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I have a function $f(\theta (t),\phi(t))$ (parameterized in $t$ with $r=1$) which describes an arbitrary closed loop on the surface of a unit sphere. How do I obtain from this the solid angle subtended by the loop?

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  • $\begingroup$ Is this closed loop a circle on the spherical surface? if not, what is the angle subtended by a generic loop? $\endgroup$ – Antonio Ragagnin Aug 4 '14 at 13:14
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It appears that you can indeed describe the solid angle as a contour integral along the loop, see this link.

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