Question

* Consider two galaxies (A and B) and imagine you have found a Cepheid variable star in each of them. The period of both stars are the same (30 days), but the one in Galaxy A is 5 magnitudes fainter than the one in Galaxy B. How far is Galaxy A from us relative to Galaxy B?

Answer 1

For cepheid variables there exist a relationship between it's Period (P) and Luminosity(absolute magnitude).

M = - [2.76 (log10(P) - 1.0)] - 4.16

Hence if the period is same for both cepheids in each galaxy and hence we can assume that they have same absolute magnitude.

Ma = Mb

Since we know absolute magnitude is related to apparent magnitude via following relationship:

m - M = 5 log10 (d/10) , where d is in parsec

For galaxy a,

And hence galaxy a is 10 time further away from us than galaxy b is from us.