The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system

Following Bekenstein's work on recoiling black holes, we calculate the gravitational wave linear momentum flux from a binary system of two point masses in Keplerian orbit. The quasi-Newtonian approach is adopted and the resulting motion of the centre of mass is calculated. As such a system decays via gravitational wave energy losses, the size of the orbit decreases until the components merge or become tidally disrupted. Thereafter, the centre of mass moves with the linear momentum necessary to balance that carried off by the gravitational waves. In the case of a binary black hole system, the velocity of the centre of mass could be of astrophysical significance, although numerical studies would be necessary to check this claim.