Professional and amateur astronomers alike can measure a star's brightness by putting a photometer or charge-coupled device on the end of a telescope. If they know the star's brightness and the distance to the star, they can calculate the amount of energy that the star puts out, or its luminosity (luminosity = brightness x 12.57 x (distance)2). Conversely, if you know a star’s luminosity, you can calculate its distance from the Earth. Certain stars -- such as RR Lyrae and Cepheid variables -- can serve as light standards. These stars change their brightness regularly and the luminosity is directly related to the period of their brightness cycle.
To determine the luminosities of the globular clusters, Shapely measured the periods of brightness of the RR Lyrae stars in the clusters. Once he knew the luminosities, he could calculate their distances from Earth. See How Galaxies Work for how astronomer Edwin Hubble used a similar technique with Cepheid variable stars to determine that spiral nebulae were farther than the limits of the Milky Way.
Globular Clusters and Spiral Nebulae
Around the time that Kapetyn published his model of the Milky Way, his colleague Harlow Shapely noticed that a type of star cluster called a globular cluster had a unique distribution in the sky. Although few globular clusters were found within the Milky Way band, there were a lot of them above and below it. Shapely decided to map the distribution of globular clusters and measure their distances using variable star markers within the clusters and the luminosity-distance relationship (see sidebar). Shapely found that globular clusters were found in a spherical distribution and concentrated near the constellation of Sagittarius. Shapely concluded that the center of the galaxy was near Sagittarius, not the sun, and that the Milky Way was about 100 kiloparsecs in diameter.
Shapely was involved in a great debate about the nature of spiral nebulae (faint patches of light visible in the night sky). He believed that they were "island universes," or galaxies outside the Milky Way. Another astronomer, Heber Curtis, believed that spiral nebulae were part of the Milky Way. Edwin Hubble's observations of Cepheid variables finally settled the debate -- the nebulae were indeed outside the Milky Way.
But questions still remained. What shape was the Milky Way, and what exactly existed inside it?