The Kepler orbit from initial conditions via the Lenz vector

We have studied the family of orbits encountered when particles are emitted in all directions from a point source, in the presence of a Coulomb potential whose centre is displaced with respect to the source. This is a simple system in which all the calculations can be done analytically. We found that, depending on the sign of the potential, the effective cross section exhibits glory or rainbow divergences. We provide an approach for studying these effects which is suited for a course on classical mechanics.

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The Kepler orbit from initial conditions via the Lenz vector

Abstract: The orientation and parameters of the orbit of a satellite under an inverse square law of force are obtained by use of the eccentricity vector, equivalent to the Lenz vector, from a typical set of initial conditions.

Cited by 2 publications

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Comments on the dynamical invariants of the Kepler and harmonic motions

Comments on the dynamical invariants of the Kepler and harmonic motions

Rainbow and glory scattering in Coulomb trajectories starting from a point in space

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