Gravitationally focused growth of a planetary core
= Gravitationally focused growth of a planetary core
Conservation of orbital energy and <angular momentum> in a two-body encounter gives $\sigma=\pi R_c^2(1+v_{\rm esc}^2/v_\infty^2)$. At fixed <density> and encounter speed in the strong-focusing limit, $R_c\propto M_c^{1/3}$ and $\sigma\propto M_c^{4/3}$. This yields runaway fractional growth until stirring or supply changes the assumptions.