Skip to main content
Log in

Mathematical Model of the Solar System with Regard for the Velocity of Gravitation

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We construct a mathematical model of the Solar system taking into account the finite velocity of gravitation. We also correct Kepler’s laws and present the properties of the studied system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. D. Myshkis, Linear Differential Equations with Retarded Argument [in Russian], Gostekhizdat, Moscow (1951).

  2. A. D. Myshkis and L. É É. El’sgol’ts, “State and problems of the theory of differential equations with deviating argument,” Usp. Mat. Nauk,22, No. 2, 21–57 (1967).

    Google Scholar 

  3. A. D. Myshkis, “Some problems of the theory of differential equations with deviating argument,” Usp. Mat. Nauk,32, No. 2, 173–202 (1977).

    MathSciNet  Google Scholar 

  4. E. Pinney, Ordinary Difference-Differential Equations, University of California, Berkeley (1958).

  5. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).

  6. V. P. Rubanik, Oscillations of Quasilinear Systems with Delay [in Russian], Nauka, Moscow (1971).

  7. L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument [in Russian], Nauka, Moscow (1971).

  8. J. Hale, Theory of Functional Differential Equations, Springer, New York (1977).

    Book  Google Scholar 

  9. E. F. Tsar’kov, Random Perturbations of Functional-Differential Equations [in Russian], Zinatne, Riga (1989).

  10. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations [in Russian], Moscow, Nauka (1991).

  11. V. Yu. Slyusarchuk, Absolute Stability of Dynamical Systems with Aftereffect [in Ukrainian], Rivne State University of Water Management and Utilization of Natural Resources , Rivne (2003).

  12. E. B. Fomalont and S. V. Kopeikin, “The measurement of the light deflection from Jupiter: experimental results,” Astrophys. J.,598, 704–711 (2003).

    Article  Google Scholar 

  13. S. M. Kopeikin and E. Fomalont, “Fundamental limit of the velocity of gravitation and its measurement,” Zemlya Vselennaya, No. 3 (2004).

  14. F. R. Moulton, An Introduction to Celestial Mechanics, MacMillian, New York (1914).

  15. A. Poincaré, Lectures on Celestial Mechanics [Russian translation], Nauka, Moscow (1965).

  16. J. Chazy, La Théorie de la Relativité et la Mécanique Céleste, Vol. 1, Gauthier-Villars, Paris (1928).

  17. G. N. Duboshin, Celestial Mechanics. Analytic and Qualitative Methods [in Russian], Nauka, Moscow (1978).

  18. V. I. Arnold, “Small denominators and the problems of stability of motion in classical and celestial mechanics,” Usp. Mat. Nauk,18, No. 6, 91–192 (1963).

    MathSciNet  Google Scholar 

  19. V. A. Brumberg, Relativistic Celestial Mechanics [in Russian[, Nauka, Moscow (1972).

  20. A. P. Markeev, Libration Points in Celestial Mechanics and Cosmodynamics [in Russian], Nauka, Moscow (1978).

  21. V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics [in Russian], URSS, Moscow (2002).

  22. Ya. B. Zel’dovich and I. D. Novikov, Gravitation Theory and Evolution of Stars [in Russian], Nauka, Moscow (1971).

  23. A. P. Ryabushko, Motion of Bodies in the General Relativity Theory [in Russian], Vyséishaya Shkola, Minsk (1979).

  24. S. Kopeikin, M. Efroimsky, and G. Kaplan, Relativistic Celestial Mechanics of the Solar System, Wiley (2011).

  25. V. P. Tsesevich, What and How to Observe in the Sky [in Russian], Nauka, Moscow (1984).

  26. G. M. Fikhtengol’ts, A Course of Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1966).

  27. V. A. Zorich, Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1984).

  28. H. B. Dwight, Tables of Integrals and Other Mathematical Data [Russian translation], Nauka, Moscow (1973).

  29. O. V. Golubeva, Theoretical Mechanics [in Russian], Vysshaya Shkola, Moscow (1968).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. Yu. Slyusarchuk.

Additional information

Translated from Neliniini Kolyvannya, Vol. 21, No. 2, pp. 238–261, April–June, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slyusarchuk, V.Y. Mathematical Model of the Solar System with Regard for the Velocity of Gravitation. J Math Sci 243, 287–312 (2019). https://doi.org/10.1007/s10958-019-04540-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-019-04540-2

Navigation