Orbits of the n-dimensional Kepler-Coulomb problem and universality of the Kepler laws


Onder M. , VERÇİN A.

EUROPEAN JOURNAL OF PHYSICS, vol.27, no.1, pp.49-55, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1088/0143-0807/27/1/005
  • Title of Journal : EUROPEAN JOURNAL OF PHYSICS
  • Page Numbers: pp.49-55

Abstract

In the standard classical mechanics textbooks used at undergraduate and graduate levels, no attention is paid to the dimensional aspects of the Kepler-Coulomb problem. We have shown that the orbits of the n-dimensional classical Kepler-Coulomb problem are the usual conic sections in a fixed two-dimensional subspace and the Kepler laws with their well-known forms are valid independent of dimension. The basic characteristics of motion in a central force field are also established in an arbitrary dimension. The approach followed is easily accessible to late undergraduate and recent graduate students.