The harmony in the Kepler and related problems
  The technique of reduction of order developed by Nucci ({\it J Math Phys} {\bf 37} (1996) 1772-1775) is used to produce nonlocal symmetries additional to those reported by Krause ({\it J Math Phys} {\bf 35} (1994) 5734-5748) in his study of the complete symmetry group of the Kepler Problem. The technique is shown to be applicable to related problems containing a drag term which have been used to model the motion of low altitude satellites in the Earth's atmosphere and further generalisations. A consequence of the application of this technique is the demonstration of the group theoretical relationship between the simple harmonic oscillator and the Kepler and related problems. 
M.C. Nucci and P.G.L. Leach