Higher order gravitational radiation losses in binary systems

The rate of emission of gravitational energy from a system of two point masses is computed with an accuracy consistent with the first-order relativistic corrections in the dynamics of the system. The computations use recently-developed post-Newtonian formalisms for the dynamics of two point masses and for the generation of gravitational waves. In the case of two point masses in (quasi) elliptic motion, standard heuristic arguments yield the expression, valid at higher relativistic order, of the rate Ṗ of decrease of the orbital period of the masses. The higher-order relativistic correction contributes to Ṗ a fractional amount of 2.15×10−5 in the case of the binary pulsar PSR 1913 + 16. This value is far smaller than the present accuracy of 1.7×10−2 in the measurement of Ṗ for PSR 1913 + 16 but this higher-order relativistic expression of Ṗ may be useful in the future for relativistic binary pulsars. Computations valid for a system of two point masses in (quasi) hyperbolic motion are also presented. In this case, the same heuristic arguments permit the study, still valid at higher relativistic order, of the capture, by radiation emission, of two point masses moving on a quasi-hyperbolic orbit with small enough energy.