(a) Collision and capture rates in the coplanar case ( ), as a function of eccentricity . Circles, squares, and triangles show the capture rates with ζ = 10 ⁻⁴, 3 × 10 ⁻⁷, and 3 × 10 ⁻⁹, respectively. Dashed and dotted lines show the numerical results of the capture rates for the prograde and retrograde cases, respectively. The solid line with crosses shows collision rate with in the gas-free case. (b) Comparison of numerical results (lines with marks) with the analytic results obtained by numerically integrating Equation (28) with Equation (26) with ζ = 3 × 10 ⁻⁷. Dashed and solid lines show the results of the case of prograde trajectories. Dotted and dot–dashed lines show the results of the retrograde case.