We first measure the angular size of the Sun and then note that
or
radius of the Sun ~ D x angle
We infer that the radius of the Sun is 696,000 km.
Finding the radii of other stars is more difficult. We cannot directly measure the angular sizes of stars in the above manner except for the largest most nearby stars using a technique known as speckle interferometry . The most important way of finding the radii of distant stars is to binary (eclipsing) star systems. Consider an Eclipsing Binary: the length of time taken for the light from the system to fall or rise is a measure of the size of the smaller star; the length of time that the system is in totality is a measure of the size of the larger star. Studies of eclipsing binary star systems can give information on the relative sizes of the stars.
