Non-normability of spaces of Keplerian orbits
  We prove that spaces of Keplerian curvilinear orbits, all orbits and elliptic orbits with marked pericenter cannot carry a norm, compatible with their standard topology. We also prove that the space of Keplerian elliptic orbits without marked pericenter cannot carry a norm, compatible with the natural metrics on it. 
Dmitry Todorov
math.MG astro-ph.EP