Noether-Li Symmetry and the Motion Constant of Kepler System

The study of symmetry and motion constant of dynamic systems is a very important concept in the field of natural science. The concept of symmetry is applied to general mechanics, and the research objects are mainly mechanical quantities and mechanical laws. It is also a development direction of analytical mechanics. In this paper, we first wrote the differential equations of motion of the Kepler system, some Noether-Li symmetry theorems and determinant equations for Kepler system were given and briefly proved. Then the theorem asserting that the Noethe-Li symmetry for the system leads to both the Noether motion constant and the Hojman motion constant were presented. Finally, the application of the results of this paper was illustrated by taking the plane kapler system as an example.