Spirals and the sun analemma

Spirals are on the basis of the sun movement. In my latest article, I have illustrated how an ether vortex could be detected in 1925 by the use of an interferometer. The speed of this vortex is comparable to the diurnal speed of the sun. Such a vortex can influence the speed of light that will not be perfectly the same in all directions all over the Earth. The difference is, however, so small that it is not detectable in our normal daily activities. The vortex is the cause of the motion of the sun.

analemma sun

A brief summary

Let’s briefly resume the trajectory of the sun as we were able to understand it till now. The sun moves on a spiral trajectory over a cone. The cone has the following measures:

Height Radius
21 June 6660 6660
21 December 3330 13320

The spiral equation of the sun

The vortex is the motor of all that motion over the cone. Can we define an equation for this trajectory? By analyzing the equation of spirals we can define an equation that seems to define a curve which is the nearer to our model. In this equation we will have two variables that are r, i.e. the distance from the North Pole, and ϑ, the angle that we measure as counterclockwise starting from the Greenwich meridian; z will describe the height. The equation is:

Our readers will immediately recognize some of the numbers of the equation. For people just now approaching our model,  I should give a brief explanation.

Some special numbers

6660 is the radius of the Tropic of Cancer. By describing the spiral, it is quite astonishing that both, the back and forth cone, can be described by a spiral with the exponent 1/1.618, 1,618 being the golden number. In fact, many spirals in nature are golden spirals. The constant 88.8 is, to my eyes, a  rather special number because it equals 111*4/5. 111 is a number having a special relationship with the Earth and the sun. 6660, 13320, 9990 are multiples of 111. This number,  111, is the constant of the sun’s magic square, as you can notice below.

One-fifth of 111 is 22,2. One-fifth of the circle is 72°, being 72  with good precision expressible by 44,4*1,618. Furthermore, 44,4 centimeters, as you probably remember, is the value of the Hebraic cubit.

The first equation describes the motion of the sun from the Tropic of Cancer to the Capricorn one. The angle ϑ describes 180 turns, i.e. a period of six months since we consider one year to be made up of 360 days. The angle varies thus from zero to 180x2Pi, being pi equal to 3. 180 turns equals 1080 radians. One turn equals  2Pi radians.

A very good first approximation

The return will be from 1080 to the double, i.e. one year or 2160 radians. The year is 360 days and Pi is 3. This is because there are irrational values that must be cut to be described. In our model and with our numbers, we chose to cut this way: 360 days for one year and Pi=3. We shall use math this way in order to obtain a very good first approximation: it will be a description of the main fractal of nature. All the other smaller fractal will just be a repetition. A more precise description would not be as good as this.

The equator is nearer to the Tropic of Capricorn

This equation confirms the idea that the equator is nearer to the tropic of Capricorn. By doing the hypothesis that at the equator the height of the sun, either on the tropic of Cancer or on the tropic of Capricorn, should define the same angle, we can find this situation:

Let’s check if this hypothesis can be confirmed:

The equator is in the middle (time speaking), thus the sun passes over it after three months, i.e. 1080/2=540 radians. If we put this angle in the first equation we obtain r = 6660+4350, very near to the 6660+4440 km that we supposed to be the position of the equator.

Drawing the image of the spiral of the sun

Below you can see the image of the spiral obtained by using Octave, free software for the numerical simulation. Unfortunately, my laptop has not a good graphics board and the image gets blurred.

If you want the code to obtain the graph, you can write me at earthmeasured@gmail.com.

Analemma is a tridimensional surface

Anyway, you know that things are not always so easy. Our model of a simple cone is probably not correct. The tridimensional magnetic field that traps the sun between the two tropics is a tridimensional surface that only with a first approximation is a cone. It is a non-orientable surface, a Klein bottle that traps the sun in a complex movement.

The fact that the movement is complex will be clear when you look at the analemma. It is a figure obtained by a secondary movement of the sun over the cone. This figure is obtained by taking a picture of the sun at the same point always at the same time every day, or maybe every week.

Checking the movement of the sun

maybe every week.

The two extremities of the analemma are the two tropics and the sun reaches these points on 21 of June and 21 of December.

Let’s check the motion of the sun after the 21 of June. The sun runs a rather long distance in July. In the graphic, on the first raw, you can see that it is as if the sun would do a 7 minute day longer than usual (the comparison is made with our clock that considers a medium day of the sun and not its real motion). The sun begins to slow in August and at the end of the month, the intersection takes place. In September, October, November, and December the sun moves slower and a medium day in November lasts 17 minutes less. Then again the sun accelerates, the day achieves to be 14 minutes more and then on the 15 of April the intersection can take place. In May and June, the real sun is slower than the medium sun.

These movements are caused by the ether that moves slower or faster than the average.

Perceiving the movement of the sun by the aid of a pine

The question is: how is it possible that the ether, in the same zone, for example near the Tropic of Cancer, during some month goes faster and during some other moves slower? The answer is that the cone is not a flat surface but rather a tridimensional one. In the same way, the analemma is not laying on a flat surface but is a tridimensional curve. To better understand, please, look at this pine cone.

This really looks like the first, lower part of our analemma and one part is in some higher position than the other. We can conclude that the ether moves at different speeds changing with the height. Remember that the ether is the motor, while the bottle is the magnetic grid that drives the sun in its path.

An approximation of the golden number

As you can see in the picture the analemma does not look like a symmetrical number eight. The upper part is smaller than the lower one. In addition, something interesting should be noticed. This is the fact that if you count the number of days in the bigger part of the analemma  (225) and make the division with the number of days of the smaller one (140), you’ll obtain an approximation of the golden number 1,618. You will understand thus that the math of the analemma is linked to the golden spiral.

This is not strange because the movements of the sun and those of the time are linked to the golden number as already explained throughout my blog. Bye, Bye, my reader.

 

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