File:Kepler hodograph family.png

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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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Author No machine-readable author provided. WillowW assumed (based on copyright claims).

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Date/TimeThumbnailDimensionsUserComment
current23:33, 28 November 2006Thumbnail for version as of 23:33, 28 November 2006323 × 643 (12 KB)WillowW (talk | contribs)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 2006Thumbnail for version as of 16:48, 22 November 2006383 × 643 (13 KB)WillowW (talk | contribs)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

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