Answer:
To find the distance to Cepheid variable stars and other pulsating stars, Astronomers find the period-luminosity relation (A relation between the pulsation period of a Cepheid variable and its absolute brightness).
The period-luminosity relationship has been calibrated by many astronomers throughout the twentieth century. A calibration was published by Michael Feast and Robin Catchpole in 1997 using trigonometric parallaxes determined by the Hipparcos satellite. The relationship between a Population I Cepheid's period P, and its luminosity, measured as its mean absolute magnitude Mv was "Mv=-2.81log(P)-(1.43±0.1)" with P measured in days.
The following relations can also be used to calculate the distance d and reddenings E(B − V) to classical Cepheids:
"5log10d=V+(3.43)log10P-(2.58)(V-I)+7.50" "5log10d=V+(4.42)log10P-(3.43)(B-V)+7.15" "E(B-V)=-(0.27)log10P+(0.41)(V-J)-0.26" Where J is on the 2MASS photometric system, and B, I and V represent blue, near infrared, and visual, respectively.