As far as I know, astronomy is generally an observational science. We see something and then try to explain why it is happening. The one exception that I know of is black holes: first it was thought of, then it was found.
Einstein's relativity is middle ground to me, he thought of light beams at the speed of light but obviously could observe gravity's effects.
Anyway, I guess my question is, what are the biggest discoveries that were thought of before they were seen in the sky?
Answer
Off the top of my head, the Cosmic Microwave Background radiation was hypothesized as a consequence of Big Bang Theory before it was observed by accident by Penzias and Wilson. Also the light element abundances, also a consequence of BBT, was theoretical and is still being refined today through observations that supported the initial theory.
I don't know what your definition of "biggest discoveries" would be, but volcanoes on Io were theoretical before observed by Voyager 2. The discovery of the most volcanically active body in the solar system seems kinda big to me, but I am a planetary astronomer.
I think you're going to get multiple people posting several different things in response, so one of us responders should try to agglomerate the responses into a single reply.
Edited to add: Since you've accepted my answer over Andrew's I'll just append his to mine so it's more likely that people who just read the accepted ones will see it: "Neutron stars were predicted in 1934 by Baade and Zwicky, one year after the discovery of the neutron. They were not observationally confirmed until 1965 by Hewish and Okoye. It's hard to beat a prediction that sat around for 30 years before being confirmed."
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