Using formulas developed by Blanchet, Damour, and Iyer, we obtain a symmetric trace-free multipolar expansion of the gravitational radiation from a coalescing binary system which is sufficiently accurate to allow a post-Newtonian calculation of the linear momentum carried off by the gravitational radiation prior to a binary coalescence. We briefly examine the structure of the post-quadrupole corrections to the wave form for an orbiting binary system near coalescence. The post-Newtonian correction to the momentum ejection allows a more accurate calculation of the system recoil velocity (radiation rocket effect). We find that the higher-order correction actually reduces the net momentum ejection. Furthermore, the post-Newtonian correction to the momentum flux has only a weak dependence on the mass ratio of the objects in the binary, suggesting that previous test mass calculations may be quite accurate. We estimate an upper bound of the center-of-mass velocity of 1 km ${\mathrm{s}}^{-1\mathrm{}}$ for neutron star binaries very near coalescence. In an appendix we give a self-contained (albeit less rigorous) derivation of the gravitational wave form using the Epstein-Wagoner formalism.

• Received 22 January 1992

DOI:https://doi.org/10.1103/PhysRevD.46.1517