Many thanks for checking this note with computer algebra. I have just sent over Note 377(2) which makes this calculation easier and clearer, but these results already look very interesting. There might be some very interesting types of precession. In addition there are some minor typo’s as follows. In Eqs.(16), (17), and (23) – 26) the sign is accidentally wrong in the Lorentz factor. It should be minus. This is corrrected in Note 377(2). Agreed that the time t should be used in the observer frame and tau in the particle’s own frame. So we can proceed like this in future work. The equation set is clarified and simplified in Note 377(2). There is a good chance that both forward and retrograde precessions will emerge. The change from -2 to -1 carries through to Eqs. (13) to (16), and (19) and (20) of Note 377(2). Can you run Note 377(2) through the computer to make sure all is OK? Many thanks. In the denominators of Eqs. (21) and (22) there should be a factor 2. I am not sure that the use of the Minkowski force produces zero precession, because we showed non zero precession in chapter 8 of “Principles of ECE”. However this is an academic point, the relativistic Newtonian force is the right one to use because it produces the right relativistic kinetic energy and the Einstein energy equation and relativistic hamiltonian. The reason why it is right is obscure, because tau is used to get the relativistic momentum, but t is used to get the relativistic force. However that is another academic point.

To: EMyrone@aol.com

Sent: 08/05/2017 11:21:49 GMT Daylight Time

Subj: Re: 377(1): Orbital Equation with the Relativistic Newton ForceI checked the note. In (21) the factor should be 4 pi instead of 2 pi, and in (22) the factor 2 should be 1.

In (23) there should be -1 instead of -2.The note gives a good explanation of the difference between Minkowski force and Newton’s law in relativistic version. Since the Lagrangian is formulated in the observer frame, it seems to me that the correct form of the Euler–Lagrange equations is with observer time t, not with time tau, in constrast to the literature. When using the time tau, the precession vanishes in my calculation.

The equation set (14, 15, 23, 24) can be solved as follows: (14, 15) decouple from (23, 24). Therefore the former can be solved first. Then one can go into (23, 24) with the solution. rho_m from (21) has to be inserted, otherwise we have a tautology. The result can be computed analytically for kappa_X, kappa_Y, giving:

(kx for kappa_X, xdd for x dot dot, etc.). It can further be simplified to

.

This is a meaningful solution because the denominator does not vanish for ellliptic orbits. I will graph it later.

Horst

Am 07.05.2017 um 15:13 schrieb EMyrone:

This is Eq. (13), whose planar Cartesian coordinate form is Eqs. (14) and (15). It gives a precessing planar orbit, and is constrained by Eq. (24) from the gravitational equivalent of the Coulomb law, the ECE2 field equation (19). A possible solution of Eq. (24) is given in Eqs. (25) and (26), which are Eqs. (14) and (15) again. However, it is possible to obtain a more general solution of Eq. (24) using spin connection components kappa sub X and kappa sub Y as input parameters. Then we have three simultaneous equations (14), (15) and (24), which should give all kinds of precessing orbits to compare with astronomical data. It is shown at the beginning of the note that the relativistic lagrangian and hamiltonian come out of the relativistic Newton law, as first shown by Einstein in about 1905. So the force equation (13) is the rigorously self consistent one in the laboratory or observer frame in which the field equations are written. The Minkowski force equation of UFT376 also gives precession, the Minkowski four force is defined by Eq. (27) as is well known. It is the relativistic four momentum differentiated by the proper time, which is the particle’s own time, the time in the frame of reference attached to the particle. The two forces are related by Eq. (30). So some very interesting results are beginning to emerge now, without any use of the obsolete Einsteinian general realtivity (EGR). In various UFT papers, precessions of different kinds have been computed in many ways. Horst has refined the computational method to the point where it can produce very many new results from theory that is analytically insoluble. Since EGR has been refuted in eighty three ways in the UFT section, no one should use it. EGR has been refuted in many more ways by Stephen Crothers, summarized in his excellent chapter nine of “Principles of ECE”. EGR was completely refuted experimentally in whirlpool galaxies nearly half a century ago, but the dogmatists continue to claim that it has not been refuted at all. Einstein would have dismised the dogmatists outright, and wrote that it would only take one experiment to refute his theory. So standard physics is in a mess, better to use ECE2 physics, where no druidical magic is used and no human sacrifices of dissidents. I never use my third class druidical licence any more, there being very little demand now for human sacrifice.