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The Great Debate (or Shapley-Curtis Debate or Curtis-Shapley Debate) was an event held in 1920, with two astronomers, Heber Curtis and Harlow Shapley debating the size of the universe, in particular, the nature of galaxies (which were at the time not called galaxies but were considered a kind of nebula), whether they are distant objects made up of stars versus whether they were closer objects within or relatively near the known expanse of stars (i.e., at no great distance from the Milky Way). At the time, there were astronomers had adopted today's view that galaxies are distant objects analogous to the Milky Way, but the notion was relatively new and not universally accepted.
At the debate, a reported observation of visible rotation of the Pinwheel Galaxy seemed to constitute proof of the latter view because visible rotation of a distant, large object is untenable, implying velocities beyond the speed of light. Edwin Hubble's eventual collection and presentation of the observational evidence was key in settling the question (some time after the debate), observing that other measures of distances to galaxies, their maximally-bright stars, and using Cepheid variables, indicated a distance far greater than typical stars. He also found these galaxy distance-determinations showed a relation with their redshift, suggesting that the further away the galaxies are, the faster their radial velocity away from us, and their speeds preclude them remaining as close as was supposed.