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The Local Group timing has been one of the first historical probes of themissing mass problem. Whilst modern cosmological probes indicate that purebaryonic dynamics is not sufficient on the largest scales, nearby galaxies andsmall galaxy groups persistently obey Milgrom's MOND law, which implies thatdynamics at small scales is possibly entirely predicted by the baryons. Here,we investigate the Local Group timing in this context of Milgromian dynamics.Making use of the latest measured proper motions and radial velocities forAndromeda and the Magellanic clouds, we integrate backwards their orbits bymaking use of the Milgromian two-body equation of motion. We find that, withthe currently measured proper motions and radial velocity of M31, MOND wouldimply that the Milky Way and M31 first moved apart via Hubble expansion afterbirth, but then necessarily got attracted again by the Milgromian gravitationalattraction, and had a past fly-by encounter before coming to their presentpositions. This encounter would most probably have happened 7 to 11 Gyr ago(0.8<z<3). The absence of a dark matter halo and its associated dynamicalfriction is necessary for such a close encounter not to trigger a merger.Observational arguments which could exclude or favour such a past encounterwould thus be very important in view of falsifying or vindicating Milgromiandynamics on the scale of the Local Group. Interestingly, the closest approachof the encounter is small enough (<55 kpc) to have severe consequences on thedisk dynamics, including perhaps thick disk formation, and on the satellitesystems of both galaxies. The ages of the satellite galaxies and of the younghalo globular clusters, all of which form the vast polar structure around theMilky Way, are consistent with these objects having been born in thisencounter.

Local Group timing in Milgromian dynamics. A past Milky Way-Andromeda encounter at z>0.8