The star Sirius has a surface temperature of 9750 K and aradius 2.4 times larger

Question

The star Sirius has a surface temperature of 9750 K and aradius 2.4 times larger than the Sun's. a) What is the ratio of the flux (energy per square meter persecond) emitted from the surface of Sirius to the flux emittedfrom the surface of the Sun? b) What is the ratio of the luminosity of Sirius to theluminosity of the Sun? The star Sirius has a surface temperature of 9750 K and aradius 2.4 times larger than the Sun's. a) What is the ratio of the flux (energy per square meter persecond) emitted from the surface of Sirius to the flux emittedfrom the surface of the Sun? b) What is the ratio of the luminosity of Sirius to theluminosity of the Sun?

Explanation / Answer

a) Use the Stefan-Boltzmann law which states that the flux isproportional to T^4. As T_Sun is 5780 K this amounts to a factor(9750/5780)^4 = 8.10 b) Use that L is proportional to R^2 T^4, the first factor beingproportional to the surface. So the ratio is 2.4^2 * 8.1 = 46.6

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