= Random-orientation absorbing-disk cross-section
{title2=$\langle\sigma_{\rm abs}\rangle=\pi R^2/2$}
A circular, opaque, geometrically thin disk has projected area $\pi R^2|\cos i|$. For isotropically oriented normals, $|\cos i|$ is uniform on $[0,1]$, so the mean interception area is half the face-on area. A nonunit covering fraction multiplies this cross-section. Finite thickness, orientation-dependent absorption thresholds and incomplete coverage can change it; this is an average over randomly placed disks, not the inclination distribution conditional on an observed interception.
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