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The observed dynamics of gas and stars on galactic and larger scales cannotbe accounted for by self-gravity, indicating that there are large quantities ofunseen matter, or that gravity is non-Newtonian in these regimes. Milgrom'sMOdified Newtonian Dynamics (MOND) postulates that Newton's laws are modifiedat very low acceleration, and can account for the rotation curves of galaxiesand some other astrophysical observations, without dark matter. Here we applyMOND to two independent physical systems: Ly-alpha absorbers and galaxyclusters. While physically distinct, both are simple hydrodynamical systemswith characteristic accelerations in the MOND regime. We find that Ly-alphaabsorbers are somewhat smaller than in Newtonian gravity with dark matter, butthe result depends crucially on the (unknown) background acceleration field inwhich they are embedded. In clusters MOND appears to explain the observed(baryonic) mass-temperature relation. However, given observed gas density andenclosed mass profiles and the assumption of hydrostatic equilibrium, MONDpredicts radial temperature profiles which disagree badly with observations. Weshow this explicitly for the Virgo, Abell 2199 and Coma clusters, but theresults are general, and seem very difficult to avoid. If this discrepancy isto be resolved by positing additional (presumably baryonic) dark matter, thenthis dark matter must have ~1-3 times the cluster gas mass within 1 Mpc. Thisresult strongly disfavors MOND as an alternative to dark matter (Abridged).Comment: Revised version. Important caveat in Ly-alpha calculation discussed;  conclusions weakened. Coma cluster and calculation of dark matter mass  required by MOND added; cluster conclusions strengthened. 11 EmulateApJ pages  with 3 embedded figures. Accepted by Ap

Problems for Modified Newtonian Dynamics in Clusters and the Lyα Forest?