Shapley used the period-luminosity relation to estimate distances. First, he collected all the available data on Cepheid stars, from his own observations and from other astronomers including Leavitt. The distance to some of the nearer Cepheids had been measured, and thus Shapley could figure out their absolute magnitudes. The only physics he needed was the simple rule that brightness decreases with the square of the distance. Then Shapley graphed period versus absolute magnitude.[The period-luminosity curve is] based upon more than 230 stars, and, except for zero-point uncertainty [the uncertainty in the distance measured by other methods to the nearer Cepheids], is probably correct within one or two hundredths of a magnitude. —Harlow ShapleyShapley made the reasonable assumption
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