Comparisons of the different capture radii discussed in this problem. The thick red line shows the capture radius for a τ = 1 pebble as a function of planet mass at 5 AU in the fiducial disk. The green and blue dashed curves show Equations (6) and (7), respectively, while the green and blue solid curves show the capture radii when modified by Equation (2). The black line indicates the physical cross section of the planet, while the dotted black line marks the Hill sphere. For reference, we add approximations to the capture radius for planetesimals of size 100 km and 1 km as gray curves (dark and light, respectively) as given in Rafikov (2004).