Image:Kepler hodograph family.png
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[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.
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File history
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| Date/Time | 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) |
