How do astronomers measure distances to stars and galaxies?
Astronomers have developed several techniques to indirectly measure the vast distances between Earth and the stars and galaxies. In many cases, these methods are mathematically complex and involve extensive computer modeling.
Parallax is the visual effect produced when, as an observer moves, nearby objects appear to shift position relative to more-distant objects. This common event is easily reproduced; hold your finger out at arm’s length, and look at your fingertip first with one eye closed, then the other. The "motion" of your fingertip as seen against background objects is caused by the change in your viewing position -- about three inches from one eye to the other.
As Earth orbits the Sun, astronomers invoke this same principle to determine the distance to nearby stars. Just like your fingertip, stars that are closer to us shift positions relative to more-distant stars, which appear fixed. By carefully measuring the angle through which the stars appear to move over the course of the year, and knowing how far Earth has moved, astronomers are able to use basic high-school geometry to calculate the star’s distance.
Parallax serves as the first "inch" on the yardstick with which astronomers measure distances to objects that are even farther.
For example, they use a class of variable known as Cepheids, which pulsate in and out like beating hearts. There is a direct relationship between the length of a Cepheid's pulsation and its true brightness. Measuring a Cepheid's apparent brightness -- how bright it looks from Earth -- allows astronomers to calculate its true brightness, which in turn reveals its distance. For this technique to work correctly, though, astronomers must first use the parallax method to get the distances to some of the closer Cepheids. This allows them to calibrate a Cepheid's true brightness, which then can be used to calculate its distance. Cepheids are especially bright stars, so they are visible in galaxies that are tens of millions of light-years away.
For more-distant galaxies, astronomers rely on the exploding stars known as supernovae. Like Cepheids, the rate at which a certain class of supernovae brighten and fade reveals their true brightness, which then can be used to calculate their distance. But this technique also requires good calibration using parallax and Cepheids. Without knowing the precise distances to a few supernovae, there is no way to determine their absolute brightness, so the technique would not work.