Planar distribution of the galaxies in the Local Group: a statistical   and dynamical analysis
  Adopting known data on positions and distances, we make use of the analytical geometry and look for the plane that minimizes the distances of all galaxies to it. A planar distribution is indeed found that, however, does not coincide with the plane found by Sawa & Fujimoto 2005. Why? The second part of this study is devoted to answer this question and to find a dynamical justification for the planar distribution. To this aim, we apply the Hamilton Method (Minimum Action) to investigate the dynamics of the two major system of the Local Group, Milky Way and Andromeda, under the action of external forces exerted by nearby galaxies or groups external to the Local Group. We find that the planar istribution is fully compatible with the minimum action and that the external force field is likely parallel to the plane. It pulls the galaxies of the Local Group without altering their planar distribution. Special care is paid to evaluate the robustness of this result. Conclusion: in this paper we have examined the spatial distribution of galaxies in the Local Group. They are confined to a plane that can be statistically and dynamically understood as the result of the Minimum Action. The planar distribution seems to be stable for a large fraction of the Hubble time. The external force field, that has likely been constant over the same time interval, does not alter the planar distribution as it is nearly parallel to it. Effects due to undetected halos of sole Dark Matter are briefly discussed. They could be a point of uncertainty of the present study. 
Stefano Pasetto & Cesare Chiosi