  A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going
to an accelerated frame, which introduces a constant gravitational field into
the system and subsequently. We consider the addition of a linear contribution
to the gravitational potential \(\phi \) which can be used to cancel the
gravitational field induced by going to the accelerated from, the combination
of these two operations produces then a symmetry. This symmetry leads then to a
Noether current which is conserved. The conserved charges are analyzed in
special cases. The charges may not be conserved if the Noether current produces
flux at infinity, but such flux can be eliminated by going to the CM (center of
mass) system in the case of an isolated system. In the CM frame the Noether
charge vanishes, Then we study connection between the Cosmological Principle
and the Newtonian Dynamics which was formulated via a symmetry (Benisty and
Guendelman in Mod Phys Lett A 35:2050131, 2020) of this type, but without an
action formulation. Homogeneous behavior for the coordinate system relevant to
cosmology leads to a zero Noether current and the requirement of the Newtonian
potential to be invariant under the symmetry in this case yields the Friedmann
equations, which appear as a consistency condition for the symmetry.
