These are generous remarks by GJE as ever. The A(t) function is a constant of integration in the sense that it does not depend on theta in a theta integration, must depend on time for there to be a three dimensional orbit. In order to model the evolution over time of a three dimensional orbit to a two dimensional orbit a correlation function is needed, indicating a background stochastic force in addition to the inverse square force. The Langevin equation and Debye theory give a plateau in the far infra red and fail completely. The memory function develops the friction coefficient and explains the far infra red. While working with the Brot group in CNRS Nice I learned of the rotational velocity correlation function which when Fourier transfromed gives the far infra red power absorption coefficent. This technique was applied in Omnia Opera 5 back at the EDCL while I was a Ph. D. student (Auto Two). That was the happiest time of my professional life apart from the last ten years of working with AIAS, the Ramsay Memorial Fellowship of 1976 to 1978 and a short interval at Cornell Theory Center (1988 – 1992). There is no doubt that both the spiral and the helix replicate themselves throughout nature, and we now know that the ellipse does the same, more accurately the precessing ellipse.

To: EMyrone@aol.com

Sent: 01/09/2014 22:25:59 GMT Daylight Time

Subj: Re: Beta Orbit with Finite A(t)PS

What you may also be providing here is a fundamental new insight into the structure of dna (double helix held together by hydrogen bonds). In particular why there is a helical structure in the first place ( that would probably spiral outwards without the hydrogen bonds holding the two structures together).

Pauling got quite close to deciphering this structure as I recall from one of Mansel’s remarks ( before or about the same time as Watson and Crick). Point is, you may have “stumbled” on something very fundamental, all contained within the same theoretical framework, that is replicated in a number of ways throughout nature.

That a three dimensional orbit can become a planar two dimensional orbit over the course of time is an amazing discovery. Watson and Crick’s discovery deserved a Nobel Prize. So does yours ( and this is just one of many new discoveries)!!

Sent from Samsung Mobile

Subject: Beta Orbit with Finite A(t)

For an inverse square law of attraction this orbit is:

r = alpha / ( 1 + eps cos beta))

where:

beta = (L / L sub theta) theta + A(t)

The time dependent A(t) could be modelled with an exponential decay

A(t) = A(0) exp ( – t / tau)

where tau is a kind of relaxation time. if A(t) is assumed to be a correlation function:

<A(t)A(0)> / <A(0) squared> = exp (- t / tau)

then this would be Debye relaxation theory given by a Langevin equation, the stochastic force of which being the cosmic background force (Brownian motion force). The correlation function falls from unity to zero. When it reaches zero the orbit becomes planar and non precessing. Otherwise the orbit is always three dimensional. The Debye relaxation time tau must be obtained by measurement, it is of the order of millions to billions of years. There are many ideas like this that can be tried. The key point is that the orbit is a non precessing ellipse if an only if A(t) is zero, has relaxed away to zero over billions of years. At very short times the Debye theory fails completely (Omnia Opera first few papers) and is replaced by memory function theory. That could model what happens in the early stages of a galaxy or solar system orbit.