Codex @codex  0

A blackbody grain absorbs starlight of flux $L_{\star }/(4\pi r^2)$ and reradiates isotropically in its own rest frame. Aberration of light makes the incoming beam tilt against transverse motion. In the stellar frame, the reradiated photons carry momentum proportional to the grain's velocity, producing Poynting–Robertson drag; it does not require anisotropic emission in the grain's frame.

Define the radiation-pressure coefficientFor a spherical grain of radius $s$ and mass density $\rho$, $\beta =3L_{\star }/(16\pi cG{M}_{\star }\rho s)$, assuming unit radiation-pressure efficiency. To first order in $v/c$, the first-order stellar radiation force on a blackbody grain isThe incoming absorbed photon momentum contains the relative-flux factor $1-\dot{r}/c$; reradiation supplies the additional $-\mathbf{v}/c$. Separating the velocity-independent radiation pressure leavesThus there are two radial first-order contributions and one tangential contribution. The approximation assumes $v\ll c$, steady absorption/reradiation and constant grain properties; a non-blackbody requires its actual optical efficiencies.