The Local Group as a test system for Modified Newtonian Dynamics
  The Local Group (LG) is {an appropriate} test system for Modified Newtonian
Dynamics, since the acceleration of M31 galaxy is fully in the deep MOND regime
$a \ll a_0$. We model the LG as a two body problem of $M31$ and the Milky Way
(MW) galaxies. {Extending previous studies, we also include the Cosmological
Constant.} The assumption that in the big bang the galaxies emerged from the
same place and approach to the measured distance and velocity today (the Timing
Argument), predicts the total mass for the LG: $(0.447 \pm 0.005)\cdot 10^{12}
M_{\odot}$. The corresponding motion of the LG predicts a past encounter. The
ratio between the baryonic mass that MOND considers to the mass that Newtonian
case predicted, which includes dark matter is $10.74 \pm 0.82$. This ratio
agrees with the ratio between the dark matter and baryonic matter in other
galaxies.
