  The Local Group timing has been one of the first historical probes of the
missing mass problem. Whilst modern cosmological probes indicate that pure
baryonic dynamics is not sufficient on the largest scales, nearby galaxies and
small galaxy groups persistently obey Milgrom's MOND law, which implies that
dynamics 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 for
Andromeda and the Magellanic clouds, we integrate backwards their orbits by
making use of the Milgromian two-body equation of motion. We find that, with
the currently measured proper motions and radial velocity of M31, MOND would
imply that the Milky Way and M31 first moved apart via Hubble expansion after
birth, but then necessarily got attracted again by the Milgromian gravitational
attraction, and had a past fly-by encounter before coming to their present
positions. 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 dynamical
friction is necessary for such a close encounter not to trigger a merger.
Observational arguments which could exclude or favour such a past encounter
would thus be very important in view of falsifying or vindicating Milgromian
dynamics on the scale of the Local Group. Interestingly, the closest approach
of the encounter is small enough (<55 kpc) to have severe consequences on the
disk dynamics, including perhaps thick disk formation, and on the satellite
systems of both galaxies. The ages of the satellite galaxies and of the young
halo globular clusters, all of which form the vast polar structure around the
Milky Way, are consistent with these objects having been born in this
encounter.
