B Question about Hertzsprung-Russell-diagram

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The relationship between a star's temperature, luminosity, and radius is explained by the Stefan-Boltzmann equation, which quantifies the radiation emitted per unit area based on temperature. Total luminosity is derived by multiplying the radiation from the star's surface area, leading to the formula L = σT^4 * 4πR^2. By knowing a star's luminosity (L) and temperature (T), one can easily calculate its radius (R). This straightforward calculation highlights the interconnectedness of these stellar properties. Understanding this relationship is fundamental in astrophysics.
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Why can you read out the radii of the stars by knowing their temperature and luminosity?
Can't make sense out of it.
 

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The Stefan-Boltzmann equation tells you the amount of radiation emitted from a unit area of the star as a function of temperature. The total luminosity is then given by just summing this over the surface area of the star, so:

L = \sigma T^4 * 4 \pi R^2

So if you know L and T, you can calculate R.
 
wow that was easy thanks!
 
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