The Earth's place in the galaxy was determined largely by an astronomer named Harlow Shapley. Shapley's work was based on regularly pulsating variable stars and the concept of absolute luminosity. Thanks to the regular periods of these stars and their presence in globular clusters, Shapley was able to map the distances to a number of clusters. These findings suggested that the Earth was in an outer spiral arm of the galaxy.
Harlow Shapley's work was dependent on the work of another astronomer, Henrietta Swan Leavitt. Leavitt established that variable stars could be used to determine astronomical distances. The key to this was the relationship between the star's absolute and apparent magnitude. Absolute magnitude or luminosity describes a star's actual intrinsic brightness, whereas apparent magnitude describes how bright a star appears to be. Astronomers can use the difference of a variable star's absolute and apparent magnitude to calculate its distance from Earth.
Cepheid and RR Lyrae Stars
Cepheid and RR Lyrae stars are two types of variable stars. Cepheid variables have periods that range from 1 to 100 days, and they are generally fairly bright. RR Lyrae stars have shorter periods of a day or less, and all have roughly the same absolute magnitude. Both of these stars can be used to determine distances. Henrietta Leavitt studied Cepheid variables in her research. Shapley, on the other hand, used RR Lyrae stars to survey distances and distributions across the galaxy.
In order to conduct his research, Shapley looked at globular clusters around the Milky Way. Globular clusters are dense collections of stars. Shapley was able to use the Cepheid variables of nearby globular clusters to calculate the distances to those clusters. Some of the more distant clusters had no visible Cepheid variables. In such cases, Shapley used the uniform brightness of RR Lyrae stars to calculate distances.
Our Position in the Galaxy
Shapley's survey of the galaxy's globular clusters showed a spherical distribution of clusters. He assumed that the center of the galaxy was at the center of that sphere. The sun, however, was not near the galactic center. Instead, the sun was towards the edge of the galaxy, about two-thirds of the way from the galactic center.