Eratosthenes was a Greek mathematician born in Cyrene in 276 B.C. He was not the first one describing the Earth as a sphere. Plato and Aristotle had done before. Aristotle’s disciple, Plato, wrote that the Creator “made the world in the form of a globe, round as for a lathe, having its extremes in every direction equidistant from the centre, the most perfect and the most like itself of all figures,” “one of those balls which have leather coverings in twelve pieces…” (Plato. Phaedro. p. 110b; Timaeus. p.33).
Eratosthenes made an amazing experiment: he measured the Earth circumference. Due to their seeming precision, its results are still considered to be stunning. You shouldn’t forget how simple were the instruments used by the Greeks.
He posited, with only a slight imprecision, that Alessandria of Egypt and Syene, were on the same meridian, Syene being on the tropic, at a distance of 800km from Alessandria.
Picture from Wikipedia.
Eratosthenes and the measures of the globe
At the solstice of the 21st of June, the sun was perfectly perpendicular at Syene and this could be verified by the aid of a well situated there. When the light of the sun had reached the bottom, the solstice was right on Syene. In that very moment, in Alessandria, a pole was projecting a shadow with an angle of 7.2 degrees.
Eratosthenes understood that 7.2 is about 1/50 of 360°, so multiplying 50x 800km he was able to state that the circumference of the globe was of 40000km.
Ok, so far so good. But here comes the poison arrow.
Now, having observed the deserved minute of silence, in due commemoration, let’s go deeper into the topic.
Discussing Eratosthenes hypothesis
Eratosthenes made two hypothesis at the start:
1) The Earth is a globe, and this is the reason why the sun projects a shadow in Alessandria with a 7.2° angle;
2) The sun’s rays are parallel (see the picture) because the sun is very far from the Earth.
This second assertion needs further discussion. Science today is stating the sun is 150 million km far from the Earth. The Sun’s diameter is reckoned to be 1391400km, while the diameter of the Earth is only 12742km. When drawing the sun and the Earth in the correct proportions and respecting the convenient distances, with a 3d cad software we obtain this model:
The pattern above makes it clear that the sun’s rays reaching the Earth should really be parallel, there is no alternative. So, dear guys, can you explain me the following images?
The sun’s diverging rays
The images above clearly show that the sun’s rays are not parallel but diverging with some quite big angle. These pictures clearly prove that the sun can’t be so far as official science states. As a consequence, Eratosthenes’ hypothesis cannot be valid. If the sun’s rays diverge, it is evident that the mathematician was wrong and the angle of the shadow he had measured had not been generated due to the fact the Earth is a sphere, but directly by the divergent sun’s rays acting on a flat surface.
This is the real situation:
Eratosthenes’ experiment and its deeper implications
The consequences of the reasoning I have till now exposed are quite surprising:
- The Earth is flat;
- The Earth is motionless;
- The Sun is not so far;
- The Sun is quite small;
- Newton’s and Einstein’s gravity laws are not reliable.
Eratosthenes and the perspective laws
|Objection 1: The sun’s rays are actually parallel, but we perceive them as diverging due to perspective.
Answer: “Ah, mmh, ok, in this case, I see, it would be the perspective to cause the divergence of rays? ah… it’s the same notation I have found in Wikipedia at the voice “Crepuscular rays”. Since some rays are nearer and other are farther, maybe not always, but at least sometimes, this perspective phenomenon could really happen. Let’s analyze the situation.
In what extension does the perspective act in our visual field?
Let’s examine the following image:
While observing the image above I am aware that there are lines that converge to one point laying on the horizon while the vertical lines continue to be parallel: perspective doesn’t act upon their being in a parallel perspective. From there I can derive a rule: all the lines that lay on a plane perpendicular to the direction of sight are not touched by the perspective; all lines parallel to the direction of sight converge on a point on the horizon.
The multi-point perspective
Let’s similarly consider the multi-point perspective below.
In the following image, there is a three-point perspective image.
The horizontal lines of the two visible walls converge in two different points laying on the horizon while the vertical lines, no more parallel one to the other, converge to a higher point in the sky. This last vanishing point is a model for an observer that is looking to a tall building or structure directly from below or from above (the observer is near to the object observed). Why is this image different from the previous one? Why do you have two different more vanishing points? Because the direction of sight is not perpendicular to any of the lines in the picture. In the previous one, the observer was perpendicular to the structure represented in the photograph.
Now, having the aforementioned considerations in mind, let’s analyze a few among the pictures with divergent sun rays which we have presented above. In all these images there is a single converging point for the rays and this is the sun, their source.
Further considerations about the perspective vanishing point
Conclusion: sun rays diverge because the sun is near to the Earth and not due to perspective reasons.
Eratosthenes and the laws of diffraction
Objection 2: Divergent sun rays are appearing with crepuscular rays that pass through the clouds. In these conditions, the diffraction is the main reason for the divergence of the rays.
Answer: Wikipedia states:” Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit. It is defined as the bending of light around the corners of an obstacle or aperture into the region of the geometrical shadow of the obstacle. In classical physics, the diffraction phenomenon is described as the interference of waves according to the Huygens–Fresnel principle. These characteristic behaviors are exhibited when a wave encounters an obstacle or a slit that is comparable in size to its wavelength.”
So the sunlight should diverge when passing through clouds because it encounters slits of the dimension of its wavelength. The wavelength of the visible light is from 390 to 700 nanometer. A nanometer is 10^-9 meter. Look again at this image:
Is that opening in the clouds less than 700nm? I don’t think, it seems to be several hundreds of meter.
Conclusion: rays diverge not because of diffraction.
Eratosthenes and the optic laws
Objection 3: sun’s rays diverge because the atmosphere acts as a diverging lens.
Answer: The atmosphere of a globular Earth is a globe and acts thus as a convex lens with the light of the Sun. In the image below you can see the behavior of a convex lens.
A convex lens is a convergent lens. We should thus see the rays arriving parallel from the sun, converging on the Earth.
Conclusion: the sun’s rays diverge because the sun is near and not because the atmosphere acts like a diverging lens.