The evolution of the orbit of a binary pulsar under the action of gravitational radiation reaction is calculated. No approximation is made of weak gravity inside the individual stars; the details of the orbital motion are given directly (to order c^-5 and G³). The calculation reveals no acceleration of the center of mass of the system, and a secular decrease of the time of return to periastron. The quantitative results agree both with the well-known "quadrupole formula" and with observations.
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T. Damour (1983) studied this question.