General Relativity and Gravitation

, Volume 13, Issue 5, pp 473–485 | Cite as

Relativistic celestial mechanics of binary stars

  • N. Spyrou
Research Articles


We present the results of a systematic study of the dynamics of realistic binary systems in the post-Newtonian approximation (PNA) of general relativity. We propose definitions valid in the PNA for the self-angular-momenta of the binary's members, as well as for the angular momentum of their relative orbital motion, and we examine under which conditions they can be considered as constant in the PNA. This enables us to define to the same approximation the plane relative orbital motion. Then we find the form of the differential equations of motion from an integration of which we prove that in the PNA the relative motion is a processing ellipse composed of a basic orbit and a correction, both of which are of post-Newtonian character. Moreover, using the polar equation of the above ellipse we define the elements of the post-Newtonian, relative, basic orbit, we generalize to the PNA the three well-known laws of classical celestial mechanics of Kepler, and we derive the precessional motion of the relative orbit's pericenter. Finally, we compare our method with other methods existing in the literature, and we expose its theoretical and conceptual differences with them.


Differential Equation General Relativity Angular Momentum Binary System Systematic Study 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Spyrou, N. (1979). Relativistic dynamical description of binary stars, Habilitation thesis, University of Thessaloniki, Greece.Google Scholar
  2. 2.
    Spyrou, N. (1977a).Gen. Rel. Grav.,8, 463 (paper I).Google Scholar
  3. 3.
    Spyrou, N. (1977b).Gen. Rel. Grav.,8, 491 (paper II).Google Scholar
  4. 4.
    Spyrou, N. (1978a).Gen. Rel. Grav.,9, 519 (paper III).Google Scholar
  5. 5.
    Robertson, H. P. (1938).Ann. Math.,39, 101.Google Scholar
  6. 6.
    Einstein, A., Infeld, L., and Hoffmann, B. (1938).Ann. Math.,39, 65.Google Scholar
  7. 7.
    Contopoulos, G., and Spyrou, N. (1976).Astrophys. J.,205, 592.Google Scholar
  8. 8.
    Spyrou, N. (1978b).Celestial Mech.,18, 351.Google Scholar
  9. 9.
    Adler, R., Bazin, M., and Schiffer, M. (1965).Introduction to General Relativity, McGraw-Hill Book Company, New York.Google Scholar
  10. 10.
    Wagoner, R. V., and Will, C. M. (1976).Astrophys. J.,210, 764 (paper IV).Google Scholar
  11. 11.
    O'Brien, G. (1979).Gen. Rel. Grav.,10, 129.Google Scholar
  12. 12.
    Synge, J. L. (1970).Proc. R. Ir. Acad. Sec. A.,69, 11.Google Scholar
  13. 13.
    Caporali, A. (1979). An approximation method for the determination of the motion of extended bodies in general relativity, Ph.D. thesis, University of Munich, West Germany.Google Scholar
  14. 14.
    Ehlers, J. (1972). InProceedings of the International School of General Relativistic Effects in Physics and Astrophysics. Experiments and Theory (3rd Course), ed. J. Ehlers, MPI Föhringer Ring 6, D 8 München 40.Google Scholar
  15. 15.
    Caporali, A., and Spyrou, N. (1979).Gen. Rel. Grav., to be published.Google Scholar
  16. 16.
    Epstein, R. (1977).Astrophys. J.,216, 92.Google Scholar
  17. 17.
    Taylor, J. H., Fowler, L. A., and McCulloch, P. M. (1979).Nature,277, 437.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • N. Spyrou
    • 1
  1. 1.Astronomy DepartmentUniversity of ThessalonikiThessalonikiGreece

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