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About a century ago it was realised that some the luminosity of some stars oscillated with a regular period, and that the period scales with the luminosity. Due to this relation, they are used to determine distance (standard candles). Such stars were originally found in the constellation Cepheus, and hence they are called Cepheids.

In the derivation of the relation between the period and the luminosity, we assume that the masses of the stars $ M $ and their temperature $ T \, $ do not change too much, but that the radius $ R $ can change considerably. The stellar time scale (or period) is given by

$ P \approx \frac{R^3}{G M} $

while the luminosity scales as

$ L \propto R^2 T^4 $

and hence

$ L \propto P^{4/3} $

This relation was originally obtained empirically by Henrietta Leavitt, and is often referred to as Leavitt law.