Angular Diameter - Formulas

Formulas

The angular diameter of a flat circular object (disc) can be calculated using the formula:

in which is the angular diameter, and and are the visual diameter of and the distance to the object, expressed in the same units. When is much larger than, may be approximated by the formula, in which case the result is in radians.

For a round spherical object whose actual diameter equals, the angular diameter can be found with the formula:

The difference is due to when you look at a sphere, the edges are the tangent points, which are somewhat on your side of the facing hemisphere cross section. measures opposite/adjacent, whereas measures opposite/hypotenuse. For practical use, the distinction between the visual diameter and the actual diameter only makes a difference for spherical objects that are relatively close.

For very distant or stellar objects, the Small-angle approximation can also be used:

\begin{align} \sin \theta &\approx \theta \approx \arcsin \theta \\ \tan \theta &\approx \theta \approx \arctan \theta \end{align}

Which simplifies the above equations to:

(for small )

Read more about this topic:  Angular Diameter

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