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square degree

{{Short description|Measure of solid angle}}

{{Infobox unit

| bgcolor =

| name = Square degree

| image =

| caption =

| standard =

| quantity = Solid angle

| symbol = deg2

| symbol2 =

| units1 = SI units

| inunits1 = ≈ {{val|3.04617|e=-4|u=sr}}

| units2 = arcsec2

| inunits2 = 12,960,000 arcsec2

}}

__NOTOC__

A square degree (deg2) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°)2. 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}})2 steradians (sr), or about {{sfrac|1|{{val|3283}}}} sr or about {{val|3.046|e=-4|u=sr}}.

The whole sphere has a solid angle of {{gaps|4{{pi}}|sr}} which is approximately {{val|41253|u=deg2}}:

: 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.

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 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}})2, or 0.2 square degrees. 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 a 2 / {{gaps|210|100}} fraction, 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 km2, 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}}, 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}}.{{Cite web|title=RASC Calgary Centre - The Constellations|url=https://calgary.rasc.ca/constellation.htm|access-date=2022-02-16|website=calgary.rasc.ca}}

See also

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