The evidence for dark matter is only indirect. What the evidence points to directly is a mass discrepancy in galaxies and other galactic systems: When we count the mass of baryonic matter in such systems-in stars, neutral and high-T gas, etc.-the total sum does not provide enough gravity to explain the observed accelerations in such systems within standard physics. If we adhere to standard dynamics, the need for dark matter is the only solution we can conceive. It is, however, possible that the laws of dynamics, proven in the laboratory and the solar system, cannot be simply applied in the realm of the galaxies. An appropriate modification of the laws of dynamics for parameters that are pertinent to these, might obviate the need for dark matter altogether, if it produces the observed accelerations with only the observed baryonic mass distribution.
But, exactly which system attribute makes the difference? Galactic systems have masses, sizes, and angular momenta that are many orders of magnitude larger than those in the solar system. The large distances involved is a natural culprit. Indeed, there were attempts to modify the distance dependence of gravity: the gravitational force is still taken as proportional to the two masses involved but the decline at large distances is not as strong as in the r-2 law. Such a modification cannot, however, explain away dark matter. If the modified law is to produce asymptotically flat rotation curves of disc galaxies, as observed, it automatically predicts the wrong form of the mass velocity relation: it gives M V2, instead of M V, with ~ 4, as required by the observed Tully-Fisher relation ([Milgrom 1983]). In even more blatant conflict with observations, such modifications predict that the mass discrepancy should increase systematically with system size. In contrast, dwarf spheroidal galaxies, among the smallest in the galactic menagerie, show very large mass discrepancies, much larger then some large galaxies. And, the much larger galaxy clusters show only moderate mass discrepancies. A semi-schematic depiction of the systematics of the mass discrepancy with distance can be seen in Fig 1 in [Milgrom (1998)], where it is obvious that the observed mass discrepancy does not increase systematically with size.
In the early 1980s I proposed a modified-dynamics based on the acceleration as the relevant system parameter, based on the fact that typical accelerations in galactic systems are many orders of magnitude smaller than those encountered in the solar system. Since then, a handful of us have been working on the development of this scheme, which has involved devising more refined theories, elaborating the observational consequences, and testing them against the data.