Translates of S-arithmetic periodic orbits and applications

We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new information regarding the sequence of best approximations to certain vectors with algebraic coordinates. In order to prove these results we generalize the seminal work of Eskin, Mozes and Shah about the equidistribution of translates of periodic measures from the real case to the S-arithmetic case.