 Precession of the Planets, or What was Plato Writing About?
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.
you Hellenes are never anything but children, and there is not an old man among you.
nor any science which is hoary with age.
and know nothing of what happened in ancient times..."
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".
"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.
Now when the spirits which were in the meadow had tarried seven days, on the eighth they were obliged to proceed on their journey, and, on the fourth day after, he said that they came to a place where they could see from above a line of light, straight as a column, extending right through the whole heaven and through the earth, in colour resembling the rainbow, only brighter and purer; another day's journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above: for this light is the belt of heaven, and holds together the circle of the universe, like the under-girders of a trireme. From these ends is extended the spindle of Necessity, on which all the revolutions turn. The shaft and hook of this spindle are made of steel, and the whorl is made partly of steel and also partly of other materials.
Now the whorl is in form like the whorl used on earth; and the description of it implied that there is one large hollow whorl which is quite scooped out, and into this is fitted another lesser one, and another, and another, and four others, making eight in all, like vessels which fit into one another; the whorls show their edges on the upper side, and on their lower side all together form one continuous whorl. This is pierced by the spindle, which is driven home through the centre of the eighth.
The first and outermost whorl has the rim broadest, and the seven inner whorls are narrower, in the following proportions — the sixth is next to the first in size, the fourth next to the sixth; then comes the eighth; the seventh is fifth, the fifth is sixth, the third is seventh, last and eighth comes the second.
Mortal souls, behold a new cycle of life and mortality."
— Plato, The Republic, Book X.
In notes to the Russian edition of Plato's dialogues there are figures of the spindle of Necessity.
Antique spindle which corresponds to the shape of the spindle of Necessity.
View of the spindle of Necessity from above.
Roman numerals denote the numbers of whorls.
Arabian numerals denote the ratio of their surfaces.
The sizes of circles (fig. 2) are calculated amenably to the description in the dialogue "Timaeus" .
"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 (27).
After this he filled up the double intervals (i.e. between 1, 2, 4, 8) and the triple (i.e. between 1, 3, 9, 27) cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes (as for example 1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and one-third of 2 less than 2), the other being that kind of mean which exceeds and is exceeded by an equal number. Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. And thus the whole mixture out of which he cut these portions was all exhausted by him.
This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three (Sun, Mercury, Venus) he made to move with equal swiftness, and the remaining four (Moon, Saturn, Mars, Jupiter) to move with unequal swiftness to the three and to one another, but in due proportion."
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.
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.
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.