Newtonian approach for the Kepler-Coulomb problem from the point of view of velocity space

Details Newtonian approach for the Kepler-Coulomb problem from the point of view of velocity space Newtonian approach for the Kepler-Coulomb problem from the point of view of velocity space

1998-09-19

arxiv.org/abs/physics/9809028v2

Physics

Classical Physics

14 pages and 6 eps figures, in a single zipped file. Submitted to Rev. Mex. Fis

Scientific paper

The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem starting from initial conditions given using nothing more than the methods of synthetic geometry so close to Newton's approach. The method works with elliptic, parabolic and hyperbolic orbits; it can even be used to derive Rutherford's relation from which the scattering cross section can be easily evaluated. We think our discussion is both interesting and useful inasmuch as it serves to relate the initial conditions with the corresponding trajectories in a purely geometrical way uncovering in the process some seldom discussed interesting connections.

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