From Wikipedia, the free encyclopedia
[edit] Summary
Family of 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. Such a family is geometrically equivalent to a family of Apollonian circles or the σ isosurfaces of bipolar coordinates. The dotted circle is not a hodograph; rather, inversion in the dotted circle transforms the Keplerian hodographs into a family of straight lines passing through a common point (see Image:Kepler_hodograph_family_trasformed.png). This figure was made by me on 22 November 2006 using Xfig and is hereby released under the GFDL.
[edit] Licensing
|
I, the author of this work, hereby publish it under the following license:
|
File links
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):
