On the Stability of Circular Orbits of a Test Body in the Restricted Three-Body Problem in GR Mechanics

M.E. Abishev, S. Toktarbay, B.A. Zhami1


The paper considers the problem of orbital stability of a circular motion of a test body in the restricted three-body problem, where perturbations from the second body are of the order of relativistic corrections to the motion of a test body from the central body. All bodies do not possess proper rotation.


  1. T. I. Maindl and R. Dvorak, Astron. Astroph. 290, 335 (1994).
  2. I. Imai, T. Chiba, and H. Asada, Phys. Lett. B 98, 201102 (2007).
  3. Kei Yamada and Hideki Asada, Phys. Rev. D 82, 104019 (2010).
  4. M. M. Abdil'din, M. E. Abishev, N. A. Beissen, and K. A. Boshkaev, Grav. Cosmol. 15, 1 (2009).
  5. L. D. Landau and E. M. Lifshitz, Theory of Fields (Nauka, Moscow, 1973).
  6. A. A. Brumberg, Relativistic Celestial Mechanics (Nauka, Moscow, 1972).
  7. C. Hans Ohanian and Remo Ruffini, Gravitation and Spacetime, 3rd ed. (Cambridge University Press, New York, 2013).
  8. G. N. Duboshin, Celestial Mechanics (Nauka, Moscow, 1968).
  9. M. M. Abdil'din, Mechanics of Einstein's Theory of Gravity (Nauka, Alma-Ata, 1988).
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