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Physics - Formulas - Small Angle Formula

Some objects in the sky have an apparent size - like the moon. By understanding geometry and the nature of circles, it is possible to determine the distance to the object, or the physical diameter of the object.

With regard to measure, the standard in Astronomy is degrees and arcseconds. Here is the conversion factors:

As an example of this equation in use, I will use the example shown in the reference text:

To determine the physical diameter of Jupiter (on July 26, 2003), we can use what is called the small angle formula:

D = linear (physical) diameter
α =  angular size in arcseconds = known for Jupiter 31.2 arcseconds
d = distance to object = known for Jupiter = 943,000,000 km
206,265 = is required (arcseconds per radian)

This is in good agreement with the actual diameter of Jupiter (142,984km).

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