What changed people’s thinking?

In the 19th century, photography and spectroscopy entered astronomy, and ultimately changed everything.  Long-exposure photographs revealed scores of beautiful nebulae and millions of previously unknown faint stars. 

Spectroscopy showed clear evidence that many of the elements we see on Earth are also in space, and it let us, via Doppler shifts, measure how fast any object on the sky is moving toward or away from us.

See also: Hubble's Law