stellar radius
/ STEL-er RAY-dee-us /
Stars are so distant that even through the largest telescopes nearly all of them appear as mere points of light, with no visible disk at all. So how can we possibly know how big a star is? It turns out we rarely measure stellar radius with a ruler; instead we deduce it cleverly from the light, combining how hot a star is with how much energy it gives off.
The most common method uses the Stefan-Boltzmann law, which says a star's luminosity equals its surface area times the fourth power of its temperature. Rearranged, this gives the radius: if you know a star's luminosity and its temperature, its size follows directly. This is why a cool red giant can be enormous — to be so luminous despite a cool surface, it must have a vast area. For a handful of nearby stars, the radius can be measured more directly: eclipsing binaries reveal radii from how long an eclipse lasts, and interferometry, which combines several telescopes to act as one giant eye, can just barely resolve the disks of the largest, nearest stars.
Stellar radii span a staggering range. A neutron star packs more than the Sun's mass into a ball about 20 km across; the Sun's radius is about 700,000 km; a red supergiant like UY Scuti can be over a thousand times wider than the Sun, big enough to swallow the orbits of the inner planets. Radius is what separates the giant and dwarf regions of the Hertzsprung-Russell diagram, and tracking how a star's radius changes over its life is central to understanding how stars age.
Two stars share the same orange colour, so the same temperature. One shines a thousand times brighter than the other. Since brightness at fixed temperature comes only from area, the brighter star must have about 30 times the radius — a quick mental calculation straight from the light.
At the same temperature, extra brightness can only mean extra size.
We almost never see a star's disk directly — radius is usually inferred from luminosity and temperature, or from eclipses, not measured with a telescope's image. Only a few dozen of the nearest, largest stars have had their disks actually resolved.