384(4): Antisymmetry Obeyed for all Planar Orbits

This note shows that antisymmetry is obeyed for Newtonian orbits (the conic sections) and for both forward and retrograde precessions in a plane. The antisymmetry laws for a planar orbit are equations (1) and (14), and in the absence of a gravitomagnetic field, Eq. (19) allows the spin connection to be calculated. The spin connection vector is different for each type of orbit (Newtonian, retrograde and forward precessions). The orbit is characterized by the gravitational vector and scalar potentials. It has been assumed that the scalar spin connection is a universal quantity which is the same for all these planar orbits. The fundamental angular frequency of the vacuum or aether particle may be calculated as in Eq. (36). The mass of the vacuum particle is given by the de Broglie Einstein Eq. (37) and accounts for the “missing mass” of the universe. Note carefully that this is an ECE2 covariant theory of general relativity. In this theory the spin connection co vector exists in the Newtonian type orbit, where it is given by Eq. (27). This is consistent with the fact that ECE2 is developed in a mathematical space with finite torsion, curvature, and spin connection, and not in a Minkowski space. So the Euler Lagrange orbital equations of ECE2 have been shown to be rigorously consistent with the gravitational field equations and antisymmetry laws of ECE2. This is a big step forward and there are many ways in which this theory can be developed.


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