The fraction of a star's disc (angular radius starRadius) covered by
an occluder's disc (angular radius occluderRadius) when their centres
are separation apart — all angles in radians, treated as flat discs on
the sky (exact enough: every angle involved here is well under a few
degrees except the occluder in a close lunar/planetary eclipse, where
the error is still small next to the umbra itself).
The standard circle–circle intersection area, over the star's own area:
0 when they don't touch, 1 in the umbra (the occluder covers the whole
star), (occluder/star)² in the antumbra of an annular eclipse.
The fraction of a star's disc (angular radius
starRadius) covered by an occluder's disc (angular radiusoccluderRadius) when their centres areseparationapart — all angles in radians, treated as flat discs on the sky (exact enough: every angle involved here is well under a few degrees except the occluder in a close lunar/planetary eclipse, where the error is still small next to the umbra itself).The standard circle–circle intersection area, over the star's own area: 0 when they don't touch, 1 in the umbra (the occluder covers the whole star), (occluder/star)² in the antumbra of an annular eclipse.