= Asteroidal core growth by crustal sinking
{title2=$b^3-b_0^3\sim3R^2J_s(t-t_0)$}
At zero liquid superheat, dense solid released by <viscous overturn of a dense crust> can sink and remain solid. For a thin crust on an asteroid of fixed radius $R$, efficient deposition and the equal-density volume approximation give $b^3-b_0^3=3R^2J_s(t-t_0)$. If surface gravity scales as $R$, the crustal flux scales as $R^{1/3}$ and the core radius as $R^{7/9}t^{1/3}$. The approximation ends when remaining liquid is exhausted or the renewed crust is no longer thin.
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