Planetesimal collision rate

For an impactor number density per size $n(D_{\mathrm{im}})$, relative speed $v_{\mathrm{rel}}$, and collision cross-section $\sigma (D,D_{\mathrm{im}})$, the differential collision rate of one target is $n(D_{\mathrm{im}})v_{\mathrm{rel}}\sigma (D,D_{\mathrm{im}})d{D}_{\mathrm{im}}$.