kepler.htm) KEPLER’S EQUATIONS a kinematical deduction

Abstract: Kepler’s equations are considered as central to Celestial Mechanics since their solutions permit ’to find the position of a body for a given time’. To obtain a kinematical deduction of them, only one new concept is introduced with the name of ”maccel”. By assuming the simultaneous conservation of the maccel and of the angular momentum, it is shown that the position vector always describes a conic section. Then, the proof includes the three main types of Kepler’s equations for elliptical, parabolic, and hyperbolic trajectories. The theoretical innovations here introduced concern mathematicians, physicists, astronomers, astronauts, cosmologists, historians, philosophers, and everyone minimally interested in the development and improvement of Science. Keywords: Lagrange’s identity, inertia, maccel, angular momentum, conic sections. 2000 Mathematics Subject Classification: 53A17, 70B05, 70F15, 70M20. Acknowledgments: To Dr. Thomas E. Phipps Jr. for his stimulant correspondence, to the editors of Who’s Who in the World for their encouraging recognition, to the staff of The Mathematics Preprint Server for their web support. Dedication: To Eng. Hideki Ishitani, an author’s schoolmate at Escola Politécnica o