= Solution
Decreasing $q=f_0/f$ increases the blueshift required for excitation. Both characteristic speeds move toward $c$:
$$
\beta_{\min}=\frac{1-q^2}{1+q^2},\qquad
\beta_\perp=\sqrt{1-q^2}.
$$
If $q$ is near one, modest approach speeds can excite the line. If $q\ll1$, only strongly relativistic motion reaches the line centre. At a fixed qualifying speed, decreasing $q$ moves the resonance toward earlier approach, since a larger $D_{\rm in}$ is required. It can also move the event outside the illumination window set by $t_e\ge-T$.
At fixed $q$, increasing $\beta$ moves the resonance from the far approaching tail, through closest approach at $\beta_\perp$, and eventually to the receding side. The received pulse <frequency> cannot be estimated simply by applying the same blueshift twice: the inward and outward <Doppler factors> are different, and decay may occur well after excitation. The critical-speed rows of part <2/c/i> make these changes explicit.
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