  The motion of satellite galaxies around normal galaxies at distances 50-500
kpc provides a sensitive test for the theories. We study the surface density
and the velocities of satellites around isolated galaxies in the Sloan Digital
Sky Survey. We find that the surface number-density of satellites declines with
the projected distance as a power law with the slope -1.5-2. The rms velocities
gradually decline: observations exclude constant velocities at a 10 sigma
level. We show that observational data strongly favor the standard model: all
three major statistics of satellites - the number-density profile, the
line-of-sight velocity dispersion, and the distribution function of the
velocities -- agree remarkably well with the predictions of the standard
cosmological model. Thus, that the success of the standard model extends to
scales (50-500) kpc, much lower than what was previously considered. MOND fails
on these scales for models which assume any single power-law number-density
profile of satellites and any constant velocity anisotropy by predicting nearly
constant rms velocities of satellites. Satellite data can be fit by fine-tuned
models, which require (1) specific non-power-law density profile, (2) very
radial orbits at large distances (velocity anisotropy beta =0.6-0.7 at 200-300
kpc), and (3) 2-2.5 times more stellar mass than what is found in the galaxies.
The external gravity force - a necessary component for MOND -- makes the
situation even worse. We argue that a combination of satellite data and
observational constraints on stellar masses make these models very problematic.
