\begin{table}%T2 \caption{\label{tab:rec-sum}Summary of the analytic recipe to obtain the impact radii $b_\sigma$ and approach velocities $v_{\rm a}$.} \small%\centering \par \begin{tabular}{p{5cm}lll} \hline \hline \noalign{\smallskip} 1. Calculate dimensionless parameters:& $\zeta_{\rm w}$ (headwind velocity) & \eq{zeta-w} \\ & $\alpha_{\rm p}$ (planet size) & \eq{alpha-p} \\ & ${\rm St} = t_{\rm s} \Omega$ (Stokes number) & \eq{drag-regimes} \\ \noalign{\smallskip} 2. Calculate impact radii: & $\tilde{b}_{\rm set}$ & \eq{cubic}, \eq{bset-tilde} \\ & $b_{\rm hyp}$ & \eq{bhyp} \\ & $b_{\rm 3b}$ & \eq{b3b} \\ \noalign{\smallskip} 3. Determine regime: & ${\rm St}<\min(1, 12/\zeta_{\rm w}^3)$ & & ${\rm St}>{\rm max}(\zeta_{\rm w}, 1)$ \\ & Settling & Hyperbolic & Three body \\ \noalign{\smallskip} 4. Results \\ Impact radius (accretion), $b_\sigma$: & ${\rm max}(\tilde{b}_{\rm set}, b_{\rm geo}$) & ${\rm max}(\tilde{b}_{\rm set}, b_{\rm hyp})$ & ${\rm max}(b_{\rm 3b}, b_{\rm geo})$ \\ Approach velocity $v_{\rm a}$: & $3b_\sigma/2 + \zeta_{\rm w}$ & \eq{bhyp-va} & $3.2$ \\ Approach radius $b_{\rm app}$: & $b_\sigma$ & $b_\sigma$ & $2.5$ \\ \hline \end{tabular} \tablefoot{Description of impact radii: $b_{\rm geo}$, geometrical impact radius ($=\alpha_{\rm p}$); $b_{\rm set}$ impact radius in settling regime; $\tilde{b}_{\rm set}$, modified $b_{\rm set}$ (to cover the transition regime); $b_{\rm hyp}$ impact radius in the hyperbolic regime; $b_{\rm 3b}$ drag-enhanced impact radius for the 3-body regimes; $b_{\rm app}$, approach distance.} \end{table}