= Mass normalization of a power-law size distribution
For spherical <planetesimals> with <mass density> $\rho$ and total-number distribution $n(D)=KD^{-\alpha}$ between $D_{\min}$ and $D_{\max}$,
$$
M_{\rm tot}=\frac{\pi\rho K}{6}\int_{D_{\min}}^{D_{\max}}D^{3-\alpha}\,dD.
$$
Thus $K=6M_{\rm tot}(4-\alpha)/[\pi\rho(D_{\max}^{4-\alpha}-D_{\min}^{4-\alpha})]$ for $\alpha\ne4$. At $\alpha=4$, use $K=6M_{\rm tot}/[\pi\rho\log(D_{\max}/D_{\min})]$. Divide $n(D)$ by belt volume to obtain the number-density distribution used in a <planetesimal collision rate>.
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