Gravitational-wave inspiral time ($t_{\mathrm{merge}}=5c^5{A}^4/(256G^3\mu M^2)$)

The leading circular, constant-mass gravitational-wave inspiral time follows by integrating the quadrupole radiation-reaction equation $\dot{A}=-64G^3\mu M^2/(5c^5{A}^3)$. It assumes initially weak gravity and neglects eccentricity, mass exchange and finite contact separation. It is $3/8$ of the associated instantaneous period-decay timescale.