## Small Angle Formula

For a planet or other object that will appear like a disk when
viewed from some other object, its angular diameter or size
can be estimated from this formula:

angular diameter diameter
in degrees = (57.3 degrees) x ----------
distance

where 57.3 degrees is from (360 degrees) / (2 x pi), and
the rest of the formula uses the actual diameter of the object
divided by its distance away. Note that this can also be written
in units of arc-seconds, that is, 1 degree = 3600 arc-seconds,
so
angular diameter diameter
in arc-seconds = (206265 arc-seconds) x ----------
distance

Both formulas only work for small angles. If you use
this formula and get a big angle (more than about 10 degrees),
it will not be accurate and would need to be calculated by
more precise geometric means.
Make sure the diameter and distance are both in the same
units, so that their units cancel.

Last update: February 4, 1998.

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