  We use the recently proposed scale-free mass estimators to determine the
masses of the Milky Way (MW) and Andromeda (M31) galaxy in a dark matter only
Constrained Local UniversE Simulation (CLUES). While these mass estimators work
rather well for isolated spherical host systems, we examine here their
applicability to a simulated binary system with a unique satellite population
similar to the observed satellites of MW and M31. We confirm that the
scale-free estimators work also very well in our simulated Local Group galaxies
with the right number of satellites which follow the observed radial
distribution. In the isotropic case and under the assumption that the
satellites are tracking the total gravitating mass, the power-law index of the
radial satellite distribution $N(<r)\propto r^{3-\gamma}$ is directly related
to the host's mass profile $M(<r)\propto r^{1-\alpha}$ as $\alpha=\gamma-2$.
The use of this relation for any given $\gamma$ leads to highly accurate mass
estimations which is a crucial point for observer, since they do not know a
priori the mass profile of the MW and M31 haloes. We discuss possible bias in
the mass estimators and conclude that the scale-free mass estimators can be
satisfactorily applied to the real MW and M31 system.
