270(2): Interpretation of the Dynamics for Constant Theta

In this note the correct interpretation of the dynamics is given for constant theta. It is sufficient to understand the orbit in terms of Eq. (16) both for constant and non constant theta, (2-D and 3-D orbits respectively). There is no reason from the inverse sqaure law why a 3 – D orbit becomes a 2 – D orbit, but the geometry shows that all 2 – D orbits must precess. Some other mechanism must be at work to make the 3 – D orbit evolve to a 2 – D orbit. The inverse square law in 3 – D always transforms to a precessing ellipse in the 2 – D limit. For over four hundred years it has been thought that the inverse square law produces a non precessing ellipse. The error in the analysis was to restrict consideration to 2 – D from the outset. This error goes right back to Newton and Hooke, and was never corrected.


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