and as a result provides a interesting lower limit on the Milky Way’s mass by a variant of the original Timing Argument. To reach its present position and radial velocity, Leo I must have passed pericentre at least once since the Big Bang and now be receding from the Galaxy for (at least) the second time.

Applying the point-mass radial orbit Equations (1) – (3) to this case gives a lower bound of about $1.6\times 10^{12}{\rm \,M_{\odot}}$. This seems likely to be a significant underestimate, since Leo I could not have passed through the centre of the Milky Way without being tidally destroyed so its orbit cannot be purely radial. Below we calibrate the Timing Argument for this case also, finding it to work well although with significantly more scatter than for the Local Group as a whole. This is because the $\Lambda$CDM paradigm predicts that the dynamics on the scale of Leo I’s orbit ($\sim 200{\rm \,kpc}$) is typically more complex than on the scale of the Local Group as a whole ($\sim 700{\rm \,kpc}$).

Our paper is organised as follows. In Section \[data\_section\], we briefly describe the Millennium Simulation and the selection criteria we use to define various 