samples of ‘Local Group-like’ pairs and of ‘Milky Way-like’ halos. In Section \[result\_section\], we plot the ratio of true total mass to Timing Argument mass estimate for these samples, and we use its distribution to define an unbiased TA estimator of true mass with its associated confidence ranges. In Section \[app\_LG\_section\] this is then applied to the Local Group in order to obtain an estimate its true mass with realistic uncertainties. Section \[app\_MW\_section\] attempts to carry out a similar calibration for the TA-based estimate of the Galaxy’s halo mass from the orbit of Leo I. We conclude in Section \[conclusions\] with a summary and brief discussion of our results.

The Millennium Simulation {#data_section}
=========================

The *Millennium Simulation* is an extremely large cosmological simulation carried out by the Virgo Consortium [@mr_nature]. It followed the motion of $N=2160^{3}$ dark matter particles of mass $8.6 \times 10^{8}
~h^{-1}{\rm \,M_{\odot}}$ within a cubic box of comoving size $500~h^{-1}{\rm \,Mpc}$. Its comoving spatial resolution (set by the gravitational softening) is 5 $h^{-1}{\rm \,kpc}$. The simulation adopted the concordance $\Lambda$CDM model with parameters $\Omega_{m}=0.25, \Omega_{b}=0.045, h=0.73, \Omega_{\Lambda}=0.75,
n=1$ and $\sigma_{8}=0.9$, where, as usual, we define the Hubble constant by $H_{0}=100h{{\rm \,km\,s^{-1}}}{\rm \,Mpc}^{-1}$. The current age of 