Left panel: relative distance and velocity for the galaxies for which at least one of the 100 orbit realisations in the perturbed potential pass close to the LMC (< 60 kpc). The black line represents the escape velocity of the initial a 1.5 × 10¹¹ M_⊙ LMC represented by a NFW profile with a scale radius r_s = 10.84 kpc, while the dashed line shows the escape velocity of the current LMC. Each coloured line shows the evolution of the relative distance and velocity of the galaxies with each point marking 100 Myr of evolution. For the galaxies that are not currently at their closest approach, the triangles show their current position on this diagram. The vertical lines at the bottom of the panel show the location of the Jacobi radius at different epochs. Right panel: same as the left panel but assuming that the LMC follows the orbit of a point mass, and does not modify the MW potential. The black lines represent the escape velocity for a LMC with a mass of respectively 1, 5, 10, 15 and 20 × 10¹⁰ M_⊙ and a scale radius that respect the observational constraint following the requirement of Vasiliev et al. (2021).