All Experts Redux Period -Luminosity Problem Solution

 Period-Luminosity Relation Problem:

Two Cepheids, Alpha and Beta, are observed to have the same period of 10 days. At maximum brightness A has an apparent magnitude of +3.0 and B has an apparent magnitude of +8.0. If the distance of A (associated with a cluster) is known to be 60 pc,  then how far away is B?   

Solution:

The magnitude difference between Alpha and Beta is (8 - 3) = 5 magnitudes, which corresponds to a brightness ratio of 100. (E.g. (2.515)⁵ = 100) so Alpha is apparently 100x brighter than B. According to the inverse square law of light, the brightness of a light source diminishes as the square of the distance.

Accordingly:

[d(Beta)/d(Alpha)]² = 100 = B(Alpha)/ B(Beta)

and

[d(Beta)/d(Alpha)] = [100]^½ = 10

and: d(Beta) = 10 {d(Alpha)}

So, Beta must be ten times more distant than Cepheid Alpha.