How do scientists determine how big stars are?
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There are a few ways of doing so, and it depends on the type of star. One way for is to look at the temperature of the star which is calculated based off the assumption that the star is a black body (it can absorb all light).
If you measure the wavelengths of the light admitted from the star then you can tell which wave length is admitted most. Using Weins law, which is an equation that shows the relationship between the temperature of a black body and the strongest wavelength admitted, you can calculate the temperature.
With that temperature value calculated we can then look at the luminosity or the star. If you measure the luminosity and you have calculated the temperature you can use the Stefan-Boltzmann law to calculate the surface area of the star.
The Stefan-Boltzmann law shows relationship between the temperature of an object, it’s surface area and the power radiated. So you can rearrange the the equation to get the surface area of the star from the equation.
As the star is an orb you can calculate the radius of the star from the surface area as it’s equal to 4piR^2.
So if you put this equation in as your value of the surface area you can rearrange the equation to give you the stars radius, based off the temperature and luminosity.
Add the values of the measurements to the equation and you have calculated the stars radius. Then you can use that value to calculate the volume, or diameter.
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