Abstract
By reconsidering anew our unitary S-description of the family of Kepler conic sections, we show how the plane sum vector S unravels at the core the existence of a constant vector N, which not only discloses in a natural way the cone structure in R3 which defines the Kepler conic sections, but also enlightens the peculiar genesis of the map devised by Levi-Civita for the regularization of the Kepler problem at collision.
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