The
small-angle formula is a
mathematical approximation, used in
astronomy. It relates the linear size (
D) of an object to its
angular size (α) and its distance from the observer (
d) and is a valid approximation if α is small.
The approximate formula is:
- D = α d / 206,265
Here, α has to be measured in arcseconds.
The number 206,265 is approximately equal to the number of arcseconds in a circle (1,296,600), divided by 2π.
The exact formula is
- D = 2 d tan(απ/1,296,600)
and the above approximation follows from this because tan(
x) is approximately equal to
x if
x is small.
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