The 'angular diameter' of an object as seen from a given position is the
diameter measured as an angle. It can be calculated using the formula:
:
,
in which
is the angular diameter, and
and
are the diameter of and the distance to the object, expressed in the same units. When
is much larger than
,
may be approximated by the formula
, in which the result is in
radians.
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
light-year, is 0.03", of the Earth 0.0003".
The angular diameter of a person on the opposite side of the earth is approximately 0.03″
[1].
This table shows the angular sizes of the most important
Solar System bodies as seen from the Earth:
★
Betelgeuse: 0.049″ – 0.060″
★
Alpha Centauri A: ca. 0.007″
★
Sirius: ca. 0.007″
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).
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 × .
See also
★
Angular resolution
★
Apparent size