How does luminosity and its positive relationship with periodicity help explain how far stars are?

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How does luminosity and its positive relationship with periodicity help explain how far stars are?

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That’s true for a type of star called a cepheid variable.

Luminosity is the total power output of a star, the total amount of energy the star gives off in a given unit of time. This quantity is directly related to how bright the star appears to be, through its distance from us. If we know the luminosity, we can measure the apparent brightness and calculate the distance.

When we look at cepheids we don’t know how far they are, but we can see them getting brighter and dimmer. We can measure the time period of that brightening/dimming. Using the period/luminosity relationship, we can determine the luminosity, which we can use to calculate the distance.