For a binary consisting of stars of masses and , in an orbit of eccentricity and period , the period decay is given by the generalization of Equation (32) :chirpmass of the binary that we defined in Equation (31). (In the third expression here, is the reduced mass of the binary and its total mass.) Since the masses of the binary and the eccentricity of the orbit can be measured by other means, one can use these parameters in the above equation to infer the rate at which the period is predicted to decrease according to general relativity. For the Hulse–Taylor binary the relevant values are: , , , . The predicted value , while the observed period decay (after subtracting the apparent decay due to the acceleration of the pulsar in the gravitational field of our galaxy, as described in Section 3.4.3) is and the two are in agreement to better than a tenth of a percent .
Observation of the decay of the orbital period in PSR B1913+16 is an unambiguous direct observation of the effect of gravitational radiation backreaction on the dynamics of the system. PSR B1913+16 was the first system in which the effect of gravitational radiation reaction force was measured. In 2004, a new binary pulsar PSR J0737-3039 was discovered [103, 249]. J0737 is in a tighter orbit than PSR B1913+16; with an orbital period of only 2.4 hrs, the orbit is shrinking by about 7 mm each day in good agreement with the general relativistic prediction. Several other systems are also known . In Sections 6.5, 6.5.2 and 6.5.3 we will discuss in some detail the dynamics of relativistic binaries and the radiation reaction as predicted by post-Newtonian theory and numerical relativity simulations.
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