Distribution of pericentre distances D_p and times t_p for M33 orbits along which M33 had a close passage around M31. These are shown for today’s distances to M31 and M33 equal to their mean value in the bottom panel while in the top panel distance dispersions around the mean are considered. Regions in the D_p − t_p plane are colour coded according to the number of orbital solutions with a close pericentre passage in the past. A total of 100 000 possible orbits have been examined.