What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
If an object is twice as far away, the angle it subtends (in the small angle approximation) is half as large. The solid angle it covers is then one quarter as large. This reflects the fact that the surface angle of a sphere of radius $R$ is $4\pi R^2$ so as $R$ doubles the portion of the sphere that the object covers is reduced by a factor $4$