how was the supergiant star discovered?
Supergiant stars were discovered initially by comparing the brightness of stars of the same temperature. For some reason certain stars that had the same temperature and distance would be much brighter than others. This can only occur if the surface area and therefore radius is much larger than the others. In all there are roughly five classifications of star brightness with supergiant being the brightest of the five. Supergiants are stars in the final stages of their life. The upper left of Orion (shoulder) Betelgeuse is a supergiant star and if the Sun was replaced with Betelgeuse it would have a surface that extended out to Jupiter.
