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General Relativity and Gravitation

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

Relativistic celestial mechanics of binary stars

  • N. Spyrou
Research Articles

Abstract

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.

Keywords

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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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

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

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