Keplerian orbits and spherical electrostatic spectrometer

The properties of Keplerian orbits in an inverse-square field are discussed in terms of the initial or launching conditions. A simple, new graphical method of constructing any elliptical orbit is presented in terms of the initial conditions. Graphs are presented showing energy relations, eccentricity, size, ratio of maximum and minimum radii, ratio of final to initial radii for 1800 traverse and ratio of extremum radii to launching radius, all in terms of the launching conditions. The effect of the potential step at the entrance to a 1800 spherical spectrometer is given, as well as exact and approximate equations for the final radius in terms of launching conditions. The effect of the fringing field is discussed with comparison of the results of Herzog and of Chase. (Auth.)