Yarkovsky removal ($t_y=BD+C/D$)

Drift driven by the Yarkovsky effect can carry a body out of a belt or into an unstable orbital region. A useful two-limit removal law is $t_y=BD+C/D$, with slow escape at both large and small diameters.

A population supplied at differential number rate $n_b(D)/t_y(D)$ and surviving externally for a size-independent time $T$ has $n_{\mathrm{out}}(D)=T{n}_b(D)/t_y(D)$. Its differential number slope changes by the negative of the removal-time exponent, unless the belt is already removal-dominated, in which case it reflects the fragment injection spectrum.

For $t_c=(A/M)D^{1/2}$, the ratio $t_y/t_c$ has its minimum at $D_{\ast }=\sqrt{3C/B}$. Removal beats collisions somewhere exactly when $M<M_y=(3^{3/4}/4)A{B}^{-3/4}{C}^{-1/4}$, provided the relevant diameters are present. This criterion uses the collision-only cascade as a reference.

The law $t_y=BD+C/D$ for positive $B,C$ has a minimum at $D_0=\sqrt{C/B}$ with value $2\sqrt{BC}$. This size differs from the minimum of the ratio of removal and collision times.