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Concept
Angular diameter
Summary
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of a lens). The angular diameter can alternatively be thought of as the angular displacement through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side. Humans can resolve with their naked eyes diameters of up to about 1 arcminute (approximately 0.017° or 0.0003 radians). This corresponds to 0.3 m at a 1 km distance, or to perceiving Venus as a disk under optimal conditions.
The angular diameter of a circle whose plane is perpendicular to the displacement vector between the point of view and the center of said circle can be calculated using the formula
in which is the angular diameter in degrees, and is the actual diameter of the object, and is 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 center of the sphere, the angular diameter can be found by the formula
The difference is due to the fact that the apparent edges of a sphere are its tangent points, which are closer to the observer than the center of the sphere. The difference is significant only for spherical objects of large angular diameter, since the following small-angle approximations hold for small values of :
Estimates of angular diameter may be obtained by holding the hand at right angles to a fully extended arm, as shown in the figure.
In astronomy, the sizes of celestial objects are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes. Since these angular diameters are typically small, it is common to present them in arcseconds (). An arcsecond is 1/3600th of one degree (1°) and a radian is 180/π degrees. So one radian equals 3,600 × 180/ arcseconds, which is about 206,265 arcseconds (1 rad ≈ 206,264.
Official source
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