= Fluorescence from a uniformly moving cloud
{title2=$D_{\rm in}=\gamma(1-\beta s),\quad D_{\rm out}=[\gamma(1+\beta s)]^{-1}$}
For a compact cloud passing a stationary source at distance $L$, put $r(t)=\sqrt{L^2+v^2t^2}$ and $s=vt/r$. Incoming and returning rays have opposite <Doppler factors>. Source return time is $t_R=t+r/c$. If $q=f_0/f<1$, line-centre excitation is possible above $\beta=(1-q^2)/(1+q^2)$ and occurs at closest approach when $\beta=\sqrt{1-q^2}$. In a weak, optically thin, isotropic <spontaneous emission> model, the excited population obeys $\dot N_*=P_{\rm abs}-N_*/(\gamma\tau)$ and the received bolometric intensity scales as $D_{\rm out}^4N_*/(\tau r^2)$. Finite lifetime and line width smear the pulse and its frequency chirp; geometry and source strength are needed for an absolute prediction.
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