Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies

We study gravitational radiation reaction in the equations of motion for binary systems of nonspinning point masses to post-Newtonian order [O((v/c${)}^2$)] beyond the quadrupole approximation, corresponding to ${\mathrm{post}}^{7/2}$-Newtonian order corrections to Newtonian motion. One method uses post-Newtonian expressions for energy and angular momentum flux to infinity, and an assumption of energy and angular momentum balance. The equations of motion so derived are valid for general binary orbits, and for a class of coordinate gauges. Another method uses explicit formulas for near-zone reaction potentials, valid to post-Newtonian order, derived by an asymptotic matching procedure in a fixed gauge. The two methods give equivalent results. © 1995 The American Physical Society.