Question

How do you find the diameter of the sun?

Answer 1

A good approximation to the diameter can be computed from the angular spacing `alpha` of the solar disc, when it is right overhead.
Vernal Equinox Sun (about Mar 21, near New Papua Guinea).

Explanation:

The formula is
Diameter of the solar disc = `2(1 AU - r)tan(alpha/2)`,
where `alpha` is the angular spacing of the right overhead Sun at equinox instant and location on the equator.
1 AU =149597871 km and r = equatorial radius of the Earth = 6378 km.
For these values, diameter = 2.992 E+08 tan (`alpha/2`)
Sample data: Against `alpha=0.267^o`, the diameter = 697600 km nearly, and vice versa..
The line of centers of the Sun and the Earth passes through the observer at the chosen instant and location.

The vernal equinox right-overhead-Sun noon occurs in the proximity of New Papua Guinea island on the equator, by Mar 21.

For any other instant and latitude,this formula indeed gives an approximation that is not so precise.

This approximation can be further improved by considering the fact that what is observed as the diameter of the glowing solar disc falls a little short of the the actual diameter of the Sun.

The answer can carry more significant digits (sd), if the radius of the Earth and the angular spacing are known with higher precision in sd.