Archive for August, 2014

## Animation of elliptic 3D orbit

This is an excellent animation and shows immediately that the 3 -D orbit is a lot more intricate than the 2 – D orbit. The inversion problem is indeed a difficult one, and goes right back to Kepler himself. The computer might be able to find the answer straightforwardly. As Horst writes this should be regarded as a first attempt, but it is already full of originality. Obviously we have opened up a completely new subject area in cosmology upon which all can agree because it is based on the spherical polar coordinates.

To: EMyrone@aol.com
Sent: 31/08/2014 14:44:45 GMT Daylight Time
Subj: Animation of elliptic 3D orbit

This is an animation for the beta ellipse in 3D, parametrized by the theta angle. Since the theta grid has been chosen equidistant, the motion speed is not physical. I am not sure if the orbit is compatible with the first 3D surface r(theta,phi) shown in paper 269,3 (Figs. 3/4). Normally this should be a trace on the surface. This has further to be analysed. It would also not be straightforward to compute the right timing behaviour because the time function has to be inverted which has to be done numerically.

Horst

## 270(2): Interpretation of the Dynamics for Constant Theta

In this note the correct interpretation of the dynamics is given for constant theta. It is sufficient to understand the orbit in terms of Eq. (16) both for constant and non constant theta, (2-D and 3-D orbits respectively). There is no reason from the inverse sqaure law why a 3 – D orbit becomes a 2 – D orbit, but the geometry shows that all 2 – D orbits must precess. Some other mechanism must be at work to make the 3 – D orbit evolve to a 2 – D orbit. The inverse square law in 3 – D always transforms to a precessing ellipse in the 2 – D limit. For over four hundred years it has been thought that the inverse square law produces a non precessing ellipse. The error in the analysis was to restrict consideration to 2 – D from the outset. This error goes right back to Newton and Hooke, and was never corrected.

a270thpapernotes2.pdf

## The Angle x = sin theta

The latest result in note 270(1) shows that there is an angle theta defined by x = sin theta in all planar precessions of m around M defined by the inverse square law of universal gravitation. So planetary precession is due simply to three dimensionality itself, a result as graceful as the swallow (y wenol). The precessing planar orbits must have evolved over a span of time from three dimensional orbits (r, theta, phi) to two dimensional orbits (r, phi) with fixed theta defined by x = sin theta, where x is the observed precession factor. Once this is realized there is no need for any further analysis unless one wishes to go deeper in to the origin of x. We already know that x is due to the ubiquitous Thomas precession of special relativity. By Ockham’s Razor the new theory is preferred to the far more complicated and incorrect Einsteinian general relativity. The observed precession factor is

x = 1 + 3MG / (alpha c squared)

= sin theta

## 270(1): Planetary Precession from the Classical Inverse Square Law

Using three dimensional orbits in the planar limit, it is shown that the planetary precession in the (r, phi) plane can be explained with

x = sin theta

where

x = 1 + 3MG / (alpha c squared).

So it is possible after four centuries (1600 to present) to explain planetary precession with the classical inverse square law. This is achieved by considering three dimensional orbits. Einstein’s theory is not needed and is completely incorrect. The factor x can be measured in astronomy and used to give a fix on theta of the (r, theta, phi) spherical polar system. Alternatively x can be understood with special relativity, the ubiquitous Thomas Precession, and converted very simply into a constant sin theta. This is yet another major advance in understanding made with x theory. It would be very interesting to graph the transition to a planar orbit from the three dimensional orbit. I don’t think anyone can have any objection to this result, it is the direct result of the spherical polar coordinates, which using a deeper analysis come from Cartan geometry. Conversely, if anyone does object to this they will reveal themselves as hopelessly prejudiced. So this is a useful note in many ways.

a270thpapernotes1.pdf

## Plans for UFT270

Having discovered a simple method of describing three dimensional orbits, it is planned in UFT270 to develop the theory of precessing 3-D orbits of various kinds, notably those found in three dimensional galaxies. I think that it is important to graph the transition from a 3-D orbit to the usual planar orbit in 2-D. This occurs as theta approaches pi / 2 and L sub theta approaches zero. The 3 – D Binet equation can be used to find the force law for any 3 – D orbit. So far all the 3 -D orbits have come from the simple inverse square law of universal gravitation. An amazing variety of results appear when we go three dimensional.

## Daily Report 29/8/14

There were 2506 hits from 351 distinct visits, spiders from baidu, google, MSN and yahoo. F3(Sp) 533, Auto1 440, Auto2 109, Essay25 306, Book of Scientometrics 206, UFT88 83, Evans Equations 60 numerous Spanish, Engineering Model 52, Englynion 40, UFT99 34, UFT267 31, CEFE 29, Principles of ECE 9, Autosonnets 7 to date in August 2014, no wiki referrals, AWStats unchanged. Denver University Autobiography Volume One; Georgia Institute of Technology LCR Resonant; British Library general. Intense interest all sectors, updated usage file attached for August 2014

## Usage Statistics for aias.us aias.us

Summary Period: August 2014 – URL
Generated 30-Aug-2014 12:00 EDT

## Immediate Interest in UFT269

There was an immediate spike of interest in UFT269 Sections 1 and 2 on the blog yesterday, because it is a fundamentally new advance in three dimensional orbits. There was also an immediate spike of interest the day before yesterday in co author Horst’s Eckardt’s graphics and analysis pencilled in for Section 3. The www.aias.us blog currently has 19,556 postings since Dec. 2006. Since 1/1/10 There have been 265,141 viewings. Since 25/2/12 these have been from 171 countries led by Britain, United States, Canada, Germany, Australia, France, ……. The average number of viewings a day was 75 in 2010; 112 in 2011; 195 in 2012; 196 in 2013 and 225 to date in 2014. This is a cultural blog and is my private diary, with entries on science, literature, genealogy and history. with occasional artwork. The new three dimensional orbits are works of art in their own right, and a rigorously scientific new discovered solution to the problem of three dimensional orbits. So many thanks again to those who helped construct the blog, notably Sean MacLachlan of Hewlett Packard in Boise, Idaho, Horst Eckardt and others. Both Sean and Horst are in “Marquis Who’s Who in the World” and their bio’s can be looked up online. Unlike Penrose and Hawking of the obsolete physics I correspond with nearly everyone, via e mail. Preferably I like to see affiliation and qualifications, but if someone is polite and sincere I correspond irrespective of qualifications. Penrose and Hawking are unable to defend their work against ECE and refuse to correspond. So that era is well and truly over. Regrettably, AIAS has no time to evaluate every theory sent to us for comment, but if something is relevant to ECE it is given consideration. AIAS is made up of volunteers and they nearly all have a full time job, so their time is limited. Douglas Lindstrom and I are able to work full time for AIAS. I am also glad to correspond on other matters covered by the blog: poetry, genealogy, history, music and art. The blog is archived by AIAS fellow Michael Jackson in Texas and then archived at the British Library in London every quarter from the National Library of Wales as part of the archiving of www.aias.us every quarter on www.webarchive.org.uk, the digital archive of outstanding websites of the countries of Britain.