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

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.