Relativistic celestial mechanics of binary stars.
Abstract
We present the results of a systematic study of the dynamics of realistic binary systems in the postNewtonian approximation (PNA) of general relativity. We propose definitions valid in the PNA for the selfangularmomenta 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 postNewtonian character. Moreover, using the polar equation of the above ellipse we define the elements of the postNewtonian, relative, basic orbit, we generalize to the PNA the three wellknown 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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 May 1981
 DOI:
 10.1007/BF00756595
 Bibcode:
 1981GReGr..13..473S
 Keywords:

 Astrodynamics;
 Binary Stars;
 Celestial Mechanics;
 Relativity;
 Differential Equations;
 Ellipses;
 Equations Of Motion;
 Kepler Laws;
 Orbital Elements;
 Astrophysics;
 Close Binaries:Relativity Theory