Final answer:
Cepheid variable stars relate the period of variability to their intrinsic luminosity via the Period-Luminosity Relation, allowing astronomers to accurately measure cosmic distances.
Step-by-step explanation:
Cepheid variable stars are incredibly useful in astronomy for determining cosmic distances. The key to their utility lies in the Period-Luminosity Relation, which states that there is a direct correlation between the period of variability of a Cepheid star and its intrinsic luminosity. Specifically, the fundamental property that makes Cepheids invaluable is that they relate the period of variability to its intrinsic luminosity. In practice, once astronomers measure the period of a Cepheid variable with precision using observations, they can employ the Period-Luminosity Relation to ascertain the star's luminosity. With the luminosity known, they can then calculate the distance to the star by comparing its luminosity with its apparent brightness as seen from Earth. This method has allowed astronomers to measure distances to stars and galaxies out to over 60 million light-years, significantly expanding our understanding of the universe.