Variable Stars used to obtain Distances
It was determined early in the 20th century that some stars varied in luminosity, and this change in luminosity had a specific repeating period.
But the final VERY important piece of information: The Period of this Luminosity change was related to their Luminosity. Very bright variable stars oscillated in brightness very slowly, while the dimmer variable stars oscillated in brightness very quickly, as shown below.
Period-Luminosity Relation for Variable Stars
Shapely was aware of Henrietta Leavitt's work on characterizing
Variable Stars, and was able to obtain distances for a few.
This allow him to calibrate the system, making all variable
stars Standard Candles (which means, as standard distance
rulers).