The Balance of Forces in a Planar Orbit

This is given by the fundamental kinematic equation:

F = m (d2r / dt2 – r omega squared)

This can be written as:

m d2r / dt2 = F + m r omega squared

Here m r omega squared is the outward or centrifugal force and F is the net force of attraction. In a Newtonian orbit (a conical section):

F = – mMG / r squared

which is the attraction between m and M, the inverse square law of universal gravitation. In a hyperbolic spiral orbit (Coats orbit):

F = – m r omega squared

so dtr/dt2 = dv / dt = 0, and v is constant as r goes to infinity as observed in the velocity curve of a whirlpool galaxy. There has always been confusion in the textbooks about the centrifugal force. It is in fact the force generated by the rotation of the plane polar axes – it is due to the spin connection of Cartan geometry. In pure Newtonian dynamics there is only the force of attraction, so m would fall into M. The rotation of the axes also generates a Coriolis force, but this vanishes in all planar orbits. The rotation of the axes also generates the orbital velocity omega x r. The angular velocity omega is a spin connection.

UFT88 has been studied intensively for about five or six years in all the best places worldwide, and describes what happens to the second Bianchi identity if torsion is present. I respectfully suggest that the vast readership of ECE continue to study Proofs One to Five as it has been doing for about half a dozen years. These proofs show why torsion MUST be present, it can never be zero without the curvature being zero. The proofs are very simple to understand. The key point is that the anti symmetry of the commutator (accepted by all) must also be the antisymmetry of the geometrical connection. To see this simply use mu = nu and the commutator vanishes, along with the torsion AND curvature. So the torsion must be non zero. The discussion on the whirlpool galaxy just posted shows that it is completely non Newtonian and non Einsteinian. The reason for light deflection due to gravitation, and perihelion precession is again the Cartan torsion (UFT261). Unfortunately the claimed accuracy of Einstein in the solar system is an illusion but the improved Einstein theory, ECE theory, cures all the errors. So I don’t see any problem in accepting ECE theory, it is after all just textbook geometry (it is all in Carroll, “Spacetime and Geometry”, and his online notes are free. Simply read chapters one to three, the commutator proof is in those chapters. In UFT99 I give a lot more detail of the commutator proof than Carroll, and in general I have given a lot more detail of many of Carroll’s proofs. So all the personal animosity is garbage. It has the effect of turning decent people off physics, and that is a pity. People do not expect a professor to indulge in gutter abuse, adn in fact this is academic misconduct verging on criminality (trolling).

Force Law for a Hyperbolic Spiral Orbit

This is precisely the negative of the centrifugal force so as r goes to infinity the net force is always zero, the orbital linear velocity of the orbit is a constant. So the attractive force for a hyperbolic spiral orbit is

F = – L squared / (m r cubed)

where mu is the reduced mass and where the angular momentum is

L = mu r squared omega

where omega is the angular velocity (the magnitude of the spin connection). So :

F = – mu r omega squared

Here mu is the reduced mass:

mu = mM / (m + M)

so M of the central part of the galaxy enters into the force in this way. This is of course completely different from Newton, not just a small correction to Newton as in the solar system. This type of force law and orbit were first investigated by Roger Coates (1682 – 1716). The received wisdom of the present age of darkness and dark matter in cosmology is that there is a “black hole” at the centre of a galaxy, if so mu would be mathematically indeterminate (infinity divided by infinity). In fact the mass M is finite but very large, so for all practical purposes:

mu = m

so the star of mass m orbits with constant velocity as r goes to infinity without being affected by M. This finding completely contradicts the idea of attraction between m and M. The real reason for the orbit is geometry, in fact the orbit is governed simply by the properties of plane polar coordinates. Note carefully that this is a theory of general relativity because there is a spin connection vector present – the angular velocity vector. Newton is restricted to motion in a straight line.

A Million Chinese Hits in May.

This is the title of my new song, for which Simon is scheduled to play the jazz trumpet, Robert the guitar, with Gerard ‘t Hooft on drums. In fact there has been a rapid growth of interest in ECE from China in the past two years, and it is the last major nation to join the fan club.

In a message dated 31/05/2014 07:12:37 GMT Daylight Time, writes:

Perhaps there are a million Chinese physicists all intensely interested in the same topic?

On 31 May 2014 07:09, <EMyrone> wrote:

To date there have been 988,742 hits, 14,024 distinct visits, 37,303 page views and 10.354 gigabytes downloaded. However the hits total was severely distorted by a Chinese site that spent almost the entire month trying to download UFT107 automatically, running up almost a million hits.The genuine hits total is estimated from the average ratio of hits to page views over the past six months, which is 1.49. So the genuine total of hits to date in May 2014 is estimated to be 55,581, or roughly about 56,000. There are still two more days of stats to come in for May. This is the last day of the month so I am taking monthly stats before they are overwritten. These will be added to the Book of Scientometrics as usual. This book is a very accurate database containing over ten years of data showing ten years of very intense interest in ECE theory from all the best places in the world. So it is easy to see that ECE will be studied intensely for the foreseeable future at all the best places. Nothing more could be asked from any theory of natural philosophy. This is the post Einstein paradigm shift, a phrase coined by Professor Emeritus Alwyn van der Merwe of Denver University, the most eminent physics editor of the past half century.

Daily Report 29/5/14

There were 1602 hits from 447 distinct visits, spiders from baidu, google, MSN, yandex and yahoo. Essay 24 944, F3(Sp) 696, Auto1 548, Auto2 91, Book of Scientometrics 190, UFT88 171, CEFE 86, Evans Equations 108, numerous (Spanish), “Llais” 76, Engineering Model 60, Englynion 24 to date in May 2014. Computer Centre Technical University Ilmenau Homopolar; Columbia University New York City UFT41; Stanford University UFT80; University of Nevada Las Vegas general; Science University of Valencia UFT143(Sp); The Park Community School Barnstable UFT25; United States National Archives A Basic Error in the Einstein Field Equation; Theoretical Physics Imperial College London UFT88; High Energy Physics University College London Home Page. Intense interest all sectors, updated usage file attached for May 2014.

Usage Statistics for aias.us aias.us

Summary Period: May 2014 – URL
Generated 30-May-2014 12:45 EDT

Monthly Statistics For May 2014

To date there have been 988,742 hits, 14,024 distinct visits, 37,303 page views and 10.354 gigabytes downloaded. However the hits total was severely distorted by a Chinese site that spent almost the entire month trying to download UFT107 automatically, running up almost a million hits.The genuine hits total is estimated from the average ratio of hits to page views over the past six months, which is 1.49. So the genuine total of hits to date in May 2014 is estimated to be 55,581, or roughly about 56,000. There are still two more days of stats to come in for May. This is the last day of the month so I am taking monthly stats before they are overwritten. These will be added to the Book of Scientometrics as usual. This book is a very accurate database containing over ten years of data showing ten years of very intense interest in ECE theory from all the best places in the world. So it is easy to see that ECE will be studied intensely for the foreseeable future at all the best places. Nothing more could be asked from any theory of natural philosophy. This is the post Einstein paradigm shift, a phrase coined by Professor Emeritus Alwyn van der Merwe of Denver University, the most eminent physics editor of the past half century.

Summary of Discoveries in Notes for UFT262

These notes show that the major obervable features of a whirlpool galaxy can be explained by fundamental kinematics. The orbit in the r infinity limit must be a hyperbolic spiral. The orbit is totally non Newtonian and non Einsteinian because the gravitational potential does not depend on M, the mass that is assumed to be at the centre of a whirlpool galaxy. The kinematics of plane polar coordinates is an example of Cartan geometry because the axes are rotating and there is a spin connection present. The geometry is more fundamental than Newton and Einstein, both of whom fail completely in a whirlpool galaxy. I am not sure whether the general public is even aware of this fact, having been fed a diet of crass dogma. I am well aware that the whirlpool galaxy is an enormously complicated system, but this kinematic theory explains it major features with great elegance and simplicity. Robert Cheshire has analyzed a whirlpool galaxy in great detail, and I am prepared to publish his findings in any format he wishes. I am also aware that the plasma theory has contributed greatly to galactic theory, for example the recent ECE papers on the Beltrami theory. However UFT262 is a beautiful result – geometry is perfect beauty. I will go on developing UFT262 in the next few notes.

Discussion of 262(2)

Agreed with this, the kinematics are based directly on geometry as you know, so I will continue the notes in this way. We can include your remarks in the final paper as usual.

In a message dated 30/05/2014 13:08:37 GMT Daylight Time, writes:

Perhaps one sould add some explanation to the deraviation of eq.(19) from (14). For limit r –> inf. the first term of (14) goes to zero but the second has to go to a constant value given by v[inf]. Since there is a factor 1/r^2, this means that d theta/dr has to go to zero.
Now eq. (11) can be considered in this limit. since the lhs is constant and r goes to inifinity, the factor omega has to go to zero. This is probably the simplest way to derive this behaviour of omega. The result is consistent with d theta/dr –> 0 as derived before.

Horst

EMyrone@aol.com hat am 28. Mai 2014 um 11:51 geschrieben:

The attached gives a description of all the main observable features of a whirlpool galaxy, and infers that its spin connection is its angular velocity. It is found that:
1) Any planar orbit becomes a hyperbolic spiral as r goes to infinity if v becomes constant. This is precisely as observed in the spirals of stars in a whirlpool galaxy.
2) The spin connection vanishes in the limit of infinite r if v becomes constant as observed in a whirlpool galaxy.
3) The velocity becomes a straight line in the limit of infinite r if v becomes constant, again as observed in whirlpool galaxies. The stars on the limbs of some spirals are straight lines.
The entire analysis is based on the covariant derivative of Cartan, Eq. (9), so this is a theory of general relativity. The next step is to link it up with the analysis of note 262(1) and UFT261.

262(3): Force Law for the Whirlpool Galaxy

In thsi note this is derived using Lagrangian dynamics and the fundamental kinematics of the plane polar coordinates, i.e. the fundamental geometry, an example of Cartan’s more general geometry. It has been shown in note 262(2) that any planar orbit must become a hyperbolic spiral if its orbital linear vlecity becomes constant as r goes to infinity. This is precisely what is observed in a whirlpool gaalxy. The force law for this hyperbolic spiral orbit is the inverse cube of Eq. (20), the potential is the inverse square of Eq. (25). These do not contain M , the mass thought to be at the centre of a galaxy. The orbit is independent of M, and this is the result of fundamental kinematics appearing in every textbook such as Marion and Thornton Classical Dynamics”. The kinematics also give Eq. (22) self consistently, indicating constant velocity again. A whirlpool galaxy is therefore totally non Newtonian, and totally non Einsteinian. Both Newton and Einstein contain M, and Einstein is only a tiny correction to Newton (Eqs. (27) and (28) of this note). Newton is non relativistic, and Einstein developed his theory without torsion, a fundamental blunder rectified by ECE theory. After all this is the Einstein Cartan Evans (ECE) theory named in honour of Einstein and Cartan. Elementary geometry is therefore necessary and sufficient to describe all the main features of a whirlpool galaxy. Cartan geometry reduces to the geometry of plane polar coordinates, in which the axes are rotating, generating a spin connection. So this is a triumph of simplicity and direct comparison with experimental data, William of Ockham and Francis Bacon. As Peter Debye write: “Complexity is lack of understanding”. This note is classic natural philosophy. The standard physics is not physics at all, it is a complete shambles made up of dogma and hyper complexity that leads nowhere at all.

a262ndpapernotes3.pdf

Daily Report 28/5/14

There were 1882 hits from 497 distinct visits, hits counter has returned to normal after being jammed for most of May by a site trying to download UFT107 out of control. Spiders from baidu, google, MSN and yahoo. Essay broadcast 24 by Robert Cheshire on the Derivation from Geometry of the Pauli Exclusion Principle, 910, F3(Sp) 688, Auto1 542, Auto2 89, Book of Scientometrics 188, UFT88 166, Evans Equations 85, numerous (Spanish), CEFE 85, “Llais” 75, Engineering Model 59, Englynion 22, Autosonnets 13 to date in May 2014. Brandon University Canada general; University of Quebec Trois Rivieres Crothers’ reply to Sharples; Duke University UFT102; Georgia Institute of Technology UFT237; Chemistry University of North Dakota UFT177; Engineering University of Michigan Spacetime Devices; University of Utah ECE Devices; University of Poitiers general; Ritsumeikan University Japan UFT80; United States Army Aviation and Missile Research and Development Center (AMRDEC) UFT41; United States Naval Marine Command general; University of Guanajuato Mexico F3(Sp); Norwegian Institute for Energy Technology Proof Five (Sp); University of Aberdeen UFT2. Intense interest all sectors, updated usage file attached for May 2014.

Usage Statistics for aias.us aias.us

Summary Period: May 2014 – URL
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