Formulas & tables/Physics/Astronomy/Angular size of a body

Angular size of a body

α=2arctan⁡ ⁣d2D≈dD\alpha = 2\arctan\!\frac{d}{2D} \approx \frac{d}{D}

Result unit: °

What it describes

The angle a body subtends in the sky. The Sun is about 0.53°, the Moon about 0.50–0.56° — almost the same.

Symbols

α\alpha
angular size (viewing angle)
[rad / °]
dd
diameter of the body
[m]
DD
distance to the body
[m]

Where it comes from

This coincidental match of angular sizes makes both total eclipses possible (the Moon nearer, covering the Sun) and annular ones (the Moon farther, leaving a ring).

When to use it

When you compare the sizes of the Sun and Moon in the sky, or explain the types of solar eclipse.

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