In: Physics
Suppose that you now have an observation of a pulsating variable star in the Pleiades (it's like a Cephid, but lets say that it's slightly different type of variable star). Suppose that you know that this type or star obeys a period-luminosity relationship that is linear such that if the period doubles then the luminosity doubles (and if the period triples then the luminosity triples, etc). The star of this type that you observe in the Pleiades has a period of 2 days.
1. Suppose you observe a variable star of the same type in a nearby galaxy, but it has a period of 8 days. However, to you, it appears to be only 10^-8 times as bright as the one that you saw in the Pleiades. Based on your knowledge of the inverse square law for light combined with the period-luminosity relationship I described above, what is the distance from Earth to this galaxy in parsecs?