range. We then search for Leo I analogues around these hosts by identifying companions in the separation range 200 to 300 kpc with $V_{max}({\rm comp}) \leq 80{{\rm \,km\,s^{-1}}}$, $M_{B} < -16.7$ and $V_{ra} \ge 0.7 V_{max}({\rm host})$ where $V_{ra}$ is the relative radial velocity of the two objects and the last condition reflects the fact that Leo I is useful for estimating the Milky Way’s mass only because its recession velocity is comparable to the Galactic rotation velocity ($V_{ra} \sim 0.8 V_{max}({\rm host})$ for the real Leo I–Milky Way system). Pairs sharing the same MW-like host are excluded in the final list.

With these cuts we find $344$ and $896$ satellite-host pairs in the samples with and without the morphology cut for the looser $V_{max}$ range, and $168$ and $374$ for the tighter range. These relatively small numbers reflect the fact that only about 10% of potential hosts actually have a faint companion in this distance range which is still bright enough to be resolved, and fewer than 5% of these satellites are predicted to have positive recession velocities comparable to that observed.

Results {#result_section}
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Calibration of the Timing Argument mass for the Local Group
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For each simulated 