Analysis by Marion and Thornton

Feed: Dr. Myron Evans
Posted on: Friday, August 26, 2011 10:30 AM
Author: metric345
Subject: Analysis by Marion and Thornton

The attempted solution of the claimed equation

d squared u / d theta squared + u – delta u squared = 1 /alpha

of EGR is given by Marion and Thornton on pp. 268 ff of their third edition of “Classical Dynamics” (Harcourt 1988). I used this as a course book as a full professor of physics, with good student reaction to the course. It consists of several approximations using arbitrary trial functions and they just ignore one term which they call a “small periodic disturbance of the normal Keplerian motion”. So they ignore an inconvenient result of EGR that is not actually observed in any orbit. Einstein himself did something similar on Nov. 22nd 1915, and was immediately criticised by Schwarzschild on Dec. 22nd, 1915. This makes me very uneasy about Einstein’s own character. There was certainly pressure on him to produce a result of EGR that could be measured, because very few accepted EGR at the time. The starting point of MArion and Thornton (their Eq. (7,73 of the third edition) is exactly the same lagrangian equation that is used in UFT 193 (in prep), so they cannot be correct because the true and stable precessing ellipse gives a force law that is the sum of an inverse square and inverse cube term. Einstein tried to force a precessing ellipse out of a force law that is the sum of an inverse square and inverse fourth term. That is just not possible, yet it has been forced on science for nearly a century.

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Another test of EGR

Feed: Dr. Myron Evans
Posted on: Friday, August 26, 2011 7:19 AM
Author: metric345
Subject: Another test of EGR

This would be to integrate the claimed equation of EGR (Marion and Thornton eq. (7.76)) numerically to find the orbit. The claimed equation is

d power 2 u / d theta squared + u = 1 / alpha + delta u squared

where u = 1 / r and where alpha and delta are constants. It is now known that this cannot give a precessing ellipse, it gives some other kind of orbit.

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193(8): The Parabola and Conic Section in Cartesian Coordinates

Feed: Dr. Myron Evans
Posted on: Friday, August 26, 2011 1:10 AM
Author: metric345
Subject: 193(8): The Parabola and Conic Section in Cartesian Coordinates

This is the derivation of the parabola and conic section in Cartesian coordinates. The meaning of alpha for a parabola can be seen from Eq. (5), when X is zero, Y = alpha. If light is trapped in a Newtonian ellipse, a closed orbit, around an object of mass M, the photon mass m can be calculated from eq. (12) knowing the angular momentum.

a193rdpapernotes8.pdf

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192(3), Final Version: m(r) Function for a Precessing Ellipse

Feed: Dr. Myron Evans
Posted on: Monday, August 15, 2011 1:14 AM
Author: metric345
Subject: 192(3), Final Version: m(r) Function for a Precessing Ellipse

This is the final version of the note, which should be checked by computer algebra. The final expression for m(r) is Eq. (6). In the previous note I dropped the sin(x theta) of Eq. (2). The final m(r) is not the “Schwarzschild”

m(r) = 1 – r0 / r

a192ndpapernotes3.pdf

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Artwork from the Precessing Ellipse and Logarithmic Spiral

Feed: Dr. Myron Evans
Posted on: Thursday, August 11, 2011 6:53 AM
Author: metric345
Subject: Artwork from the Precessing Ellipse and Logarithmic Spiral

A lot of art can be made from the precessing ellipse. One could also try the log spiral:

r = r0 exp (zeta theta)

where zeta is the pitch. For a very large pitch the outer arms are drawn out into a nearly straight line as observed in the Hubble space telescope. In a recent paper (UFT 190), the velocity curve of a spiral galaxy was explained with zeta goes to infinity as r goes to infinity. Einsteinian GR has no explanation at all, in fact fails completely to describe a whirlpool galaxy. The log spiral appears in shells and other natural phenomena. The so called “precision tests of the Schwarzschild metric” are complete nonsense. This can be shown very easily as in the following postings on this bog.

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192(5): Comparison of Solar System and Whirlpool Galaxy m(r) Functions

Feed: Dr. Myron Evans
Posted on: Thursday, August 11, 2011 3:57 AM
Author: metric345
Subject: 192(5): Comparison of Solar System and Whirlpool Galaxy m(r) Functions

These are given in this table, and are similar functions, suggesting that the dynamics of the solar system and whirlpool galaxy have an underlying cause, i.e. a new cosmology based on ECE theory. The next note will develop this theme in terms of

m(r) = 2 – exp(2exp(- r / R))

obtained from the correct torsional geometry with a single antisymmetric connection. Various analytical curves can be used to produce their own m(r) functions in spherical spacetime. In UFT 108 the binary pulsar was considered, a precessing ellipse spiralling inwards. This also has its own m(r) function and is a precessing ellipse with alpha getting smaller, where 2 alpha is the latus rectum, a characteristic of the ellipse. Ray Delaforce and Horst Eckardt could graph this function. It is, for a fixed eccentricity epsilon:

r = alpha(r) / (1 + epsilon cos(x theta))

where alpha decreases with r. For example

alpha = alpha sub 0 exp ( – r / R0)

where R0 is a characteristic radial length. This ought to be a precessing ellipse spiralling inwards and that can be checked graphically. Its m(r) function can then be found.

a192ndpapernotes5.pdf

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192(2): Proof that General Relativity does not give a Static Ellipse

Feed: Dr. Myron Evans
Posted on: Wednesday, August 10, 2011 5:42 AM
Author: metric345
Subject: 192(2): Proof that General Relativity does not give a Static Ellipse

This is the final version of note 192(2). If it is assumed that general relativity in any spherical spacetime gives a static ellipse then the resulting m(r) function must be Eq. (29). In order to give a static ellipse the Newtonian limit must be reached, in which case m(r) must go to unity. It only reaches this limit if the ellipse becomes a circle. The standard model asserts that a precessing ellipse is obtained from

m(r) = 1 – r0 / r

However, if GR is to reduce to a precessing ellipse, the m(r) function must again be Eq. (29). The properties of Eq. (29) can be evaluated by computer for various alpha and epsilon, a and b. So UFT 192 can again be a two authored paper. Also, these calculations can be checked by computer. It is pointless claiming precision tests of GR when the basic Einsteinian theory is so wrong. It is also pointless challenging computer algebra.

a192ndpapernotes2.pdf

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192(3) : Einsteinian GR never produces a precessing elliptical orbit

Feed: Dr. Myron Evans
Posted on: Wednesday, August 10, 2011 7:37 AM
Author: metric345
Subject: 192(3) : Einsteinian GR never produces a precessing elliptical orbit

This is a greatly simplified and strengthened proof that for a spherical spacetime, Einsteinian general relativity (m(r) =? 1 – r0 / r) gives a precessing ellipse if an d only if Eq. (7) is true. The correct m(r) for a precessing ellipse is Eq. (8), which is not the function 1 – r0 / r, misattributed to Schwarzschild. In a letter of 22nd Dec. 1915 to Einstein, the latter was severely and correctly critical of Einstein’s claims of Nov. 22nd 1915 about precessing orbits. Einstein was just plain incorrect. The proof in this note is so simple that it cannot be refuted and so Einsteinian GR with the “Schwarzschild metric” is meaningless, as are all those “precision tests” of a theory that is totally wrong. Using ECE theory we have started to work on a correct GR which is briefly described in pages 2 ff. of this note. Computer algebra can now be used to compare eq. (8), (10), and the completely incorrect

m(r) = 1 – r0 /r

This is the simplest and best method that can be used now in UFT 192. After this, anyone who adheres to Einsteinian GR is not a scientist. ECE theory offers a completely new approach to cosmology. So now Horst can check my simple calculations of this note with computer algebra and we can proceed from there. Those hyperexpensive satellite trips are still very useful sources of data, but for a totally new theory. Why wasn’t this seen before? I don’t know. My guess is that it must have been sen before and covered up as usual. “Is everything we know about standard cosmology totally wrong” as the BBC asked recently? Totally right. My advice is stop reading wiki in favour of ECE and J. Found. Phys. Chem.

a192ndpapernotes3.pdf

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192(1): Simple Angular Velocity Test of General Relativity

Feed: Dr. Myron Evans
Posted on: Monday, August 08, 2011 3:51 AM
Author: metric345
Subject: 192(1): Simple Angular Velocity Test of General Relativity

This is a suggestion for an angular velocity (omega = dtheta / dt) test of general relativity by measuring to maximum precision possible the change in angle theta over time t of an object such as the moon, and measuring the distance to the moon directly with a laser. Repeat all around the orbit. According to the standard model the result should en eq. (10). However the correct result is

m(r) = omega r squared / y

where

y = L c squared / E = constant of motion

a192ndpapernotes1.pdf

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