In 1610, Galileo set incorrect maps of the cosmos on the right path. Our mental model of Earth at the center of the universe had to evolve to match observations.
In 1842, Christian Doppler wrote about the doppler effect in stars. It was first confirmed with sound in 1845, then with light in 1848. The big moment came in 1868 when, for the first time, we could tell which stars were coming and going.