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Through International System of Units, Unit of measurement and Sphere
Analogous to one degree being equal to π/180 radians, a square degree is equal to (π/180)2 steradians (sr), or about 1/3283 sr or about 0.3046 msr (millisteradian). The whole sphere has a solid angle of 4π sr, which is approximately 41253 deg2:
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 12960000 square arcseconds. The whole sphere contains about 148.51 million square arcminutes and about 534.64 billion square arcseconds.
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Examples
- 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°), so the moon's disk covers a circular area of π(0.5°/2)2, or 0.2 deg2. The moon varies from 0.188 to 0.244 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 0.2 deg2 as well.
- It would take 210100 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 / 210100, or less than 1/1000 of a percent (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 (14130 km2) represents a solid angle of 1.14 deg2, Connecticut (14357 km2) represents a solid angle of 1.16 deg2, and Equatorial Guinea (28050 km2) represents a solid angle of 2 deg2.
- The largest constellation, Hydra, covers a solid angle of 1303 deg2, whereas the smallest, Crux, covers only 68 deg2.
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