Dwarf spheroidal galaxies and non-Newtonian gravity

We derive a virial theorem and an analog for King's formula in modified Newtonian dynamics (MOND; Milgrom 1983) and use these to estimate the mass-to-light ratios (M/Ls) in MOND of the dwarf spheroidal galaxies in the Local Group. We find that the low-velocity dispersion observed in the Fornax dwarf galaxy implies low values for its M/L in MOND: 0.3-1. In particular the derived value in the core of Fornax (0.3) is much lower than expected for a normal old stellar population. Conversely, the velocity-dispersion measurements in Draco and Ursa Minor appear to still require dark matter in MOND. We show that M/L must vary between the dwarf spheroidals around the Galaxy by a factor of order at least 20, even in MOND.