An exoplanet discovery mission measures the total power output (luminosity) of a…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

An exoplanet discovery mission measures the total power output (luminosity) of a Sun-like star in a distant system to be 3.5×1027 W3.5\times10^{27}\,\text{W}. Spectroscopic data indicate an effective surface temperature of 5.5×103 K5.5\times10^{3}\,\text{K}. Treat the star as an ideal thermal radiator. (a) Calculate the radius of the star in meters. (b) Express the result from part (a) as a multiple of the Sun’s radius R⊙=6.96×108 mR_{\odot}=6.96\times10^{8}\,\text{m}. Comment briefly on how the size of this star compares to that of the Sun.

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