= Angular-diameter ratio under a collinear boost
{title2=$|v|/c=(r^2-1)/(r^2+1)$}
For two coincident observers with relative motion along the sightline to a small distant source, its <angular diameter> changes by a <rapidity> factor. A boost toward the source compresses its incoming angular cone: $\tan(\vartheta'/2)=e^{-\eta}\tan(\vartheta/2)$ for angular radius $\vartheta$. For a small source the larger-to-smaller diameter ratio is $r=e^{|\eta|}$, giving the displayed relative speed. A finite angular size requires the half-angle formula, and arbitrary transverse relative motion cannot be inferred from one diameter ratio alone.
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