= Speed-radius attractor of an accreting raindrop
{title2=$v^2/a\longrightarrow8g/(7c+6k),\quad\dot v\longrightarrow cg/(7c+6k)$}
For the <accreting raindrop with quadratic drag>, set $q=v^2/a$ and $B=7c/8+3k/4$. Its exact equation is $\dot q=2(v/a)(g-Bq)$. Dividing by $\dot a=cv/4$ gives $q(a)=g/B+(q(a_0)-g/B)(a_0/a)^{7+6k/c}$. Thus $q$ stays between its positive initial value and positive equilibrium. Since $d\sqrt a/dt=c\sqrt q/8$, the radius grows without finite-time divergence and tends to infinity. The power correction then vanishes, proving both limits. Positive drag makes the limiting <acceleration> strictly less than $g/7$.
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