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For the Dohnanyi collisional cascade exponent $\alpha =7/2$ and $D_{\max }\gg D_{\min }$,Substitution in part (iv) yieldsThusThe $M^2/V$ dependence is the pair-collision scaling. Longer-lived clumps are more numerous, stronger bodies disrupt less often, and smaller fragments put more geometric cross-section into each event. At fixed total mass, increasing $D_{\max }$ lowers the normalization of the power-law size distribution and therefore lowers the event rate.

A size-independent $Q_D^{\ast }$ gives the steady Dohnanyi collisional cascade exponent $\alpha =7/2$. The preceding results becomeThus, under these idealized prescriptions, cratering collisions remove target mass about three times faster than catastrophic collisions. The conclusion concerns mass removed from targets; both processes contribute fragments to the collisional cascade.