Kepler's laws of planetary motion planets. However, Newton states in his Principia that he considers forces from a mathematical point of view, not a physical, thereby taking an instrumentalist view. Moreover, he does not assign a cause to gravity. Newton defined the force acting on a planet to be the product of its mass and the acceleration (see Newton's laws of motion). So: The Sun plays an unsymmetrical part, which is unjustified. So he assumed, in Newton's law of universal gravitation: As the planets have small masses compared to that of the Sun, the orbits conform approximately to Kepler's laws. Newton's model improves upon Kepler's
Kepler's laws of planetary motion that the second law is not special to the inverse square law of gravitation, being a consequence just of the radial nature of that law; while the other laws do depend on the inverse square form of the attraction. Carl Runge and Wilhelm Lenz much later identified a symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law. The mathematical model of the kinematics of a planet subject to