Paradox of radiation of charged particles in a gravitational field continuously "upward". Whether the acceleration is from motion or from gravity makes no difference in the laws of physics. One can also understand it in terms of the equivalence of so-called gravitational mass and inertial mass. The mass in Newton's law of universal gravitation (gravitational mass) is the same as the mass in Newton's second law of motion (inertial mass). They cancel out when equated, with the result discovered by Galileo Galilei in 1638, that all bodies fall at the same rate in a gravitational field, independent of their mass. A famous demonstration of this principle was performed on the
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