Alpha Institute for Advanced Studies

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

where x is a very complicated function of r. This is not a precessing ellipse as EGR claims because a precessing ellipse needs a constant x close to unity. This conclusion follows from the fact that the EGR force law is of the type

F(r) = A / r squared + B / r fourth

Equating this with eq. (16) will produce a very complicated x(r), and not a constant x. To find x(r) will need computer algebra, it is so complicated. The EGR claim is seen to be wildly incorrect without having to do any calculation, because a constant x is obtained if and only if the force is

F(r) = – mMG x squared / r squared + ( x squared – 1) L squared / (m r cubed)

As Quintilian would have said in the first century A. D., there is virtue in truth.

cos (ix theta) = cosh (x theta)

as is well known. So it has been proven that the fractal conical sections can be transformed into the fractal hyperbolic spirals. Using lagrangian dynamics, I will now proceed to find the force law when x is a function of r, and not a constant.

paper216-3.pdf

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

with

epsilon < 0

It will be very interesting to explore this new class of conical sections systematically. It will probably give all types of spiral orbits as found in whirlpool galaxies, and all kinds of new orbits hitherto unknown when x is allowed to range over all its values. This class is discarded as “undefined” by Marion and Thornton.

a218thpapernotes3.pdf

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

The world is your proverbial oyster. In general any orbital anomaly can be looked for and new explanations sought.

In a message dated 05/05/2012 09:03:37 GMT Daylight Time, writes:

Prof. Evans,

A while back (2/23/12 to be exact) Rob Fell sent a link to the following NASA youtube video showing water droplets spiraling around an electrically charged knitting needle in microgravity.

[youtube http://youtube.com/w/?v=qHrBhgwq__Q&feature=relmfu” title=”http://www.youtube.com/watch?v=qHrBhgwq__Q&feature=relmfu]

Some water droplets orbited in an inward spiral until finally sticking to the needle. However, other droplets orbited first in an inward spiral and then spiraled OUTWARD again!

The logarithmic (ever decreasing r) orbit can explain the former, but one can get the inward/outward orbit with an ‘elliptical orbit’ having an x value < 1 such that x is a reduced fraction p/q, where p=1, q = some N where the number of inward (and outward) spiral loops appears to be N/2. (See attached example.)

Ray Delaforce

Subject: Agreement between Concepts and Methods

This is excellent agreement between concepts and methods, thanks again. I will proceed in the next notes to hyperbolic orbits, the circular orbit was first inferred in UFT193 ff and again confirmed numerically by Horst Eckardt, who noted that it could mean trapped light.

In a message dated 04/05/2012 19:43:07 GMT Daylight Time, writes:

This is what I found already numerically: an inward spiralling orbit appears if x goes to zero and becomes complex valued.

Horst

Am 04.05.2012 15:44, schrieb EMyrone

This note shows how a fractal conical section can be transformed into a logarithmic spiral orbit (7) in which r goes to zero with increasing theta. The condition is very small x but identically non-zero. If x is identically zero a circular orbit results. So if the claims for a decreasing r are true in binary pulsars, then it can be explained very easily with the new universal gravitational potential entirely without EGR, and without gravitational radiation which has never been observed. Such simple explanations are too inexpensive to be funded. So in the exigencies of the physics machine simple explanations are rejected for hugely elaborate hyperexpensive nonsense which, however, can be funded.

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

and this equation describes the precessing elliptical orbits, a large class of orbits. Using lagrangian dynamics the new universal force law was discovered. It turns out that the above equation can describe ALL orbits using only x. It would be very difficult to find an orbit that it does not describe. In addition it gives the fractal conical sections, hitherto unknown in pure mathematics, the multi leaved petal orbits and so on. If one places oneself back in 1788, when Lagrange inferred his method, the reasonable enlightenment of his contemporaries such as Voltaire or Mozart would have smiled the smile of reason. EGR cannot produce this equation, it produces a scowl of dark matter and the junk rap of false authority in science.

delta theta = 2 pi (x – 1)

per revolution of 360 degrees in theta. Usually for Mercury this is claimed to be 43 arcseconds per century, but the Miles Mathis site for example criticises this claim severely. The above angle is however the precession of the perihelion for any type of fractal orbit:

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

One arcsecond = 4.848 microradians, so x – 1 for 43 seconds of arc is about ten power minus six per hundred orbits (a century), or ten power minus eight per orbit, so x is very close to unity. Mathis claims (quite convincingly but ignored by EGR dogmatists) that Einstein mixed up the Mercury year with the earth year and that in the traditional method some precessions are treated classically with Newton, while only the 43 arcseconds one is treated with EGR (again that is convincing but of course ignored by EGR dogmatists). In great contrast the above two equations are very simple and treat all precessions in the same way. As x increases, the precession angle increases and all kinds of amazing new orbits appear, all unknown to science.

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

So how is it possible for a theory as wildly wrong as EGR to give “precise” results? If people want to continue to be dogmatic they can, but not at the expense of the tax payer. The force law given by EGR is also completely wrong, it is a sum of inverse square plus inverse fourth power. How is it possible for EGR to come up with a “precise” value for light deflection when it basics are incorrect? One can forget about big bang and black hole theory if one wants to be a scientist. All this is a prime example of Langmuir’s pathological science – often repeated dogma. When the elegant and powerful eighteenth century methods are used, EGR disintegrates.

217(2).pdf