Vera Rubin's confirmation of dark matter
On October 11th, 1979, Vera Rubin submitted her most influential paper. She noticed stars rotating around galaxies did not move at the expected rate. They moved much faster than Newtonian physics would allow given the mass of the galaxies. This evidence suggested that either Newtonian gravity does not apply universally or that, conservatively, more than of 50% of the mass of galaxies is contained in the relatively dark galactic halo.
Source: Cosmos: A Spacetime Odyssey. Directed by Brannon Braga. Hosted by Neil deGrasse Tyson. Fox/National Geographic, 2014.
Copyright by American Institute of Physics (left). And NASA, ESA, M.J. Jee and H. Ford (Johns Hopkins University) (right)
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Full disclosure, I may occasionally borrow a sentence from Will Durant's Story of Civilization. I absolutely love that collection!