Question

Two stars have the same luminosity. The first star is one light year away from your telescope. The second star is two light years away from your telescope. The first star’s brightness is:A. two times as great as the second star’sB. four times as great as the second star’s.C. sixteen times as great as the second star’s.D. equal to the second star’s.

Answer 1

f = L / (4pi'd2), where:

f: apparent brightness

L: luminosity

d: distance of star

(p and i' stay constant between the two stars, so let's make them both equal to 1)

Let's say the closer star has a distance of 1 and the further has a distance of 2, and they both have a luminosity of L.

Apparent brightness of further star:

f = L/(4*2^2) = L/16

Apparent brightness of closer star:

f = L/(4*1^2) = L/4

As you can see here, the apparent brightnesses of the two stars differ by a factor of 4.

Answer: B. four times as great as the second star’s.