= Apparent angular radius of a spherical star in Schwarzschild spacetime
{title2=$\sin\psi=\frac{R}{r_0}\sqrt{\frac{1-2m/r_0}{1-2m/R}}$}
A spherical surface with <areal radius> $R>3m$, where $m=GM/c^2$, has apparent angular radius $\psi$ for a static exterior observer at $r_0>R$. Its grazing <null geodesic> has <impact parameter> $b=R/\sqrt{1-2m/R}$. Projecting the photon tangent into the observer's local <rest frame> gives $\sin\psi=b\sqrt{1-2m/r_0}/r_0$, yielding the displayed result. The condition $R>3m$ ensures the grazing ray escapes, since the surface is outside the <photon sphere>. For $R=4m$, the distant image radius is $\sqrt2$ times the flat-space prediction.
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