= Slow circular inspiral under tangential drag
{title2=$\dot r=-\frac{rD}{(1+q)V_c},\quad q=d\log V_c/d\log r$}
For a slowly evolving <circular orbit> with tangential deceleration $D>0$, the <specific angular momentum> is $j=rV_c(r)$ and its <torque> is $\dot j=-rD$. Differentiating $j$ gives the displayed drift when $1+q\ne0$. The positive local decay time $r/(2|\dot r|)$ is $(1+q)V_c/(2D)$. In a uniform-density core $q=1$, so it is $V_c/D$; for a flat <galaxy rotation curve> $q=0$, it is $V_c/(2D)$. Simply setting $\dot V_c=-D$ neglects the radial contribution to <angular momentum> change.
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