Aristotelian physics laws of physics". The Persian polymath Abū Rayhān al-Bīrūnī (973-1048) was the first to realize that acceleration is connected with non-uniform motion (as later expressed by Newton's second law of motion). During his debate with Avicenna, al-Biruni also criticized the Aristotelian theory of gravity firstly for denying the existence of levity or gravity in the celestial spheres; and, secondly, for its notion of circular motion being an innate property of the heavenly bodies. In 1121, al-Khazini, in "The Book of the Balance of Wisdom", proposed that the gravity and gravitational potential energy of a body varies depending on its distance
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