File:Kepler hodograph family transformed.png

English: Family of transformed circular hodographs sharing the same total energy E for the Kepler problem of determining the motion of two particles interacting by force that varies as the inverse-square of the distance between them. In the sense taken here, hodographs are plots of the path of the momentum vector over the orbit; the coordinate system is chosen so that the orbit lies in the x-y plane. These hodographs are normally circular, but they have been transformed by circular inversion into a family of straight lines passing through a common point. The original axes have been kept to help illustrate the transformation. For more details, please see Image:Kepler_hodograph_family.png. This figure was made by me on 22 November 2006 using Xfig and is hereby released under the GFDL.