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.

分析了牛顿动力学的新对称性，这对应于进入加速坐标系，该坐标系将恒定的引力场引入系统并随后引入。我们考虑对引力势\(\phi \)的线性贡献它可以用来抵消由加速产生的引力场，这两个操作的结合产生了对称性。这种对称性导致了守恒的诺特电流。在特殊情况下分析守恒电荷。如果 Noether 电流产生无穷远的通量，则电荷可能不守恒，但在孤立系统的情况下，可以通过进入 CM（质心）系统来消除这种通量。在 CM 坐标系中，Noether 电荷消失，然后我们研究了宇宙学原理和牛顿动力学之间的联系，它是通过这种对称性（Benisty 和 Guendelman in Mod Phys Lett A 35:2050131, 2020）制定的，但没有行动公式。