Inspection of the orbital parameters. Top: time to the next or since the last pericentric passage, t_peri, as a function of the satellites’ orbital period, P, both in units of Gyr; the red solid line at t_peri = 0 indicate when satellites are at pericentre, the thin dashed lines indicate the apocentre limits, while the dotted lines mark the half-orbit; the thick dashed line, shown for illustrative purposes, is parallel to the upper apocentre line, shifted by ∼1 Gyr. Bottom: satellite orbital phases, ϕ, as a function of the orbital eccentricity; thin dotted lines represent the limits when a satellite has just left its pericentre (ϕ close to 0), or is approaching it (ϕ close to −1). Panels on the left show values obtained with the low-mass MW potential, while those on the right with the high-mass MW potential. In all panels, symbols and colours are as described in Fig. 3.