Two stars have the same mass and luminosity, but the surface of one of them is twice as hot as the surface of the other.

Two stars have the same mass and luminosity, but the surface of one of them is twice as hot as the surface of the other. Which star has a higher average density? How many times?

According to the Stefan-Boltzmann law, the luminosity of a star is proportional to R ^ 2T ^ 4, where R and T are its radius and temperature. Equality of luminosities at temperatures other than two times means that a cooler star has a radius 4 times larger than that of a hot star. And if the masses are equal, this means that the density of a cooler star is 64 times less than that of a hot star.

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