Spirals and the sun analemma

Spirals are on the basis of the sun movement. A few months ago, I have illustrated how an ether vortex could be detected in 1925 by the use of an interferometer (Michelson Gale experiment made with a huge Sagnac 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 at the origin of any motion along the cone. Can we define an equation for the trajectory of the sun? By analyzing the equation of spirals we can find an equation able to define a curve fit to describe the path of the sun. In this equation there are two variables: r, i.e. the distance from the North Pole, and ϑ, the angle that we measure in a counterclockwise direction starting from the Greenwich meridian; z will indicate 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 have to give a brief explanation.

Some special numbers

6660 is the radius of the Tropic of Capricorn. By describing the spiral, it is quite astonishing that the sun trajectory 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 equal to 111*4/5. 111 is a number having a special relationship with the Earth and the sun. 6660, 13320, 9990 are all multiples of 111.

Theta (ϑ) varies from minus 360pi to plus 360pi. They represent the number of turns necessary to make an entire cycle from the Tropic of Cancer to the Tropic of Capricorn, and back to return.

A very good first approximation

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 fractals will just be a repetition. A more precise description would not be as good as this.


However, it could be necessary to make a more precise calculation. For example, someone could desire to build a more precise model, maybe with the help of the calculator by using software like Matlab or Octave.

For example, 6660 km is the first fractal to define the position of the tropic of Cancer. But, if I want to make a more precise calculation using the math till now considered, we have to remember that in the globe the tropic is reckoned to stay at 7400km from the North Pole. Thus, we will define the smaller fractals this way:


On the globe, the Capricorn tropic is at 12600 km from the North Pole. Consider this series:


The spiral of the sun can be described by using these numbers. It will become:

In this equation, it will be clear the role of the number 666 in the description of the trajectory of the sun. The equation can, in fact, be rewritten:

This equation is still valid and considers not only the main fractal but also some smaller fractal and is incredibly precise by using the math studied till now.

The equator is nearer to the Tropic of Capricorn

We said in the past that, by using 6660 and 13320 km as radiuses of the two tropics, the equator is not set in the center. It is, on the contrary, nearer to the Tropic of Capricorn, as shown in the following picture.

This means that the equator is at 6660+4440=11100 km from the North Pole. But this is only the first fractal. On the globe, the equator is at about 10000km from the North Pole.

We can check our result by using this last more precise equation to see the position of the equator with some more fractal.

The equator is in the middle (time speaking), thus the sun passes over it after three months, i.e. ϑ=365.25/2pi=574 radians. If we put this angle in the first equation we obtain r = 7400+3377=10777km This result confirms the idea that the equator is nearer to the Capricorn tropic. It is due to the fact the Earth is not symmetrical as science states since it is flat.


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.

The 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 with 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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