# The binary star consists of a blue star with a surface temperature of 30,000 K and a magnitude of 0 ^ m and a red star with a surface

The binary star consists of a blue star with a surface temperature of 30,000 K and a magnitude of 0 ^ m and a red star with a surface temperature of 3000 K and a magnitude of 5 ^ m. How do the radii of these stars compare?

The 5m difference in brightness between the two components of the physical binary means that the hot star is exactly 100 times luminous than the cold one. But, as you know, the luminosity of a star is proportional to R2T4, where R and T are its radius and temperature. Since the temperature of a hot star is 10 times higher, then, taking into account the luminosity ratio, it turns out that its radius, on the contrary, should be 10 times less than that of a cold star.

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