This is given by Eq. (13) from the Wolfram online integrator. This result can be checked with Maxima, which is probably more accurate than Wolfram. At the perihelion, the constant of integration A is adjusted to give exact agreement with the apsidal method, also used in the near circular approximation. This known to give precession at the perihelion. The analytical orbit is given by Eq. (15). The elliptical orbit is given by Eq. (17), which can be compared graphically with Eq. (15). The overall result is that the origin of any precession is vacuum fluctuation, a major advance in cosmology of all kinds.

## 403(9): Analytical Orbit in the Near Circular Approximation

March 17, 2018## Spanish translation of full UFT402 paper

March 17, 2018Greatly appreciated!

Date: Fri, Mar 16, 2018 at 6:14 PM

Subject: Spanish translation of full UFT402 paper

To: "burleigh.personal" <burleigh.personal>, Myron Evans <myronevans123>

Hello Dave,

Please find enclosed the Spanish translation of the full UFT 402 paper, for posting.

Thanks.

Regards,

## Book of Scientometrics Volume Two Updated to 15/3/18

March 17, 2018Attached is the half monthly update showing the usual intense international interest. From the world’s top twenty uiniversities there were consultations from Caltech, MIT, Wisconsin Madison, UCLA, Cambridge, University College London and extensive spidering by Edinburgh.

## Daily Report 15/3/18

March 17, 2018The equivalent of 205,247 printed pages was downloaded (748.330 megabytes) from 4,007 downloaded memory files (hits) and 609 distinct visits each averaging 5.2 memory pages and 10 minutes, printed pages to hits ratio 51.22, top referrals total 2,393,046, 44.5% spiders mainly from Baidu, Google, MSN and Yahoo. Collected ECE2 1419, Top ten 959, Collected Evans / Morris 495 (est), Collected scientometrics 359, F3(Sp) 337, Principles of ECE 212, Barddoniaeth 103, Autobiography volumes one and two 97, MJE 93, Collected Eckardt / Lindstrom 84, Llais 69, Engineering Model 65, Evans Equations 65, UFT88 62, Collected Proofs 54, CV 39, ADD 37, SCI 21, PLENR 20, UFT311 20, UFT321 15, PECE 15, PECE2 11, UFT313 12, UFT314 11, UFT315 22, UFT316 8, UFT317 12, UFT318 31, UFT319 18, UFT320 16, UFT322 11, UFT323 16, UFT324 31, UFT325 22, UFT326 11, UFT327 11, UFT328 15, UFT329 15, UFT330 13, UFT331 15, UFT332 35, UFT333 17, UFT334 20, UFT335 16, UFT336 13, UFT337 9, UFT338 9, UFT339 12, UFT340 9, UFT341 11, UFT342 20, UFT343 18, UFT344 11, UFT345 18, UFT346 17, UFT347 21, UFT348 31, UFT349 18, UFT351 16, UFT352 18, UFT353 15, UFT354 22, UFT355 16, UFT356 20, UFT357 14, UFT358 20, UFT359 11, UFT360 12, UFT361 14, UFT362 15, UFT363 20, UFT364 10, UFT365 8, UFT366 11, UFT367 16, UFT368 15, UFT369 17, UFT370 16, UFT371 9, UFT372 7, UFT373 8, UFT374 15, UFT375 9, UFT376 12, UFT377 17, UFT378 13, UFT379 3, UFT380 6, UFT381 16, UFT382 27, UFT383 17, UFT384 10, UFT385 11, UFT386 13, UFT387 18, UFT388 19, UT389 10, UFT390 14, UFT391 21, UFT392 24, UFT393 23, UFT394 20, UFT395 9, UFT396 35, UFT397 14, UFT398 12, UFT399 17, UFT400 34, UFT401 24, UFT402 25 to date in March 2018. University of Quebec Trois Rivieres UFT402; U. S. Office of Naval Research Self charging inverter; Internet Census general; University of the Punjab general; University of Edinburgh spidering. Intense interest all sectors, webalizer file attached.

## Analytical Correction Integral

March 16, 2018Analytical Approximations

The correction integral is analytical in the approximation alpha about r, which is the near circular approximation. It then reduces to integral (u squared / (1 + u)) power (3/2) log sub e u du which has an analytical solution according to Wolfram. In the same near circular limit it is known from the apsidal method that there is precession of the perihelion due to vacuum fluctuations. So it looks promising. This will avoid having to deal with singularities.

## VR Tour of Brecon Cathedral

March 16, 2018Brecon Cathedral VR Tour

Very interesting and many thanks! The Havard Chapel was built by my ancestors as you know, they are also your ancestors by intermarriage of Awbrey and Havard. It would be interesting to complete the Havard line back to Sir Walter Havard. I have been able to go back to only the late eighteenth century as the website shows, but there is only one Havard Family in Wales, all descended from Sir Walter Havard. I am going to write to the Bishop of Brecon and others to try to organize an interdenominational protest against the use of a chapel in Clydach as a boxing ring. This is a terrible degradation of civilization. It is like selling fish and chips in the Havard Chapel.

Just to let you know that a VR tour of the Cathedral has been launched has been launched this week, via the Cathedral website.

If you take your time with it, you can crawl all over every inch of the Havard Chapel plus other floors.

Stuart Davies

## Resolven

March 16, 2018Agreed.

Dear Steve,

A conference in and around the Waterfront Museum in Swansea is a good idea. All we need are the dates that you will be in Wales.

You can stay in my house around the conference dates, as we can easily get to Swansea by car in an hour and a little longer by bus.

We can also continue our tour of industrial sites of historical importance.

Kerry

On 14 March 2018 at 14:48, Steve Bannister <steve.bannister> wrote:

Hello again Myron. It is possible I may be in Europe again this summer, and could be very interested in your conference. I am awaiting information on other conferences that should arrive this month that will help determine my summer schedule.

Steve

Steve Bannister Stephen C. Bannister, Ph.D. Assistant Professor Department of Economics University of UtahOn 3/14/2018 4:14 AM, Myron Evans wrote:

This looks like a new bus route that comes out on the heads of the valleys road. My uncle farmed near Crynant in the Dulais valley as described in Auto One. A small conference could be organized at the Maritime Museum in Swansea

Tue, Mar 13, 2018 at 4:57 PM Subject: Resolven

To: Myron Evans <myronevans123>Back home. Found the resolven bus starts from hirwaen. View from resolven down the neath valley to swansea.

## note 403(6)

March 16, 2018Very interesting integrands.

Date: Fri, Mar 16, 2018 at 9:49 AM

Subject: Re: Fwd: note 403(6)

To: Myron Evans <myronevans123>

The integral of delta phi with exponent 3/2 is not analytically integrable according to Maxima. I have plottet the integrands I(u) and I(phi), see attachments. Both have a pole, we will see if we have to integrate up to this value for realistic orbital parameters.

Horst

Am 16.03.2018 um 09:41 schrieb Myron Evans:

Many thanks again, I plan to use this note as the main part of UFT403, Sections 1 and 2. Your check is very interesting, and I will include it in the final paper.. I will rework Note 403(7) it is probably power 3/2 in the denominator, a minor error of hand calculation. Use of the computer to mend these errors is obviously of key importance. Maxima may have an analytical or numerical solution for the correction function delta phi, giving the complete orbit phi + delta phi as well as the precession of the perihelion for orbits of small eccentricity from Note 403(6). Einstein’s famous or infamous result for the precession of the perihelion did not attempt to give the orbit. The major advance in knowledge is that precession is due to vacuum fluctuations.

Subject: note 403(6)

To: Myron Evans <myronevans123>The Schwarzschild radius is 3*10^3 m, not 3*10^5 m, a small typo.

In eq. (34) there is a sign typo but it has been corrected in (35).A check for the correctness of the result (37) is as follows:

assume

omega = a/r

as in previous papers. Then eq.(37) givespsi = pi (1+a).

For a small a, a<<1, we have psi ~ pi which is the result for vanishing precession.

Horst

## 403(8): Final Version of Note 403(7)

March 16, 2018This leads to the integral (25), which has no analytical solution, but at the perihelion for nearly circular orbits leads to the result (27). It is seen that teh precesion at the perihelion is due to vacuum fluctuations. The result (25) is a small correction to an ellipse, and this correction is a precession.

## note 403(6)

March 16, 2018Many thanks again, I plan to use this note as the main part of UFT403, Sections 1 and 2. Your check is very interesting, and I will include it in the final paper.. I will rework Note 403(7) it is probably power 3/2 in the denominator, a minor error of hand calculation. Use of the computer to mend these errors is obviously of key importance. Maxima may have an analytical or numerical solution for the correction function delta phi, giving the complete orbit phi + delta phi as well as the precession of the perihelion for orbits of small eccentricity from Note 403(6). Einstein’s famous or infamous result for the precession of the perihelion did not attempt to give the orbit. The major advance in knowledge is that precession is due to vacuum fluctuations.

Subject: note 403(6)

To: Myron Evans <myronevans123>

The Schwarzschild radius is 3*10^3 m, not 3*10^5 m, a small typo.

In eq. (34) there is a sign typo but it has been corrected in (35).

A check for the correctness of the result (37) is as follows:

assume

omega = a/r

as in previous papers. Then eq.(37) gives

psi = pi (1+a).

For a small a, a<<1, we have psi ~ pi which is the result for vanishing precession.

Horst