391(9): Exact Agreement between ECE2 and Any Orbital Precession

This note is a simple demonstration that precise agreement between ECE2 and the precession of the perihelion can always be obtained by calculating the relativistic hamiltonian at the perihelion according to Eqs. (13) and (14). This hamiltonian, a constant of motion, characterizes the precession for any orbit assumed to be of type (17). The Newtonian hamiltonian is Eq. (15) and the two hamiltonians can be compared. This is meant to be the simplest possible type of analytical theory, using Okham’s Razor. The precise theory depends on the numerical lagrangian method and these theories rigorously conserve antisymmetry. So I will write up sections 1 and 2 of UFT391 along these lines. There is very intense interest at present in UFT380 – UFT390.

a391stpapernotes9.pdf

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Daily Report 20/10/17

The equivalent of 194,307 printed pages was downloaded (708.443 megabytes) from 2,753 downloaded memory files (hits) and 618 distinct visits each averaging 4.0 memory pages and 8 minutes, printed pages to hits ratio of 70.58, top referrals total 2,314,768, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 2729, Top ten 1088, Collected Evans Morris 660, Collected Scientometrics 425, F3(Sp) 357, Principles of ECE 211, Collected Eckardt / Lindstrom 201, Barddoniaeth (Collected Poetry) 194, Collected Proofs 168, Autobiography volumes one and two 163, UFT88 119, MJE 98, PLENR Evans Equations 83, Engineering Model 69, PECE 59, CV 59, PLENR 57, UFT311 47, CEFE 40, PECE2 38, 83Ref 37, SCI 35, UFT321 33, ADD 30, Llais 28, UFT313 28, UFT314 34, UFT315 41, UFT316 25, UFT317 38, UFT318 37, UFT319 40, UFT320 37, UFT322 34, UFT323 42, UFT324 52, UFT325 38, UFT326 28, UFT327 31, UFT328 43, UFT329 38, UFT330 22, UFT331 51, UFT332 52, UFT333 28, UFT334 18, UFT335 41, UFT336 30, UFT337 19, UFT338 22, UFT339 31, UFT340 30, UFT341 32, UFT342 30, UFT343 31, UFT344 32, UFT345 43, UFT346 40, UFT347 33, UTF348 30, UFT349 31, UFT351 50, UFT352 36, UFT353 26, UFT354 35, UFT355 33, UFT356 22, UFT357 36, UFT358 31, UFT359 27, UFT360 19, UFT361 23, UFT362 27, UFT363 28, UFT364 30, UFT365 20, UTF366 38, UFT367 35, UFT368 37, UFT369 42, UFT370 36, UFT371 35, UFT372 31, UFT373 32, UFT374 30, UFT375 26, UFT376 25, UFT377 38, UFT378 35, UFT379 26, UFT380 28, UFT381 47, UFT382 61, UTF383 58, UFT383 58, UFT384 54, UFT385 76, UFT386 55, UFT387 58, UFT388 42, UFT389 69, UFT390 40 to date in October 2017. University of Toronto “Evans Equations”; IBM Watson “Evans Equations”; Complutense University Madrid UFT88; Physics National Technical University of Athens UFT354; City University of Hong Kong general; Ville d’Esch sur Alzette Luxembourg general; National Tsing Hua University Taiwan UFT88; X Ray and Observational Astronomy Group University of Leicester UFT158; Rhodes University South Africa UFT33. Intense interest all sectors, updated usage file attached for October 2017.

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Daily Report 19/10/17

The equivalent of 298,135 printed pages was downloaded (1.087 gigabytes) from 2,976 downloaded memory files (hits) and 670 distinct visits each averaging 3.8 memory pages and 9 minutes, printed pages to hits ratio 100.18, top referrals total 2,314,487, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 2639, Top ten 1051, Colelcted Evans / Morris 627(est), Collected scientometrics 423, F3(Sp) 341, Principles of ECE 197, Collected Eckardt / Lindstrom 193, Barddoniaeth (Collected Poetry) 187, Collected Proofs 158, Autobiography volumes one and two 153, UFT88 125, MJE 94, Evans Equations 76, Engineering Model 68, CV 59, PLENR 57, PECE 54, UFT311 45, CEFE 39, 83Ref 37, PECE2 35, ADD 30, UFT321 30, Llais 28; UFT313 26, UFT314 32, UFT315 40, UFT316 25, UFT317 38, UFT318 37, UFT319 37, UFT320 37, UFT322 32, UFT323 40, UFT324 51, UFT325 37, UFT326 25, UFT327 31, UFT328 42, UFT329 36, UFT330 21, UFT331 50, UFT332 51, UFT333 28, UFT334 18, UFT335 40, UFT336 28, UFT337 18, UFT338 19, UFT339 30, UTF340 28, UFT341 30, UFT342 30, UFT343 31, UFT344 31, UFT345 36, UFT346 39, UFT347 32, UFT348 28, UFT349 31, UFT351 50, UFT352 35, UFT353 25, UFT354 33, UFT355 32, UFT356 22, UFT357 35, UFT358 32, UFT359 24, UFT360 19, UFT361 20, UFT362 25, UFT363 26, UFT364 28, UFT365 20, UFT366 35, UFT367 32, UFT368 36, UFT369 40, UFT370 34, UFT371 31, UFT372 29, UFT373 31, UTF374 29, Uft375 26, UFT376 25, UFT377 36, UFT378 35, UFT379 25, UFT380 27, UFT381 45, UFT382 57, UFT383 53, UFT384 51, UFT385 72, UFT386 53, UFT387 55, UFT388 40, UFT389 63, UFT390 36 to date on October 2017. University of Quebec Trois Rivieres, UFT366 – UFT390; Rhine Westphalia Technical University Aachen UFT238b; Florida State University UFT177, University of Maryland UFT43; Science University of Malaga Essay 104; University of Tel Aviv CV, UFT278; University of Lancaster UFT33, UFT313; Bodleian Library Oxford general. Intense interest all sectors, updated usage file attached for October 2017.

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Discussion of 391(7)

Thanks again, I think that Note 391(9) solves the problem in quite a simple way.

To: EMyrone@aol.com
Sent: 20/10/2017 11:18:29 GMT Daylight Time
Subj: Re: Discussion of 391(7)

PS: I replaced gamma-1 by an adjusted number so that more decimal places are effective. Using

gamma – 1 =

leads to

delta phi = arc sec per earth century

but this is pure numerical tricking.

Horst

Am 20.10.2017 um 09:45 schrieb EMyrone:

Agreed about the typo. I suggest adjusting epsilon and alpha to get the experimental phi. This calculation depends on the assumption that the orbit is r = alpha / (1 + epsilon cos (phi + delta phi)). The numerical methods used in previous UFT papers show that the numerical orbit is the correct one, but the numerical methods cannot be used for a small delta phi. So this calculation is meant to give a first theory only. It looks as if the result may be sensitive to the exact value of epsilon and alpha. It has been found that these values vary quite a lot between NASA and Wikipedia, so adjusting them to get the precise delta phi is justifiable. This looks like a better idea than using a constant aether potential energy.

To: EMyrone
Sent: 19/10/2017 20:56:50 GMT Daylight Time
Subj: Re: 391(7): Some More Details of the ECE2 calculation of Precession

In (24) is a typo, last term should be 1/alpha instead of 1/epsilon.
Evaluation of this eq. gives a value slightly above 1 at the RHS. Therefore the acos function cannot be taken from this. Should rather come out a value slightly below 1 ? Then we would obtain a small delta phi.

Further results:
H(Newton) / H(relativistic) approx. gamma-1 = 1 + 1.e-8

i.e. the modulus of H(Newton) is slightly larger than that of H(relativistic).

Horst

Am 19.10.2017 um 13:45 schrieb EMyrone:

In view of the catastrophic failure of the Einstein theory, the ECE2 theory is the only one that can be applied in cosmology and in precession theory. In this note the precession is expressed as Eq. (33). in which the hamiltonian H sub 0 is a constant of motion. In order to obtain precise and exact agreement with data, H sub 0 must be adjusted with a background, vacuum or aether potential defined in Eq. (36). Note carefully that delta phi must not be multiplied by 2 pi, and that the Newtonian orbital velocity at the perihelion, v sub N, is given by Eq. (11), and cannot be varied. It has also been found that the experimental value of precession is different according to which set of data is used. NASA data used by Horst Eckardt give 42.98 arc seconds per earth century, and Wikipedia data give 41.17 arc seconds per earth century for the Mercury precession.

Discussion of 391(7)

Many thanks, agreed about the numerical difficulties. I just sent over a note that gives exact agreement between ECE and any observed precession by using the universal orbital eccentricity defined by Eq. (33) of Note 391(9). I think that this by passes all numerical difficulties and the ECE2 orbit is always stable.

To: EMyrone@aol.com
Sent: 20/10/2017 10:34:18 GMT Daylight Time
Subj: Re: Discussion of 391(7)

Varying epsilon or alpha does not change much of the result. The problem is the gamma factor. The result for cos(delta phi) very sensitively depends on this factor because the kinetic energy term mc^2 is very large. gamma must be precise in more than 16 decimal places to give a delta phi of 10 power -8 as required. This is numerically not achievable. This method seems not to be a viable numerical solution, although it is conceptually much better than Einstein’s method.

Horst

Am 20.10.2017 um 09:45 schrieb EMyrone:

Agreed about the typo. I suggest adjusting epsilon and alpha to get the experimental phi. This calculation depends on the assumption that the orbit is r = alpha / (1 + epsilon cos (phi + delta phi)). The numerical methods used in previous UFT papers show that the numerical orbit is the correct one, but the numerical methods cannot be used for a small delta phi. So this calculation is meant to give a first theory only. It looks as if the result may be sensitive to the exact value of epsilon and alpha. It has been found that these values vary quite a lot between NASA and Wikipedia, so adjusting them to get the precise delta phi is justifiable. This looks like a better idea than using a constant aether potential energy.

To: EMyrone
Sent: 19/10/2017 20:56:50 GMT Daylight Time
Subj: Re: 391(7): Some More Details of the ECE2 calculation of Precession

In (24) is a typo, last term should be 1/alpha instead of 1/epsilon.
Evaluation of this eq. gives a value slightly above 1 at the RHS. Therefore the acos function cannot be taken from this. Should rather come out a value slightly below 1 ? Then we would obtain a small delta phi.

Further results:
H(Newton) / H(relativistic) approx. gamma-1 = 1 + 1.e-8

i.e. the modulus of H(Newton) is slightly larger than that of H(relativistic).

Horst

Am 19.10.2017 um 13:45 schrieb EMyrone:

In view of the catastrophic failure of the Einstein theory, the ECE2 theory is the only one that can be applied in cosmology and in precession theory. In this note the precession is expressed as Eq. (33). in which the hamiltonian H sub 0 is a constant of motion. In order to obtain precise and exact agreement with data, H sub 0 must be adjusted with a background, vacuum or aether potential defined in Eq. (36). Note carefully that delta phi must not be multiplied by 2 pi, and that the Newtonian orbital velocity at the perihelion, v sub N, is given by Eq. (11), and cannot be varied. It has also been found that the experimental value of precession is different according to which set of data is used. NASA data used by Horst Eckardt give 42.98 arc seconds per earth century, and Wikipedia data give 41.17 arc seconds per earth century for the Mercury precession.

391(9): Eact Agreement between ECE2 and all Orbital Precessions

This note shows that exact agreement with orbital precession of all kinds in the universe can be obtained with the universal eccentricity (35): eps sub 0 = 0.0217, a new concept in cosmology and physics. This gives the observed precession (36) and the effective orbit (34). Another way of obtaining exact agreement is to adjust the relativistic hamiltonian in Eq. (38). The ECE2 universal orbit is always stable. It is a new concept in physics. The universal eccentricity is similar to the Newton constant G, a constant of universal gravitation. So once this note has been discussed I will write up UFT391, Sections 1 and 2. The paper will contain the definitive numerical demonstration by Horst Eckardt that the Einstein theory fails catastrophically when properly tested. So ECE2 takes over from the Einsteinian general relativity.

a391stpapernotes9.pdf

Discussion of 391(7)

Agreed about the typo. I suggest adjusting epsilon and alpha to get the experimental phi. This calculation depends on the assumption that the orbit is r = alpha / (1 + epsilon cos (phi + delta phi)). The numerical methods used in previous UFT papers show that the numerical orbit is the correct one, but the numerical methods cannot be used for a small delta phi. So this calculation is meant to give a first theory only. It looks as if the result may be sensitive to the exact value of epsilon and alpha. It has been found that these values vary quite a lot between NASA and Wikipedia, so adjusting them to get the precise delta phi is justifiable. This looks like a better idea than using a constant aether potential energy.

To: EMyrone@aol.com
Sent: 19/10/2017 20:56:50 GMT Daylight Time
Subj: Re: 391(7): Some More Details of the ECE2 calculation of Precession

In (24) is a typo, last term should be 1/alpha instead of 1/epsilon.
Evaluation of this eq. gives a value slightly above 1 at the RHS. Therefore the acos function cannot be taken from this. Should rather come out a value slightly below 1 ? Then we would obtain a small delta phi.

Further results:
H(Newton) / H(relativistic) approx. gamma-1 = 1 + 1.e-8

i.e. the modulus of H(Newton) is slightly larger than that of H(relativistic).

Horst

Am 19.10.2017 um 13:45 schrieb EMyrone:

In view of the catastrophic failure of the Einstein theory, the ECE2 theory is the only one that can be applied in cosmology and in precession theory. In this note the precession is expressed as Eq. (33). in which the hamiltonian H sub 0 is a constant of motion. In order to obtain precise and exact agreement with data, H sub 0 must be adjusted with a background, vacuum or aether potential defined in Eq. (36). Note carefully that delta phi must not be multiplied by 2 pi, and that the Newtonian orbital velocity at the perihelion, v sub N, is given by Eq. (11), and cannot be varied. It has also been found that the experimental value of precession is different according to which set of data is used. NASA data used by Horst Eckardt give 42.98 arc seconds per earth century, and Wikipedia data give 41.17 arc seconds per earth century for the Mercury precession.