389(4) Spin Connections for Precessing Planar Orbits

This not gives the spin connections for a forward and retrograde precession using the gravitational potential (3). The results are equations (13) to (16) and can be graphed. They are maps of spacetime, the vacuum or gravitational aether. In order to compute the vector potential Q it is necessary to compute Eqs. (17) to 919), the antisymmetry equations. Having found the vector potential, the scalar spin connection is found from the Lindstrom constraint,and finally the total vector potential found as in the previous note. If it is assumed that the spin connection is two dimensional for a planar orbit, the omega sub Z = 0. Computer algebra can be used to solve Eqs. (17) to (19), which are three simultaneous differential equations. I will look for a simple solution by hand. The differential equations are of the type dy / dx = f(x, y)y and so on. I am sure that there are code packages that can integrate such equations (e.g. Maxima, Mathematical,Maple, NAG, IBM ESSL, and so on) . A great deal of new information about precessing planar orbits will emerge from this complete theory, which in general is a new type of cosmology.

a389thpapernotes4.pdf

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