= Strength-dependent steady collisional-cascade slope
{title2=$\alpha=(21+b)/(6+b)$}
With size-independent collision speed and <catastrophic disruption threshold> $Q_D^*\propto D^b$, the <catastrophic planetesimal collision rate> scales as $R\propto D^{3-\alpha+b(1-\alpha)/3}$. Multiplying by <mass per logarithmic size bin> gives processed mass proportional to $D^{7-2\alpha+b(1-\alpha)/3}$. <Constant mass flux in a collisional cascade> sets the exponent to zero, yielding the displayed differential-number index when $b\ne-6$. This is the zero-velocity-exponent case of a <velocity-dependent collisional cascade>.
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