Physics
Physics
Problem
An exoplanet discovery mission measures the total power output (luminosity) of a Sun-like star in a distant system to be . Spectroscopic data indicate an effective surface temperature of . 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 . Comment briefly on how the size of this star compares to that of the Sun.Intuitive explanation
The Stefan–Boltzmann law connects a star's total power output to its surface temperature and size—the key is recognizing that luminosity depends on both how hot the surface is and how much surface area is radiating. Once you account for temperature's strong effect (it enters as the fourth power), you can solve for the star's radius and compare it to our Sun to understand its true scale.
Intuitive explanation
The Stefan–Boltzmann law connects a star's total power output to its surface temperature and size—the key is recognizing that luminosity depends on both how hot the surface is and how much surface area is radiating. Once you account for temperature's strong effect (it enters as the fourth power), you can solve for the star's radius and compare it to our Sun to understand its true scale.