Question

A cepheid variable in a nearby galaxy looks "10^6" times fainter than an identical Cepheid in the Milky Way? The Cepheid in the Milky Way is 1000 parsecs away. How far away is the nearby galaxy?

Answer 1

`10^6` parsecs

Explanation:

The absolute brightness (i.e. number of photons per unit time for a fixed size detector) decreases as the square of the distance.

To prove this for yourself, think of the photons passing through the surface of a sphere of radius `r`. The surface area is `4pi r^2`, proportional to the square of the radius.

So if the absolute brightness decreases by a factor of `10^6` that means that the distance is a factor of `sqrt(10^6) = 10^3` greater.

That makes the distant cepheid variable `10^3*10^3 = 10^6` parsecs away.