Angular diameter

From Wikipedia, the free encyclopedia

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

$\delta = 2 \arcsin \left( \frac{1}{2}\,d / D \right)$ ,

in which $δ$ is the angular diameter, and $d$ and $D$ are the diameter of and the distance to the object, expressed in the same units. When $D$ is much larger than $d$ , $δ$ may be approximated by the formula $δ = d / D$ , in which the result is in radians.

In astronomy the size of objects in the sky is 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.

Sun	30'
Moon	29' – 33'
Venus	10″ – 58″
Jupiter	32″ – 49″
Saturn	16″ – 20″
Mars	4″ – 16″
Uranus	3″ – 4″
Neptune	2″

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).

[edit] 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 5° 20′ × 3° 5′.