A size-independent $Q_D^*$ gives the steady <Dohnanyi collisional cascade> exponent $\alpha=7/2$. The preceding results become
$$
t_{\rm cr}\simeq\frac{0.4}{R_{\rm cc}},
\qquad
t_{\rm cat}\simeq\frac{2(6.22)}{9.94}\frac1{R_{\rm cc}}
\simeq\frac{1.25}{R_{\rm cc}}.
$$
Thus, 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>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 1 / vii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-316/1/vii/solution