Α star has a radius similar to that of the Sun but half the Sun's luminosity. What is the surface temperature of this star using this data

Question

Quizplus · Accepted Answer

The luminosity (L) of a star is related to its radius (R) and surface temperature (T) by the Stefan-Boltzmann law, L = 4πR^2σT^4, where σ is the Stefan-Boltzmann constant. If the star has half the Sun's luminosity (L = 0.5L_Sun) but the same radius (R = R_Sun), we can set up the ratio of the star's luminosity to the Sun's luminosity in terms of temperature: (T/T_Sun)^4 = 0.5. Solving for T/T_Sun gives (0.5)^(1/4) ≈ 0.84, indicating that the star's surface temperature is 0.84 times that of the Sun.

Α Star Has a Radius Similar to That of the Sun