Star A has 4 times the radius of star B and is twice as hot.How does the luminosity of star A compare to that of star B?
A)8 times as great
B)1024 times as great
C)16 times as great
D)256 times as great

Question

Quizplus · Accepted Answer

The luminosity of a star is directly proportional to the fourth power of its radius and directly proportional to the square of its temperature.

Let's use L to represent luminosity, R to represent radius, and T to represent temperature.

For star A: 
L(A) = k(R(A)^4)(T(A)^2)

For star B: 
L(B) = k(R(B)^4)(T(B)^2)

We know that R(A) = 4R(B) and T(A) = 2T(B). Substituting these values into the equations, we get:

L(A) = k((4R(B))^4)(2T(B))^2 = 1024k(R(B)^4)(T(B)^2)

L(B) = k(R(B)^4)(T(B)^2)

Therefore, L(A) is 1024 times greater than L(B).

The best choice is D.

Star a Has 4 Times the Radius of Star B