Two red stars have surface temperatures of 3000 K, but Star A's luminosity is about 5% ofthe Sun's and Star B's luminosity is about 32,000 times the luminosity of the Sun. How muchbigger is star B than star A?
A)They are the same size.
B)Star B's radius is about 16 times larger than star A's radius.
C)Star B's radius is about 800 times larger than star A's radius.
D)Star B's radius is about 640,000 times larger than star A's radius.
E)This cannot be determined from the information given.

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to its radius squared and temperature to the fourth power. Since both stars have the same temperature, the ratio of their luminosities is equal to the square of the ratio of their radii. Therefore, the ratio of the radii is the square root of the ratio of their luminosities, which is √(32,000/0.05) = √640,000 = 800.

Two Red Stars Have Surface Temperatures of 3000 K, but Star