Short Answer
Modified Newtonian Dynamics? The case for dark matter in the Milky Way can be viewed as a failure of stars and gas far from the galactic center to obey Newton's law of gravitational attraction-- that is, the stars and gas seem to orbit too quickly for the visible matter their orbits enclose. Why do you think that astronomers choose to "save" Newton's form of gravitational attraction by postulating unseen dark matter, as opposed to regarding the observed orbital motion as a falsification of Newtonian gravitation on the scale of the Milky Way? [Note: At the distance scales involved, the gravitational forces in the galaxy are all fairly weak, much weaker than those encountered in a neutron star or black hole, and hence Einstein's theory of gravity (General Relativity)gives the same predictions as Newton's gravitational law].
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