Addressing the missing matter problem in galaxies through a new
  fundamental gravitational radius
  We demonstrate that the existence of a Noether symmetry in $f(R)$ theories of
gravity gives rise to a further gravitational radius, besides the standard
Schwarzschild one, determining the dynamics at galactic scales. By this
feature, it is possible to explain the baryonic Tully-Fisher relation and the
rotation curve of gas-rich galaxies without the dark matter hypothesis.
