Kepler_hodograph_family.png
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Summary
Description Kepler hodograph family.png |
English:
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_transformed.png
). This figure was made by me on 22 November 2006 using Xfig and is hereby released under the GFDL.
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Source | No machine-readable source provided. Own work assumed (based on copyright claims). |
Author | No machine-readable author provided. WillowW assumed (based on copyright claims). |
Licensing
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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This licensing tag was added to this file as part of the GFDL licensing update . http://creativecommons.org/licenses/by-sa/3.0/ CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 true true |