The extra symmetry of the Kepler problem corresponding to the conservation of the Runge–Lenz vector can be visualized by studying how entire Kepler ellipses evolve under symmetry transformations. After discussing the general case, we show that the evolution generated by a component of the Runge–Lenz vector in the plane of the orbit yields the same family of ellipses in the plane as the projection onto the plane of a rotation of a certain circle in three dimensions.
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© 2005 American Association of Physics Teachers.
2005
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