  Prompted by the recent successful predictions of the internal dynamics of
Andromeda's satellite galaxies (McGaugh & Milgrom 2013a,b), we revisit the
classical Milky Way dwarf spheroidal satellites Draco, Sculptor, Sextans,
Carina, and Fornax in the framework of Milgromian dynamics (MOND). We use for
the first time a Poisson solver with adaptive mesh refinement (AMR) in order to
account simultaneously for the gravitational influence of the Milky Way and its
satellites. This allows to rigorously model the important external field effect
(EFE) of Milgromian dynamics, which can reduce the effective acceleration
significantly. We make predictions on the dynamical mass-to-light ratio
(Mdyn/L) expected to be measured by an observer who assumes Newtonian dynamics
to be valid. We show that Milgromian dynamics predicts typical Mdyn/L ~ 10-50
Msun/Lsun. The results for the most luminous ones, Fornax and Sculptor, agree
well with available velocity dispersion data. Moreover, the central power-law
slopes of the dynamical masses agree exceedingly well with values inferred
observationally from velocity dispersion measurements. The results for Sextans,
Carina and Draco are low compared to usually quoted observational estimates, as
already pointed out by Angus (2008). For Milgromian dynamics to survive further
observational tests in these objects, one would thus need that either (a)
previous observational findings based on velocity dispersion measurements have
overestimated the dynamical mass due to, e.g., binaries and contaminant
outliers, (b) the satellites are not in virial equilibrium due to the Milky Way
tidal field, or (c) the specific theory used here does not describe the EFE
correctly (e.g., the EFE could be practically negligible in some other
theories), or a combination of (a)-(c).
