Many thanks, this is an excellent result and it would be very helpful to add it to the Section 3, making clear that 1 / a should be negative. I will also fix this erratum in Sections 1 and 2. It is clear from the apsidal method that the change in the ellipse is a precession, because the apsidal angle is no longer pi. So it has been proven that the ECE orce equation produces orbital precession, Q. E. D.
To: Myron Evans <myronevans123>
I tried to integrate eq.(53). For omega_r=0 this should give the result phi=pi when integrated from u_min to u_max. There seems to be a problem with the Constant C1. From (55) it is seen that the term must be negative since 2mH is negative. However in (60) you used +1/a for this term. Numerical tests show that the result phi=pi comes indeed out if the constant term is set to -1/a. Otherwise it is -0.43 or so.
The effect of the term 2 omega_r log(u) is seen by plotting the integrand for three omega_r values (see Figure). The additional term shifts the minimum of the u range to right, i.e. the ellipse becomes smaller in a non-linear way. Therefore the integration bounds would have to be modified.
I could add this diagram to section 3 of the paper.
Horst
Am 26.03.2018 um 09:45 schrieb Myron Evans:
FOR POSTING : Section 3 of UFT403
Many thanks. Incisive numerical results as usual. I would say that reversing the sign of the spin connection would reverse the sign of the integral and the precession. This can seen from Eq. (41) if the apsidal method is used. so both forward and retrograde precessions can be described, whereas EGR can describe only forward precessions. The sign in eq. (53) is correct because of the change of variable r to 1 / u. It would be very intersting to try to integrate Eq. (53) numerically, although I realize that it is a difficult procedure. That would give the orbit itself. Wen my computer returns from the workshop today I will repost sections 1 and 2 with errors corrected.
To: Myron Evans <myronevans123>, Dave Burleigh <burleigh.personal>
This is section 3 of the paper. The Integral in eq.(60) comes out negative for the planet Mercury. Can we be sure that the sign of the integral is correct? The sign changes when going from the r to the u coordinate, but I think this was rightly changed in the notes.
Horst
