## Discussion of Note 376(2)

Agreed, all your work in the well known Eckardt / Lindstrom papers applies to these equations. I have just sent over an example of interdependence today, for gravitostatics. There are a lot of interesting things in these equations. Everything has simplified and clarified in the past two or three months. One example is that the Minkowski force equation produces a precessing ellipse (this was not clear in UFT238 ff) and follows from the lagrangian through a relativistic Euler Lagrange equation with proper time. Fluid gravitation adds an entirely new dimension as you know, and you have demonstrated many new species of orbit from those equations. One important point is that a magnetogravitational field is needed for gravitational radiation. Therefore there is no gravitational radiation from gravitostatics. There is no electromagnetic radiation from electrostatics as you know. One needs an oscillatory source and the Ampere Maxwell and Faraday laws together with the Gauss law of magnetism. UFT318 describes how the continuity equation emerges. Another example: in order to get gravitational radiation the magnetogravitational field must be non zero.

To: EMyrone@aol.com
Sent: 29/04/2017 13:31:04 GMT Daylight Time
Subj: Re: 376(2): Numerical Solution The Complete Equations of Gravitodynamics

It is known from electrodynamics that eqs.(1) and (3) are not independent of (2) and (4). Doug and I showed this in an earlier paper. For example electromagnetic waves are computed from the Faraday and Ampere-Maxwell law alone. As far as I know, also the continuity equation follows from them. Anyway, it is important to discuss (1-6) for the gravitational case.

Horst

Am 26.04.2017 um 13:08 schrieb EMyrone:

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.