Geometric collision cross-section

Two spheres of diameters $D_1,D_2$ collide geometrically when their projected centre separation is at most $(D_1+D_2)/2$, giving cross-section $\sigma =\pi (D_1+D_2{)}^2/4$.

For an equal-density sphere of diameter $D$, the ratio of geometric cross-section to mass isBreaking a fixed mass into smaller pieces therefore increases its total cross-section in inverse proportion to fragment size.