The observational fact about a Cepheid variable star that leads to a measurement of its distance from us is that its period of variation is directly related to its:

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The period of variation of a Cepheid variable star is directly related to its absolute magnitude, meaning that the longer the period, the more luminous the star. By measuring the apparent magnitude of the star from Earth, and then using the period-luminosity relationship to determine its absolute magnitude, we can calculate its distance from us using the inverse square law of light.

The Observational Fact About a Cepheid Variable Star That Leads