  (abridged) The Milky Way (MW) and Andromeda (M31) galaxies possess rotating
planes of satellites. Their formation has not been explained satisfactorily
yet. It was suggested that the MW and M31 satellites are ancient tidal dwarf
galaxies, which could explain their configuration. This suggestion gained
support by an analytic backward calculation of the relative MW-M31 orbit in the
MOND modified dynamics paradigm by Zhao et al. (2013) implying their close
flyby 7-11 Gyr ago. Here we explore the Local Group history in MOND in more
detail using a simplified first-ever self-consistent simulation. We note the
features induced by the encounter in the simulation and identify their possible
real counterparts. The simulation was set to approximately reproduce the
observed MW and M31 masses, effective radii, separation, relative velocity and
disk inclinations. We used the publicly available adaptive-mesh-refinement code
Phantom of RAMSES. In the simulation, matter was transferred from the MW to M31
along a tidal tail. The encounter induced formation of several structures
resembling the peculiarities of the Local Group. Most notably: 1) A rotating
planar structure formed around M31 from the transferred material. It had a size
similar to the observed satellite plane and was oriented edge-on to the
simulated MW, just as the real one. 2) The same structure also resembled the
tidal features observed around M31 by its size and morphology. 3) A warp in the
MW developed with an amplitude and orientation similar to that observed. 4) A
cloud of particles formed around the simulated MW, with the extent of the
actual MW satellite system. The encounter did not end by merging in a Hubble
time. The simulation thus demonstrated that MOND can possibly explain many
peculiarities of the Local Group and, moreover, that non-merging galaxy
encounters in MOND can produce tidal features in galaxies.
