# How do you measure the diameter of the sun?

Mar 6, 2016

$\angle$ spacing of Sun (S) disc = $\theta$. Radius of Earth (E) = r. ES = d. . Answer: $2 \left(d - r\right) \sin \left(\frac{\theta}{2}\right)$ = 1.395 E+06 km, nearly..

#### Explanation:

This is an approximation, with negligible error.
The formula is perfect for right-overhead-noon observation-.

Best location is equator-equinox-noon-location, around March 21.
Of course, there is limitation, in the precision for measurement of the angular spacing, of about 0.001".

The observer O's distance from the center S of the Sun is $d - r$.
The formula is from a right angled $\triangle$OSP right angled at P.
OP a tangent to the solar disc.
SP is a radius of the Sun.
Using d = 1 AU = 149597870 km, r = 6378 km, $\theta$ = 0.5344 deg, the diameter is 1395 thousand km, nearly.

There are slight variations in the reported diameter, in different sources.

I have given only 4-significant digits (sd) approximation. If more sd are needed, $\theta$ and r should carry more correct sd.