Two stars are found to have the same luminosity. However, one star has twice the surface temperature of the other. From this information, what can one determine about their radii?
A) The hotter star has half the radius of the cooler star.
B) The cooler star has half the radius of the hotter star.
C) The hotter star has a quarter the radius of the cooler star.
D) Nothing can be determined about the radii from this information.

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to its radius squared and the fourth power of its surface temperature (L ∝ R²T⁴). If one star has twice the temperature of the other but the same luminosity, its radius must be smaller to compensate for the higher temperature. Specifically, the hotter star's radius must be a quarter of the cooler star's radius to maintain the same luminosity.

Two Stars Are Found to Have the Same Luminosity