Square degree

A square degree (deg²) is a non-SI-compliant 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 π / 180 radians, a square degree is equal to (π / 180)², or about 1 / 3283 or 3.0462×10⁻⁴ steradian (0.30462 msr).

The number of square degrees in a whole sphere is approximately 41253 deg². This is the total area of the 88 modern constellations in the sky.

$4 \pi \left(\frac{180}{\pi}\right)^2 \, \mathrm{deg^2} = \frac{360^2}{\pi}\,\, \mathrm{deg^2} = \frac{129\,600}{\pi} \,\, \mathrm{deg^2} \simeq 41\,252.96 \,\, \mathrm{deg^2}$

Examples

• A whole sphere has 41253 deg²
• The full moon covers only about 0.2 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 0.5 deg), so the moon's disk covers a circular area of: π (0.5 deg/2)², or 0.2 square degrees.
• Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only 0.2 deg² as well.
• It would take 210100 times the full moon (or the Sun) to cover the entire celestial sphere.
• Assuming the Earth to be a sphere with a surface area of 510 million km², the area of Northern Ireland (14130 km²) and Connecticut (14357 km²) represent a solid angle of 1.1 deg² and 1.2 deg², respectively.
• The largest constellation, Hydra, covers a solid angle of 1303 deg², whereas the smallest, Crux, covers only 68 deg².^[1]

See also

• Steradian
• Spat (unit)
• Minute and second of arc
• List of constellations by area

References

1. RASC Calgary Centre - The Constellations

External links

• http://calgary.rasc.ca/constellation.htm#square