How is the distance to Cepheid variable stars determined?

The distance to Cepheid variable stars is determined using their period-luminosity relationship.

Cepheid variable stars are pulsating stars that vary in brightness over a regular period of time. The period of their brightness variation is directly related to their luminosity, or intrinsic brightness. This relationship was discovered by Henrietta Leavitt in 1912, who found that the brighter the Cepheid, the longer its period.

By measuring the period of a Cepheid variable star, astronomers can determine its intrinsic brightness. They can then compare this to its apparent brightness, as seen from Earth, to calculate its distance using the inverse square law of light. This law states that the apparent brightness of an object decreases with the square of its distance from the observer.

The accuracy of this method has been refined over the years, with the use of more precise instruments and techniques such as parallax measurements and the Hubble Space Telescope. Cepheid variable stars have been used to determine the distances to nearby galaxies, and have played a crucial role in the development of our understanding of the size and age of the universe.