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Square degree

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A square degree (denoted deg2) is a non-SI unit measure of solid angle. 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 steradian. The number of square degrees in a whole sphere is

4 \pi \left(\frac{180}{\pi}\right)^2 = \frac{129\,600}{\pi},

or approximately 41,253 deg2.

For example, observed from the surface of the Earth, the Moon has a diameter of approximately 0.5°, so it covers an solid angle of approximately 0.20 deg2, which is 4.8 × 10−6 of the total sky sphere.

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