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We investigate the success and problems of MOdified Newtonian Dynamics (MOND)in explaining the structural parameters and dynamics of remote Galacticglobular clusters (GCs) and dwarf spheroidal (dSph) galaxies. Using the MONDvalue for the mass of the Milky Way as inferred from the Galactic rotationcurve, we derive the tidal radii of Galactic GCs, and compare to observedvalues. Except for Pal 14, the predicted tidal radii of GCs are systematicallylarger than the observed nominal values. However, the associated uncertaintiesare so large that tidal radii are consistent on the $1\sigma$ level. We haveconsidered the importance of the Galactic tidal force on the survival of dSphsunder MOND. Assuming mass-to-light ratios compatible with a naked stellarpopulation, we found that the present Galactic dSphs preserve their integrityover one Hubble time, except Sextans which may survive the tidal interactiononly for several Gyr. Mass-to-light ratios as inferred from the internalkinematics of dSph galaxies can be used, but they appear too large to beaccounted for only by the stellar population in Willman 1, Coma Berenice, UrsaMinor, Draco, Ursa Major and possibly Bo\"{o}tes dwarves. Finally, the abilityof the Sculptor dwarf to retain the observed population of low-mass X-raybinaries (LMXBs) is examined. Under the MOND paradigm, we find that theretention fraction in Sculptor is likely not larger than a few percent.Compared to the dark matter scenario, it turns out that MOND makes theretention problem worse. We propose that measurements of the radial velocitiesof the observed LMXBs in Sculptor could provide a way to distinguish betweenmodified gravities or extended and massive dark matter halos.Comment: 14 pages, including 3 figures and 1 table. Revised version accepted  for publication at ApJ, clarified presentation, and dSph list updated to a  month ag

Masses, Tidal Radii, and Escape Speeds in Dwarf Spheroidal Galaxies under MOND and Dark Halos Compared