russian], Nauka, Moscow (1972).zbMATHGoogle Scholar
  2. 2.
    V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics [in Russian], URSS, Moscow (2002).zbMATHGoogle Scholar
  3. 3.
    F. R. Moulton, An Introduction to Celestial Mechanics [Russian translation], ONTI NKTP SSSR, Moscow (1935).Google Scholar
  4. 4.
    O. V. Golubeva, Theoretical Mechanics [in Russian], Vysshaya Shkola, Moscow (1968).Google Scholar
  5. 5.
    S. M. Kopeikin and ÉFomalont, “Fundamental limit of the velocity of gravitation and its measurement,” Zemlya Vselennaya, No. 3 (2004); URL:
  6. 6.
    V. Yu. Slyusarchuk, “Mathematical model of the Solar system with regard for the velocity of gravitation,” Nelin. Kolyv., 21, No. 2, 238–261; English translation: J. Math. Sci., 243, No. 2, 287–312 (2019).Google Scholar
  7. 7.
    G. M. Fikhtengol’ts, Course in Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1966).Google Scholar
  8. 8.
    A. D. Myshkis, Linear Differential Equations with Delayed Argument [in Russian], Gostekhizdat, Moscow (1951).Google Scholar
  9. 9.
    R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).zbMATHGoogle Scholar
  10. 10.
    L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument [in Russian], Nauka, Moscow (1971).zbMATHGoogle Scholar
  11. 11.
    V. Yu. Slyusarchuk, Absolute Stability of Dynamical Systems with Aftereffect [in Ukrainian], Rivne State University ofWater Management and Utilization of Natural Resources, Rivne (2003).Google Scholar
  12. 12.
    V. P. Tsesevich, What and How to Observe in the Sky [in Russian], Nauka, Moscow (1984).Google Scholar
  13. 13.
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1968).Google Scholar
  14. 14.
    V. A. Sadovnichii, Theory of Operators [in Russian], Moscow University, Moscow (1986).Google Scholar
  15. 15.
    A. D. Myshkis, Lectures on Higher Mathematics [in Russian], Nauka, Moscow (1969).Google Scholar
  16. 16.
    T. Miura, H. Arakida, M. Kasai, and S. Kuramata, “Secular increase of the astronomical unit: a possible explanation in terms of the total angular-momentum conservation law,” Publ. Astron. Soc. Japan, 61, No. 6, 1247–1250 (2009).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National University of Water Management and Utilization of Natural ResourcesRivneUkraine

Personalised recommendations