Parallelogram Law Summations

Goeton

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Feb 26, 2015
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Hi all. I have worked out a geometric method of tracing planetary orbits and projectiles, using Parallelogram Law summations. But I am trying to determine an equation that relates the precession angle relative to distance [inverse square law]. My math skills in this regard are non-existent and I looked up this forum and thought this was the right place to look for a solution. See the following image: http://3.bp.blogspot.com/-tFDkItTrHWY/Ug-bh0x_NRI/AAAAAAAAE6U/PKx81419uBA/s1600/Kepler%27s+Second+Law_4.bmp

At 1, the initial velocity is v; the sun's gravity vector is g, and the resultant is r. This is repeated at 2 and 3, and so on that traces an orbit. As you can see the orbit is not a closed loop and one gets an orbit that looks this: https://directory.eoportal.org/imag...1-17a837c48763&groupId=163813&t=1339489834815

Thanks for your help, in advance. G.
 
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