Constraining dark matter sub-structure with the dynamics of
  astrophysical systems
  The accuracy of the measurements of some astrophysical dynamical systems
allows to constrain the existence of incredibly small gravitational
perturbations. In particular, the internal Solar System dynamics (planets,
Earth-Moon) opens up the possibility, for the first time, to prove the
abundance, mass and size, of dark sub-structures at the Earth vicinity. We find
that adopting the standard dark matter density, its local distribution can be
composed by sub-solar mass halos with no currently measurable dynamical
consequences, regardless of the mini-halo fraction. On the other hand, it is
possible to exclude the presence of dark streams with linear mass densities
higher than $\lambda_{\rm st}> 10^{-10} \Msun/\AU$ (about the Earth mass spread
along the diameter of the SS up to the Kuiper belt). In addition, we review the
dynamics of wide binaries inside the dwarf spheroidal galaxies in the MW. The
dynamics of such kind of binaries seem to be compatible with the presence of a
huge fraction of dark sub-structure, thus their existence is not a sharp
discriminant of the dark matter hypothesis as been claimed before. However,
there are regimes where the constraints from different astrophysical systems
may reveal the sub-structure mass function cut-off scale.
