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 red 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 \sim 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 R = 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 .