Mordehai Milgrom (see Scientific American Aug. 2002) postulates a modification to Newtonian dynamics which reveals itself when accelerations are smaller than a given value that is proposed as a new constant of nature.
This modification is claimed to explain most features of galactic dynamics without recourse to dark matter, including the Tully-Fisher correlation between galaxy brightness and the orbital speeds of stars in the outskirts of spiral galaxies.
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