Archive for April, 2012

New Representations by Ray Delaforce of the Conventional Conical Sections

Feed: Dr. Myron Evans
Posted on: Friday, April 27, 2012 12:02 AM
Author: metric345
Subject: New Representations by Ray Delaforce of the Conventional Conical Sections

These representations by Ray Delaforce show that for x = 1 even the conventional ellipse, parabola and hyperbola have hidden mathematics hitherto undiscovered. The next posting will contain Ray’s own detailed analysis, which is planned for section 4 of UFT216. As soon as the x parameter is allowed to vary from unity a vast array of new fractal type structures appears. All of these could be orbits in theory. So this is a complete surprise and a new subject area for both mathematics and physics and astronomy. In the solar system x is very close to unity for planets, so only a tiny fraction of possible orbits are observed in the solar system. In binary pulsars x is larger, but as x is increased or decreased the orbit takes on a myriad of new possibilities that can be looked for by astronomers. In a whirlpool galaxy the conical sections transform into spirals as planned for Section 3 of UFT216 by Horst Eckardt. Finally in Section 5 of UFT216 by Gareth Evans all of these structures emerge from one universal law of gravitation. It is now obvious to all that the Einstein general relativity is completely obsolete and should be taught as science history only. All claims based on EGR should be disregarded. This is the verdict of simple but powerful mathematics.

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Description by Ray Delaforce for Section 4 of UFT216

Feed: Dr. Myron Evans
Posted on: Friday, April 27, 2012 12:04 AM
Author: metric345
Subject: Description by Ray Delaforce for Section 4 of UFT216

This is the description by Ray Delaforce of these amazing properties of the conventional ellipse, hyperbola and parabola, taught at every good school. As far as I know these properties were all hitherto unknown, and are all for x = 1. As soon as x varies a complete new fractal type subject appears.

In a message dated 27/04/2012 00:08:16 GMT Daylight Time, writes:

Prof. Evans,

I wondered about the same thing: For epsilon=1 there is obviously a “singularity” where r -> infinity, so what distinguishes a parabola from a hyperbola, both having singularities in the equation, r = alpha/(i+epsilon*cos(x*theta))?

Attached is a combined plot for epsilon < 1, epsilon = 1, and three values of epsilon > 1 (alpha=1 and x=1 for all plots).

One important thing I did was to plot a range of theta for a large number of periods (to make sure passage thru any singularities and to show any pattern that may emerge — my plotting software has a setting to suppress divide-by-zero errors and keep going).

What I found was one difference between a parabola and a hyperbola is that the parabola has a single point per period which is singular and the value of the radius is ALWAYS POSITIVE. The singularity of the parabola can be considered an arbitrarily large POSITIVE value as well because arbitrarily large values of the radius on either side of infinity is positive.

However, plotting a multi-period hyperbola produces what at first appears to be two STRAIGHT LINES between the “other side of the universe” and r=0!

In reality, for a hyperbola, there are TWO SINGULARITIES per period, each having an associated theta value. Between these two singularity points is a range of theta which produces the ‘conventional hyperbola’ having positive radius value, but there is a range of theta producing negative radius value. Also each singularity of the hyperbola is different that of the parabola as the hyperbolic singularities are approached on one side from the positive direction but from the other side from the negative direction. This Is the reason why the ‘non-conventional’ trajectory of a hyperbola has two straight lines in polar coordinates: In Cartesian coordinates there are both (+) and (-) ‘way out there’ directions, while in polar coordinates ‘way out there’ is always positive r. If one allows negative values in the polar coordinate system, there is only one way for it to go – ‘deeper’ into the r=0 area, so a polar plot of a +/- singularity point is a straight line between r=0 and r = +infinity, but notice that polar infinities HAVE A DEFINITE VALUE OF THETA!!

I’ve made a second plot which allows negative r and one can see this. There is a surprise – each hyperbola has a loop in the negative radius area! Also, plotting for both negative and positive radius values shows with more emphasis how a hyperbola curves away in the positive radius area. The parabola appears to maintain almost straight lines which gradually spread apart as it approaches (+)infinity.

Ray Delaforce

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Closed Orbits

Feed: Dr. Myron Evans
Posted on: Saturday, April 28, 2012 6:41 AM
Author: metric345
Subject: Closed Orbits

Many thanks! This is a neat result by Horst. In binary pulsars open orbits may also be of interest, because it is thought that the orbit shrinks and does not close.

In a message dated 28/04/2012 13:15:22 GMT Daylight Time, writes:

The background that p/q must be rational to give closed orbits is probably the following:

An orbit closes if

r_1(theta+ m*2 pi) = r_1(theta + n*2 pi)

for a point of return r_1 and two integers m and n. If we describe the advancement of theta for one round by

theta –> x*theta,

this means there must exist an x with

x = n/m,

i.e. x must be rational.


Am 27.04.2012 15:56, schrieb EMyrone

Many thanks again, very important results. All of them could be analysed in UFT216 Section 4 and subsequent papers.

In a message dated 27/04/2012 14:01:48 GMT Daylight Time,

Prof. Evans,

I made my own plots for the parabola and variation of x. I see the same relationship holds as for the ellipse in that one must express x as a fraction p/q in reduced terms. The parabola will repeat p times and q will determine the closed areas which a bisector line will intersect. Also, an irrational value of x will eventually fill the plane if one keeps plotting more and more parabolas.

The plots attached have both a near and far views. One can confirm the equation for asymptotes occur at 2Pi(x-1)/x or in terms of deflection angle of a straight path as pi(2-x)/x.

Also, I noticed a ‘repulsive’ type notch right at the perihelion of some. I used Maxima to plot 3D curvature (z-axis) vs x and vs theta. I do see between x = 1.4 to x = 1.6 that the curvature goes negative for some range of theta. (Let me know if you can’t view an ‘EMF’ format graphic file – this was what Maxima/Gnuplot exports it as.)

Ray D.

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The Fractal Type Orbital Equation

Feed: Dr. Myron Evans
Posted on: Thursday, April 26, 2012 7:14 AM
Author: metric345
Subject: The Fractal Type Orbital Equation

This is

dr / d theta = (x epsilon / alpha) r squared sin (x theta)

This simple equation produces a fractal like result and so it produces an essentially infinite number of new conical sections. The Newtonian result is x = 1, and the precessing elliptical orbits (of any kind) are obtained with x close to unity. When x is allowed to vary the fractals appear. The equation can describe all known orbits and predicts an infinite variety of new orbits. It is obtained simply by differentiating:

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

the precessing, or fractal, conical sections. Einsteinain general relativity does not even work for epsilon about one, and fails completely to produce the fractals. Standard model dogmatists are now completely exposed to heavy criticism if they continue to ignore the refutations of EGR. That includes Hawking and Penrose and all the big names whose work is totally wrong in so many ways.

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Effect of x on Orbital Structure

Feed: Dr. Myron Evans
Posted on: Wednesday, April 25, 2012 3:48 AM
Author: metric345
Subject: Effect of x on Orbital Structure

It is clear that very small changes in x can result in dramatic changes in orbit for a given ellipticity epsilon and half right latitude alpha. It is truly amazing that all of this results from the addition of one term to the Newtonian gravitational potential. So are orbits what we thought they were? It seems that a very slight pertubation can induce a massive orbital shift. This is certainly true mathematically, the precessing conical sections have an incredibly rich structure wholly unknown until now. None of this was even hinted at by the Einstein theory. The subject is similar to nonlinear and fractal physics. The first conical section to be used as an orbit was the ellipse, (x = 1, epsilon < 1). Kepler discovered this for the orbit of Mars using the data of Brahe. Later it was found that the ellipse precesses (x slightly greater than or less than one). The precession in the solar system is a few arcseconds a century, but is much larger in binary pulsars and similar. We now know, very suddenly in a classic paradigm shift, that the precessing orbit can evolve into an amazingly rich pattern simply by varying x. So if orbits are conical sections (as accepted for several hundred years) there may be orbits in astronomy which have these amazing properties. A book for CISP with all these orbits classified would be timely and in my opinion, very important for mathematics and physics. The Royal Society is being informed of these new results automatically and already knows about them.

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Orbits by Ray Delaforce

Feed: Dr. Myron Evans
Posted on: Wednesday, April 25, 2012 3:28 AM
Author: metric345
Subject: Orbits by Ray Delaforce

These are some of the new conical sections and orbits produced by the equation

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

for values of epsilon, the ellipticity, and x, the precession factor, considered here to be a constant.

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Binary Pulsar Orbits and New Ephemeris Based on The Precession Factor x

Feed: Dr. Myron Evans
Posted on: Monday, April 23, 2012 11:30 PM
Author: metric345
Subject: Binary Pulsar Orbits and New Ephemeris Based on The Precession Factor x

It would be very interesting to make a very careful graphical study with a range of x values for the precessing elliptical orbit to see if the orbit behaves at some point as in the binary pulsars, where it decreases by a few millimetres per orbit. The old interpretation of this was gravitational radiation from the Einstein theory, but it is now known that that is completely wrong. At some value of x close to unity the orbit will start to deviate slightly from a precessing ellipse, the type of deviations might be different for x less than one and greater than one, but very close to one. The orbit may cease to become a closed orbit and may start to behave like a binary pulsar orbit – a “shrinking precessing ellipse”, the true curve being given by x. There is no experimental evidence that a binary pulsar orbit will eventually collapse. The only experimental evidence is that the orbit decreases by a few millimetres an orbit, and a huge amount of horse hair was brushed away from this observation, revealing a wooden construction bearing Greek gifts. Gravitational radiation has never been observed, LIGOS has been a complete failure, covered up of course. I suspect that the true orbit of a binary pulsar will be given by varying x very carefully. A catalogue of orbits needs to be built up by varying x in order to classify the new information for mathematics and as well as physics. Our graphics experts here are Horst Eckardt, Robert Cheshire and Ray Delaforce, and it would be really interesting if they could build up such a catalogue or ephemeris, classifying the orbits or conical sections. We were going to do this for a new CISP book. The entire book could be lavishly illustrated in colour and orbits compared from known objects and the new theory. For example Halton Arp’s peculiar galaxies book. It is delightful to be able to work with such a simple equation as:

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

As my old Viking Uncle Olaf used to say, there’s a lot of finding to do, in the nicest way of course. I admit he could be a little cutting on occasions until he heard about cynghanedd.

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