Angular diameter

The angular diameter or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view. In the vision sciences it is called the visual angle. The angular diameter can alternately be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side.

Formula

The angular diameter of a circle whose plane is perpendicular to the displacement vector between the point of view and the centre of said circle can be calculated using the formula

in which is the angular diameter, and and are the actual diameter of and the distance to the object. When , we have , and the result obtained is in radians.

For a spherical object whose actual diameter equals and where is the distance to the centre of the sphere, the angular diameter can be found by the formula

The reason for the difference is that when looking at a sphere, the edges are the tangent points, which are closer to the observer than the centre of the sphere. For practical use, the distinction is only significant for spherical objects that are relatively close, since the small-angle approximation holds for :