371(4): Scheme of Computation for the 3D Orbit

This note gives the scheme of computation that gives all information about a spherical orbit governed by an inverse square force law of attraction. Maxima can now be used to compute any type of information needed, notably the orbits r(beta), r(theta) and r(phi). Some of the analytical results from UFT270 to UFT276 on three dimensional orbits are reviewed. The planar orbit is recovered in the limit theta goes to pi / 2, theta dot goes to zero. The planar orbit is given by Eq. (33), and does not precess for an inverse square law as is well known. In three dimensions however it precesses in various ways. There is a typo in Eq. (31), which should read theta goes to pi / 2. We are now ready to use Maxima for the lagrangian in ECE2 relativity, both for planar and three dimensional orbits.


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