376(2): Numerical Solution The Complete Equations of Gravitodynamics

This note summarizes the ECE2 covariant equations of gravitodynamics, Eqs. (1) – (5) in the notation of UFT318. It is shown that they make up an exactly determined set of nine equations in nine unknowns when expressed in Cartesian coordinates. This opens up a vast number of new possibilities, in gravitation, electrodynamics and hydrodynamics, and cross correlations of these subject aeas. The equations of gravitostatics are Eqs. (19) to (22), and are six equations in six unknowns. The equations of magnetogravitostatics are Eqs. (39) to (42), and are again six equations in six unknowns. All these equations are automatically ECE2 covariant, so are equations of ECE2 relativity. It follows that the relativistic Minkowski force equation (34) must be used as in UFT238 ff. This gives Eqs. (37) and (38), which should give a precessing elliptical orbit. It is known from Horst’s computations that the non relativistic version of these equations gives an ellipse. In the non relativistic Hooke / Newton limit the force equation is the Hooke Newton equation (23). This is the non relativistic limit of Eqs. (37) and (38). The equations of fluid gravitation are Eqs. (24) and (25) and are examples of the Cartan covariant derivative as shown in previous work. Eqs. (24) and (25) are non relativistic, but can be developed into the Minkowski force equation of relativistic fluid dynamics. ECE2 fluid gravitation is automatically ECE2 covariant and relativistic. Its field equations have been shown in previous papers (UFT349 ff) to have the same structure as the ECE2 field equations (1) to (5) of gravitodynamics, and the ECE2 field equations of electrodynamics. In Cartesian coordinates these sets of equations are also exactly determined, and indeed in any coordinate system. If gravitational radiation exists, it must be calculated in exactly the same way as in well known electromagnetic radiation theory. This can be done by numerical methods because Eqs. (1) to (5) are exactly determined. One example is plane wave gravitational radiation. This would be about twenty three orders of magnitude weaker than electromagnetic radiation.

a376thpapernotes2.pdf

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