Theorem of the keplerian kinematics viXra（开普勒运动学viXra的定理）.pdf

1 Theorem of the keplerian kinematics Hervé Le Cornec, France, herve.le.cornec@free.fr Abstract : Any mobile having a velocity which is the addition of a rotation velocity and a translation velocity, both with a constant modulus, will follow a trajectory that respects the three laws of Kepler. This article demonstrate this theorem and discuss it. An important result is to forecast the mathematical structure of the Newtons acceleration of attraction, not any more as a prior, but as a consequence, the subsequent centripetal acceleration due to the rotation velocity. 1 Introduction Since the work of Kepler we know that, at a first approximation, the trajectories of all celestial satellites are following three peculiar laws[1]. These laws are kinematic ones, they do not refer to any physical consideration, as the mass for instance. We can then expect to forecast them only from the kinematics. This is what we are going to achieve here by the mean of a kinematic theorem that applies to all keplerian mobiles. We will not postulate any physical reason to explain the existence of this theorem in the real world, but just demonstrate its validity from a mathematical point of view. We will see however that this theorem forecasts the Newtons attraction law as a consequence, but not any more as a mandatory foundation of the keplerian motion. 2 Theorem of the keplerian kinematics 2.1 Statement Let us state the following theorem : Theorem 1 : Any mobile having a velocity which is the addition of a rotation velocity and a translation velocity, both with a constant modulus, will follow a trajectory that respect the three laws of Kepler. At a mathematical point of view the velocity described by this theorem is written as follows :