An astronomer observes two stars of the same surface temperature, but one has twice the diameter of the other. How many times larger is the luminosity from the larger star compared with that from the smaller star?
A) 2
B) 4
C) 16
D) They are the same.

Question

Quizplus · Accepted Answer

The luminosity of a star (how much energy it emits per unit of time) is directly proportional to its surface area and its surface temperature to the fourth power. Since both stars have the same surface temperature, we only need to consider the surface area. The surface area of a sphere (like a star) is given by 4πr^2, where r is the radius. If one star has twice the diameter of the other, it has twice the radius, and thus its surface area is 4 times larger (2^2 = 4). Therefore, the larger star is 4 times more luminous than the smaller one.

An Astronomer Observes Two Stars of the Same Surface Temperature