Question

Why are Cepheid variable stars important to astronomers? How is the information they impart any more or less useful than using stellar parallax?

Answer 1

The period of variability of a Cepheid is directly proportional to its intrinsic brightness.

Explanation:

If we can observe how long it takes for a Cepheid to go from bright, to dim, back to bright, we can use that to tell exactly how bight the star is, because in this type of star, brightness and period (time for one complete cycle) are connected.

If we know exactly how bright a star is, as well as how bright it looks from Earth, we can tell how far away it is.

This principle is a bit less precise than stellar parallax, but can be used for stars that are much, much farther away.