A simple derivation of Kepler's laws without solving differential equations - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue European Journal of Physics Année : 2009

A simple derivation of Kepler's laws without solving differential equations

Résumé

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest.

Dates et versions

hal-03786095 , version 1 (23-09-2022)

Identifiants

Citer

Jean-Pierre Provost, Christian Bracco. A simple derivation of Kepler's laws without solving differential equations. European Journal of Physics, 2009, 30, pp.581-586. ⟨10.1088/0143-0807/30/3/014⟩. ⟨hal-03786095⟩
4 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More