  It was discovered by Gordon in 1977 that Keplerian ellipses in the plane are
minimizers of the Lagrangian action and spectrally stable as periodic points of
the associated Hamiltonian flow. The aim of this paper is to give a homotopy
theoretical proof of these results through a self-contained, explicit and
simple computation of the Conley-Zehnder index.
  The techniques developed in this paper can be used to investigate the higher
dimensional case of Keplerian ellipses, where the classical variational proof
no longer applies.
