For cepheid variable stars, what property of those stars can be observed that reveal its true brightness (which can then be used to calculate distance)?

Pulsation period

Explanation:

Cepheid Variable stars are stars that have a changing diameter which causes a change in the luminosity of the star.

The relation between luminosity and pulsation period was discovered by Henrietta Swan Leavitt. Edwin Hubble later modified the relation where the Cepheid variables which were considered to be in the Milky way were discovered to be in the Andromeda Galaxy.

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