The Steradian
The solid angle,
is the two-dimensional angle in three-dimensional space that an object subtends at a point and is a measure of how large that object appears to an observer looking from that point. A small object nearby may subtend the same solid angle as a larger object farther away. During a solar eclipse, the moon, which is smaller and closer to the Earth than the Sun, occupies almost the same solid angle as the Sun, and hides it almost totally from view. An object's solid angle is equal to the area of the segment of a unit sphere (centred at the vertex of the angle) restricted by the object.
The unit of solid angle is the steradian (
). An area on a sphere, equal to the square of its radius and observed from its centre, subtends precisely one steradian. The solid angle of a sphere viewed from internally is
and the solid angle of a face of a cube viewed from the centre is
More technically, we can define the solid and of an object as the cross sectional area presented by divided by an the distance, or the area of a shape on a sphere divided by the radius:
This is illustrated below.
