Everything about Angular Size totally explained
The
angular diameter of an object as seen from a given position is the "visual diameter" of the object measured as an angle. The visual diameter is the
diameter of the
perspective projection of the object on a
plane through its centre that's
perpendicular to the viewing direction. Because of
foreshortening, it may be quite different from the actual physical
diameter for an object that's seen under an angle. For a disk-shaped object at a large distance, the visual and actual diameters are the same.
Formulas
The angular diameter of an object can be calculated using the formula:
» only makes a difference for spherical objects that are relatively close.
Use in astronomy
In
astronomy the sizes of objects in the sky are often given in terms of their angular diameter as seen from
Earth, rather than their actual sizes.
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
light-year, is 0.03", and that of the Earth 0.0003".
The angular diameter 0.03" of the Sun given above is approximately the same as that of a person at a distance of the diameter of the
Earth.
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This table shows the angular sizes of noteworthy
celestial bodies as seen from the Earth:
This meaning 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).
Even though Pluto is physically larger than Ceres, when viewed from Earth, for example through the
Hubble Space Telescope, Ceres has a much larger apparent size.
While angular sizes measured in degrees are useful for larger patches of sky (in the constellation of Orion, for example, the three stars of the belt cover about 3 degrees of angular size), we need much finer units when talking about the angular size of galaxies, nebulae or other objects of the night sky.
Degrees, therefore, are subdivided as follows:
360 degrees (º) in a full circle
60 arc-minutes (′) in one degree
60 arc-seconds (′′) in one arc-minute
To put this in perspective, the full moon viewed from earth is about ½ degree, or 30 arc minutes (or 1800 arc-seconds). The moon's motion across the sky can be measured in angular size: approximately 15 degrees every hour, or 15 arc-seconds per second. A one-mile-long line painted on the face of the moon would appear to us to be about one arc-second in length.
Non-circular objects
Many deep sky objects such as galaxies and nebulas are non-circular and are thus typically given two measures of diameter: Major Diameter and Minor Diameter. For example, the Small Magellanic Cloud has a visual apparent diameter of × .
Further Information
Get more info on 'Angular Size'.
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