Angular diameter

In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of a lens).

A person can resolve with their naked eyes diameters down to about 1 arcminute (approximately 0.017° or 0.0003 radians).

[1] This corresponds to 0.3 m at a 1 km distance, or to perceiving Venus as a disk under optimal conditions.

is the angular diameter (in units of angle, normally radians, sometimes in degrees, depending on the arctangent implementation),

The difference with the case of a perpendicular circle is significant only for spherical objects of large angular diameter, since the following small-angle approximations hold for small values of

:[5] Estimates of angular diameter may be obtained by holding the hand at right angles to a fully extended arm, as shown in the figure.

This table shows the angular sizes of noteworthy celestial bodies as seen from Earth:

(The Sun's diameter is 400 times as large and its distance also; the Sun is 200,000 to 500,000 times as bright as the full Moon (figures vary), corresponding to an angular diameter ratio of 450 to 700, so a celestial body with a diameter of 2.5–4″ and the same brightness per unit solid angle would have the same brightness as the full Moon.)

However, much finer units are needed to measure the angular sizes of galaxies, nebulae, or other objects of the night sky.

Degrees, therefore, are subdivided as follows: To put this in perspective, the full Moon as viewed from Earth is about 1⁄2°, or 30′ (or 1800″).

The Moon's motion across the sky can be measured in angular size: approximately 15° every hour, or 15″ per second.

A one-mile-long line painted on the face of the Moon would appear from Earth to be about 1″ in length.

Defect of illumination is the maximum angular width of the unilluminated part of a celestial body seen by a given observer.

Angular diameter: the angle subtended by an object
Diagram for the formula of the angular diameter
Approximate angles of 10°, 20°, 5°, and 1° for the hand outstretched at arm's length
A 19th century depiction of the apparent size of the Sun as seen from the Solar System's planets (incl. 72 Feronia and the then most outlying known asteroid, here called Maximiliana ).
Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.
Comparison of angular diameter of the Sun, Moon and planets. To get a true representation of the sizes, view the image at a distance of 103 times the width of the "Moon: max." circle. For example, if this circle is 5 cm wide on your monitor, view it from 5.15 m away.
This photo compares the apparent sizes of Jupiter and its four Galilean moons ( Callisto at maximum elongation ) with the apparent diameter of the full Moon during their conjunction on 10 April 2017.