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 2&pi.
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