There are certain stars that have a lot of Helium distributed throughout their structure. If such a star is hot enough it will ionize that Helium stripping it of one, or even both, of its electrons. A Helium ion with with one electron is singly ionized, and is relatively transparent. A helium ion with no electrons is doubly ionized and is relatively opaque.

Very hot stars will doubly ionize their Helium. The opacity of the ion will absorb the light coming from deeper within the star; and the star will appear to dim. But that absorption also heats the outer envelope of the star which expands. As it expands it cools. Eventually it cools enough so that the doubly ionized Helium will pick up a free electron and become singly ionized and more transparent. Light is now free to leave the star, and it appears to brighten. The freeing of that energy causes the outer envelope to cool and contract until the singly ionized Helium is dense enough to heat up and lose that electron again.

And so the star pulsates, growing brighter and dimmer with a period of a few days. Such a star is called a Cepheid Variable (CV), and there are many around the sky.

In 1921 Henrietta Swan Leavitt was studying these variable stars within a Southern Hemisphere nebula called the Small Magellenic Cloud (SMC)

The reason Leavitt was studying variable stars within the SMC is because that nebula is very far away from us and so all the stars within it are all the same distance from us. This means that distance could be removed as a variable.

What she learned, as she studied the CVs in the SMC was that the period of the pulsations was proportional to the average brightness of the star. This became known as the Period-Luminosity relationship.

Delta Cepheus is a nearby CV with a 5 day period. Leavitt found a star with the same period in the SMC and measured it's magnitude as 10,000 times dimmer. From that measurement, and the inverse square law, she was able to show that the SMC was 100 times farther from us than Delta Cepheus.

Eventually CVs were found whose distances from us could be directly measured, and Leavitt's formula was calibrated. Now, given brightness and period, it was possible to calculate distance.

There are hundreds of globular clusters orbiting the core of our galaxy. These objects are gravitationally bound spheres roughly a light-year in diameter and densely packed with ~100,000 stars. They are some of the most gorgeous objects visible through a backyard telescope. And almost all of them contain CVs.

Using Leavitt's formula, the distance to all the Globular clusters can be calculated, and this allows us to create a 3D model. It turns out the clusters are arranged in a giant sphere whose center is 30,00 light-years away in the constellation of Sagittarius.

If we assume the center of that sphere is also the center of our galaxy, then we are 30,000 light years from that center. If we turn around 180° and look directly away from the center, we see about the same amount of galaxy in that direction. So we can infer that the radius of our galaxy is ~60,000 light years, and that our home, the Milky Way Galaxy is ~120,000 light years in diameter.

Source: x.com/unclebobmartin/status/1828476607192764692