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Perturbation methods are employed to calculate time variation in the orbital elements of a compact binary system. It turns out that the semi-major axis and eccentricity exhibit only periodic variations. The longitude of periastron and mean longitude of epoch exhibit both secular and periodic variation. In addition, the relativistic effects on the time of periastron passage of binary stars are also given. Four compact binary systems (PSRJ0737-3039, PSR1913+16, PSR1543+12 and M33X-7) are considered. Numerical results for both secular and periodic effects are presented, and the possibility of observing them is discussed.

General Relativistic Orbital Effects in Compact Binary Stars (Solution by the Method of Celestial Mechanics)