Angular size calculator
Compare a sphere’s apparent diameter with a flat circular disk of the same diameter at the same centre distance. Enter both lengths in the same unit.
At centre distance 384,400, diameter 3,474.8 subtends 0.51793° for a sphere and 0.51792° for a face-on disk. Changing both lengths by the same factor leaves these angles unchanged.
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Sphere: 2 asin(D / 2d); face-on disk: 2 atan(D / 2d)
For a sphere, the two edge rays are tangent to the surface. For a disk facing the observer, they meet the rim in a plane. The expressions approach the same small-angle result when diameter is much smaller than distance.
A smaller apparent object can result from greater distance. A part hidden behind a nearer surface is a separate occlusion measurement: changing angular size does not restore a geometrically blocked ray.