A Cepheid variable star with a pulsation period of a few days is seen in the spiral arm of a galaxy.Its apparent brightness is measured as 10⁴ times fainter than an equivalent star 1000 ly away from the Sun in the Milky Way Galaxy.Assuming no light absorption between galaxies,what is the distance to the far Cepheid and hence to the galaxy?
A) 10⁷ ly (10⁴ times farther away)
B) 10,000 ly (10 times farther away)
C) 10 ly (100 times closer)
D) 100,000 ly (100 times farther away)

Question

Quizplus · Accepted Answer

The apparent brightness of a star follows an inverse square law with distance. Therefore, the ratio of the apparent brightness of two stars is equal to the ratio of their distances squared.

Let's call the distance to the Cepheid variable star in the other galaxy "d". We know that the apparent brightness of this star is 10⁴ times fainter than an equivalent star at a distance of 1000 ly from the Sun.

So,

(apparent brightness of Cepheid variable star) / (apparent brightness of equivalent star in Milky Way) = (distance to equivalent star in Milky Way)² / d²

We can plug in the numbers we know:

(1/10⁴) = (1000)² / d²

Solving for "d", we find:

d = 100,000 ly

So the distance to the far Cepheid variable star is 100,000 ly, which means the galaxy is also 100,000 ly away from us. Therefore, the correct answer is D.

A Cepheid Variable Star with a Pulsation Period of a Few