File:Laplace Runge Lenz vector.png

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Figure showing the Laplace-Runge-Lenz vector at four points (labelled 1, 2, 3 and 4) on an elliptical orbit. The major and minor axes are proportional to 5 and 3, respectively, so that the foci of the ellipse are located at a distance 4; hence, the eccentricity is 0.8. Once the magnitude of mk is set, the vector A may be determined from the perpendicularity of pxL to the orbit at position #2; copying A to the other points (#1, #3 and #4) then gives pxL at those points. I created this image using Xfig and my own calculations on 4 November 2006, and I hereby release it under the GFDL. The momenta/velocity vectors are not shown, since this diagram holds regardless of whether the particle is rotating clockwise or counterclockwise; it's also cool that pxL always points outwards, away from the ellipse.

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