Orbital decay timescale
= Orbital decay timescale
{title2=$\tau_P=P/|\dot P|$}
An instantaneous <orbital decay timescale> is positive even when the orbital period decreases. For a constant-mass circular binary with $\dot A=-C/A^3$ and $P\propto A^{3/2}$, $\tau_P=2A^4/(3C)$. Integrating to formal zero separation instead gives $t_{\rm merge}=A^4/(4C)=3\tau_P/8$. A local logarithmic decay time is not generally the remaining lifetime.