{{short description|Unit of solid angle}} {{infobox unit | bgcolor = | name = square degree | image = | caption = | standard = | quantity = solid angle | symbol = deg<sup>2</sup> | symbol2 = | units1 = SI units | inunits1 = ≈ {{val|3.04617|e=-4|u=sr}} | units2 = arcsec<sup>2</sup> | inunits2 = {{val|12,960,000|u=arcsec2}} }} thumb | right | An illustration of a solid angle formed by a rectangular pyramid, whose apex angles are both 10 degrees. The resulting solid angle is about {{val|99.747369}} square degrees. The size of Moon, as seen from Earth, is shown in yellow for comparison. __NOTOC__ A '''square degree''' ('''deg<sup>2</sup>''') is a non-SI unit measure of solid angle. Other denotations include ''sq. deg.'' and (°)<sup>2</sup>. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere.
Analogous to one degree being equal to {{sfrac|{{pi}}|180}} radians, a square degree is equal to ({{sfrac|{{pi}}|180}})<sup>2</sup> steradians (sr), or about {{sfrac|1|{{val|3283}}}} sr or about {{val|0.3046|u=msr}} (millisteradian). The whole sphere has a solid angle of {{val|4|end={{pi}}|u=sr}}, which is approximately {{val|41253|u=deg2}}: : <math>4 \pi \left(\frac{180}{\pi}\right)^2 \, {\deg}^2 = \frac{360^2}{\pi} ~ {\deg}^2 = \frac{129\,600}{\pi} ~ {\deg}^2 \approx 41\,252.96 ~ {\deg}^2.</math>
== Subdivisions == Each square degree is equal to 3600 '''square arcminutes''', and each square arcminute is equal to 3600 '''square arcseconds'''. So, each square degree is equal to {{val|12,960,000}} square arcseconds. The whole sphere contains about 148.51 million square arcminutes and about 534.64 billion square arcseconds.
== Examples == * The full moon covers only about {{val|0.2|u=deg2}} of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly {{val|0.5|u=deg}}), so the moon's disk covers a circular area of {{pi}}({{sfrac|0.5°|2}})<sup>2</sup>, or {{Val|0.2|u=deg2}}. The moon varies from 0.188 to {{val|0.244|u=deg2}} depending on its distance from the Earth. * Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only {{val|0.2|u=deg2}} as well. * It would take {{gaps|210|100}} times the full moon (or the Sun) to cover the entire celestial sphere. * Conversely, an average full moon (or the Sun) covers the fraction 2 / {{val|210100}}, or less than 1/1000 of a percent ({{val|0.00000952381}}) of the celestial hemisphere, or above-the-horizon sky. * Assuming the Earth to be a sphere with a surface area of 510 million square kilometres, the area of Northern Ireland ({{val|14130|u=km2}}) represents a solid angle of {{val|1.14|u=deg2}}, Connecticut ({{val|14357|u=km2}}) represents a solid angle of {{val|1.16|u=deg2}}, and Equatorial Guinea ({{val|28050|u=km2}}) represents a solid angle of {{val|2|u=deg2}}. * The largest constellation, Hydra, covers a solid angle of {{val|1303|u=deg2}}, whereas the smallest, Crux, covers only {{val|68|u=deg2}}.<ref>{{cite web |title=RASC Calgary Centre – The Constellations |url=https://calgary.rasc.ca/constellation.htm |access-date=2022-02-16 |website=calgary.rasc.ca }}</ref>
== See also == * Steradian * Spat (angular unit) * Minute and second of arc<!-- this article is about plane angles, but the concept of minutes, seconds, thirds and fourths exists also for solid angles. To be expanded at a later stage. --> * List of constellations by area
== References == {{reflist}}
== External links == * {{cite web |url=http://calgary.rasc.ca/constellation.htm#square |title=Square Degrees – the Area of something on the sky |publisher=The RASC Calgary Centre |date=2018-11-05 |accessdate=2022-01-21 }}
{{DEFAULTSORT:Square Degree}} Category:Units of solid angle