Distance between the centre of mass of G_LMC and that of G_SMC. The solid (dashed) lines corresponds to the G_LMC + G_SMC + G_MW (G_LMC + G_SMC) models. The different panels each represent a different set of simulations (see labels within each panel). The vertical purple solid (dashed) lines correspond to the G_LMC − G_SMC pericentres of the G_LMC + G_SMC + G_MW (G_LMC + G_SMC) models. The vertical grey dashed line corresponds to the time we choose as the present time t = 0 (see Sect. 2.2). For the sake of comparison, in shadowed blue lines we plot the orbital history of the MCs for the models of the fiducial set. The set corresponding to a different G_LMC disc mass and Toomre parameter is not shown since it shows no difference in comparison to the fiducial set.