= First-order stellar radiation force on a blackbody grain
{title2=$\boldsymbol F_{\rm rad}$}
For a <blackbody> grain with <geometric cross-section> $\sigma$, <mass> $m$ and stellar-frame <velocity> $\boldsymbol v$, define the <radiation-pressure coefficient> $\beta=L_\star\sigma/(4\pi cGM_\star m)$. To first order in $v/c$, steady absorption and isotropic rest-frame reradiation give
$$
\boldsymbol F_{\rm rad}=\frac{m\beta GM_\star}{r^2}
\left[\left(1-\frac{\dot r}c\right)\widehat{\boldsymbol r}-\frac{\boldsymbol v}c\right].
$$
The relative incoming flux provides $1-\dot r/c$; <photon> reradiation carries stellar-frame <momentum> proportional to $\boldsymbol v/c$. Subtracting static <radiation pressure> gives radial drag $-2m\beta GM_\star\dot r/(cr^2)$ and transverse drag $-m\beta GM_\star v_\theta/(cr^2)$. Non-blackbody grains require their actual <radiation-pressure efficiency>.
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