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The angular diameter of an object as seen from a given position is the diameter measured as an angle. It satisfies the formula <math>\delta = \arctan (diameter/ distance)<math>.
In astronomy the size of objects in the sky are often measured in terms of their angular diameter as seen from Earth, rather than their actual size.
The angular diameter of Earth's orbit around the Sun, from a distance of one parsec, is 2" (two arcseconds).
The angular diameter of the Sun, from a distance of one lightyear, is 0.03", of the Earth 0.000,3".
This table shows the angular sizes of the most important Solar System bodies.
Thus the angular diameter of the Sun is ca. 250,000 that of Sirius (it has twice the diameter and the distance is 500,000 times as much; the Sun is 10,000,000,000 times as bright, corresponding to an angular diameter ratio of 100,000, so Sirius is roughly 6 times as bright per unit solid angle).
The angular diameter of the Sun is also ca. 250,000 that of Alpha Centauri A (it has the same diameter and the distance is 250,000 times as much; the Sun is 40,000,000,000 times as bright, corresponding to an angular diameter ratio of 200,000, so Alpha Centauri A is a little brighter per unit solid angle).
The angular diameter of the Sun is about the same as that of the Moon (the diameter is 400 times as large and the distance also; the Sun is 200,000-500,000 times as bright as the full Moon (figures vary), corresponding to an angular diameter ratio of 450-700, 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).
See also Angular resolution, apparent size.
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