Cepheid stars are peculiar stars very important to astrophysics: they are pulsating stars (variables ) that allow us to estimate distances. And the estimation of distances are, of course, are the largest obstacle to overcome in order to know the characteristics of an astro object under study. By knowing the distance, we other variables such as the mass, radius of a star & its intrinsic luminosity can be estimated.
It was Herrietta Swan Leavitt ( July 4, 1868 - December 12, 1921), a pioneer female astronomer who worked at the Harvard College Observatory as "calculator" who by examining photographic plates managed to measure and catalog the brightness of stars including the Cepheids. Also she managed to discover the relationship between brightness and period of Cepheid variable stars. This well he could have done to win a Nobel prize, but she got no recognition. By knowing this relationship and using Cepheid stars in Andromeda, it was later learned that the Andromeda galaxy was "outside" our Milky Way and in fact, that all galaxies are island universes outside our own galaxy (see "The Great Debate of the Great by Harlow Shapley and Curtis on the size of the Universe, 1920 " here ). Furthermore, this relationship was later used by Edwin Hubble to determine that the universe is expanding (see Hubble 's law).
In this image we can see one of the most important stars in the sky: RS Pup. (following text from apod.nasa.gov). This is partly because, by coincidence, it is surrounded by a dazzling reflection nebula. Pulsating RS Puppis, the brightest star in the image center, is some ten times more massive than our Sun and on average 15,000 times more luminous. In fact, RS Pup is a Cepheid type variable star, a class of stars whose brightness is used to estimate distances to nearby galaxies as one of the first steps in establishing the cosmic distance scale. As RS Pup pulsates over a period of about 40 days, its regular changes in brightness are also seen along the nebula delayed in time, effectively a light echo. Using measurements of the time delay and angular size of the nebula, the known speed of light allows astronomers to geometrically determine the distance to RS Pup to be 6,500 light-years, with a remarkably small error of plus or minus 90 light-years. An impressive achievement for stellar astronomy, the echo-measured distance also more accurately establishes the true brightness of RS Pup, and by extension other Cepheid stars, improving the knowledge of distances to galaxies beyond the Milky Way. Photo: Telescopio Espacial Hubble Legacy Archive, NASA, ESA - Processing: Stephen Byrne.