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 ( \mu _ { l } , \mu _ { b } ) = ( 38 \mu { as~ { } yr } ^ { -1 } , -49 \mu { as~ { } yr } ^ { -1 } ) .
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 .