We can use the time period (the amount of time it takes for the variable star to undergo a full cycle) of a Cepheid Variable star to find out its absolute magnitude using a graph similar to the one on here, and using that absolute magnitude, we can find the star's distance from Earth using a rearrangement of the equation:

M = m + 5 - 5*log*d

Using this graph, we can work out the absolute magnitude of a Cepheid Variable, which means that we can work out the distance to that star. This is vital for working out distances to far away systems, for which using parallax does not work.

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