File:Kepler hodograph family.png

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Summary

DescriptionKepler 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.
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 licensing tag was added to this file as part of the GFDL licensing update.CC BY-SA 3.0truetrue

File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	23:33, 28 November 2006		323 × 643 (12 KB)	WillowW	Revised version in which I eliminate the circle of inversion. Made by me on 28 November 2006 using Xfig and released under the GFDL.
	16:48, 22 November 2006		383 × 643 (13 KB)	WillowW	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 a