Small Angle Equation
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Transcript: The width of your fist at arm’s length is about ten degrees. The width of your thumbnail at arms length is about one degree. The angular diameter of the Moon or the Sun is half a degree. For angles of a degree or smaller astronomers can use a very useful equation called the small angle equation. This equation relates the angular diameter of an object to its distance and true diameter. If any two of these quantities are known the third can be deduced. Fro example, the Sun and the Moon subtend the same angle in the sky, half a degree. But the Sun is vastly farther away than the Moon, and so its size is substantially larger too. The small angle equation is heavily used in astronomy for measuring linear sizes once the distance and the angular size are known.
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