Abstract. The data of modern astronomy enables us to understand what Plato wrote about more than 2000 years ago. The precession law of the planets of the solar system is formulated. The diatonic structure of the solar system is shown.
Key words: Plato, Ptolemy, Kepler, Hawkins, precession, planets, solar system, precession law, diatonic, temperament scale, pyramids, crop circle, calendar message, music.
"Thereupon one of the priests, who was of a very great
Reading Plato's dialogues, I have found out that the structure of celestial spheres described by him is very similar to the description of a precessional motion of planets. His description is also similar to a picture that I got from the data contained in the Calendar Message . I shall present my results of the analysis of the text of Plato in this article.
Plato (427-347 BC), the ancient Greek philosopher; the founder of Academy — a philosophical school which existed about 1000 (till 529). Plato knew the mathematical and cosmological doctrines of Pythagoreans. Plato wrote about a structure of space in two dialogues — "The Republic" and "Timaeus".
In his dialogue "Timaeus" Plato wrote about seven celestial bodies — "planets":
"The sun and moon and five other stars, which are called the planets, were created by him in order to distinguish and preserve the numbers of time..."
In this article, I shall incorporate the Sun in the number of planets in order to not mention it each time separately.
The information from Plato's dialogue "The Republic" which will be analyzed further, apparently, was so unusual to Plato that he has stated it as a tale about traveling after life . In my opinion, this myth can be understood as a general description of the planets precession and a law to which their precession submits. All this myth is a paraphrase of the saved ancient knowledge which weren't understandable in days of Plato.
"Well, I said, I will tell you a tale; not one of the
tales which Odysseus tells to the hero Alcinous, yet this too is a tale of a
hero, Er the son of Armenius, a Pamphylian by birth. He was slain in battle, and
ten days afterwards, when the bodies of the dead were taken up already in a
state of corruption, his body was found unaffected by decay, and carried away
home to be buried. And on the twelfth day, as he was lying on the funeral pile,
he returned to life and told them what he had seen in the other world.
— Plato, The Republic, Book X.
In notes to the Russian edition of Plato's dialogues there are figures of the spindle of Necessity.
The sizes of circles (fig. 2) are calculated amenably to the description in the dialogue "Timaeus" .
Plato wrote about a structure of space:
"And he proceeded to divide after this manner: - First
of all, he took away one part of the whole (1), and then he separated a second
part which was double the first (2), and then he took away a third part which
was half as much again as the second and three times as much as the first (3),
and then he took a fourth part which was twice as much as the second (4), and a
fifth part which was three times the third (9), and a sixth part which was eight
times the first (8), and a seventh part which was twenty-seven times the first
— Plato, "Timaeus"
This description corresponds to the following figure.
The celestial equator and the ecliptic are really intersected, forming the letter X as wrote Plato.
So, I have described the necessary minimum of data from Plato's dialogues which I shall analyze further.
It is considered that a Greek astronomer, Hipparchus of Nicea (about 160 BC), discovered the phenomenon of a precession. That is, much later, after Plato's time. Therefore, Plato could know nothing about this undiscovered phenomenon yet. What has drawn my attention in Plato's descriptions?
I have paid attention to the spindle (fig. 1) looking like a truncated cone. A rotation axis of a planet delineates a cone during a precession. I wrote about it in the book .
In Plato's description there is also the strange correspondence between numbers of whorls (planets) and the sizes of their circles. It doesn't correspond to any model of the geocentric system known in days of Plato. How to explain such a mixed order of planets?
My attention was drawn more to figure 2 where circles are grouped in three groups on their sizes (2, 2, and 3). The eighth exterior circle is the sphere of the fixed stars.
Now we shall consider the modern data.
Spindle of Necessity
In the Calendar Message  there are data about periods of the precession of the seven planets. When I drew the figure corresponded to these data, it was similar to figure 2. Therefore, the figure 2 created under Plato's description has drawn my attention. Unfortunately, a modern astronomy still has no data about the periods of precession of the planets. However at least, we now have data about the coordinates of the North Poles of planets. These data allow us to get a figure similar to figure 2. Further, I shall show you how to draw such a figure.
On the website Planetary Fact Sheet (NSSDC, NASA Goddard Space Flight Center) there are data about equatorial coordinates of North Pole of all planets. Having made a conversion of coordinates from the equatorial system in the ecliptic and galactic systems I produced the following table.
North Pole of Rotation
I shall take Galaxy to represent the external sphere of Plato's fixed stars (our galaxy "Milky Way").
Let's marked on a celestial chart, the positions of the poles of seven planets (Sun, Mercury, Venus, Earth, Mars, Jupiter, and Saturn) and the North Pole of the Galaxy, and we shall draw through each of them the circles with center on the Ecliptic North Pole.
The astronomical program SkyMap created this image. Ecliptic North Pole is located in the center of image.
Certainly, the figure 5 doesn't show the precise tracks of planets poles during a precession, but as a whole this picture looks so.
Radiuses of circles in the figure 5 are equal (90° - βe) where βe is an ecliptic latitude (see tab. 1). Rows of the following table are ordered on increase of radius.
Now, when we remove the background of the sidereal sky in the figure 5, we see the image of these circles only.
Compare the figure 6 to figure 2 (a view of the spindle of Necessity from above) constructed under Plato's description. They are practically identical. Here we find the same separation of the seven planets into 3 groups (2, 2, 3), and the external eighth circle. Here again there is also a mixed order of planets.
The side view of this picture (without the external circle) can be imagined so.
There you have it. We've got a picture of the antique spindle. Compare the figure 7 to figure 1.
Thus, Plato's description corresponds to the modern picture of a precessional motion of the planets.
I get the impression that someone has popularly explained a precessional motion of planets to our ancestors, paying attention to the importance of this phenomenon for the existence of civilization.
Further, I shall show, that Plato's words about the harmony of celestial spheres are confirmed by the modern data.
To be continued (see Part Two)
Thank you for visiting my website!