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A Dynamical Model for the Orbit of the Andromeda Galaxy M31 and the Origin of the Local Group of Galaxies

We propose a new model for the origin and evolution of the Local Group of Galaxies (LGG) which naturally explains the formation of the Magellanic Clouds and their large orbital angular momenta around the Galaxy. The basic idea is that an off-center hydrodynamical collision occurred some 10 Gyr ago between the primordial gas-rich Andromeda galaxy and the similar Galaxy, and compressed the halo gas to form the LGG dwarf galaxies including the Magellanic Clouds. In this model, new-born dwarf galaxies can be expected to locate near the orbital plane of these two massive galaxies. In order to see the reality of this model, we reexamine the two-dimensional sky distribution of the LGG members and the Magellanic Stream, we confirm an earlier and widely-discussed idea that they align along two similar great circles, each with an angular width of $\sim 30^{\circ}$, and the planes of these circles are approximately normal to the line joining the present position of the sun and the Galactic center. Further we make a three-dimensional distribution map of these objects, and observe it from various directions. A well-defined plane of finite thickness is found, within which most of the member galaxies are confined, supporting the existence of the above circles on the sky. Thus we could determine the orbital elements of M31 relative to the Galaxy through reproducing the well-studied dynamics of the LMC and the SMC around the Galaxy. The expected proper motion of M31 is $(μ_l, μ_b)=(38 μas/yr, -49 μas/yr)$. Probable orbital motions of the other dwarfs are also determined, and the corresponding proper motion for each object is given to compare with observations in near future.