The Local Group (LG) offers us a chance to test the present scenario of galaxy formation in ways that are impossible elsewhere. It contains about 50 know galaxies, most of which are dwarfs so faint that they would not be detected beyond the LG. Hence, ourunderstanding of low-mass galaxy formation physics, strongly tied to models of galaxy feedback and ram pressure interactions, is almostentirely set by the LG environment.The present standard cosmological scenario (Λ-CDM) gives the dwarf galaxies a key role in the galaxy formation mechanism, since large galaxies would be the result of the merging and disruption of sub-galactic halos. In this context, the dwarfs nowadays observable in the LG can be considered the debris of the large galaxy formation process and retain the traces of their evolutionary history and interactions. They are also excellent test particles for studying the global dynamics of the LG and, in particular, to determine its total mass. However, accurate 3D information of their individual star velocities is ecessary to face these problems.

Our project has two main general objectives in the context of the study of the LG dwarf galaxies:

(1) to study their orbital histories

(2) to study their internal kinematics. Two galaxy samples have been selected: sample A (Cetus, Tucana, Leo A and Sag DIG) and sample B (Bootes I, Carina, Draco, Fornax, Sculptor, Sextans and Ursa Minor). They are respectively best suited for each of the two objectives. More in detail, on the one side the orbital histories derived in objective (1) will drive to determine the total mass of the Local Group with a higher degree of accuracy than former estimates and will allow the study of the connection between orbital and star formation histories of the analyzed dwarf galaxies.

On the other side, the internal kinematics studied in objective (2) will be connected with the star formation histories and the stellar metallicities to search for traces of tidal interactions and kinematical evolution. Both objectives will provide information on the properties of a small galaxy group, such as the LG, and are related with the following topics of major general interest: the evolution of the LG, with a fundamental hint to the evolution of small galaxy groups in general; the quenching of the star formation in dwarf galaxies and its environment dependency, and the missing satellite problem. Observationally, our project is aimed to the exploitation of front-line data from the HST and Gaia to measure proper motions of individual stars in the two samples of dwarfs. Proper motions are necessary in order to derive 3D velocities that will drive to the orbital determination.