Johannes Kepler: from "Mysteries" to "Harmony"

Johannes Kepler is known for all educated mankind as the author of the three famous astronomical laws inverted the astronomical ideas existed from antique times. But it is less known, that these laws were obtained by Kepler as the private outcomes of his grandiose program on research of the Universe harmony put forward by him in young age.

Johannes Kepler

Johannes Kepler was born in 1571 in the poor protestant family. In 1591 he enrolled in the Tubingen Academy where he got a quite good mathematical education. Just there the future great astronomer was acquainted with the heliocentric system by Nickolai Copernicus. After graduation completion of the Academy Kepler obtained a Master degree and then was appointed mathematics teacher in the Graz High School (Austria). The small book with the intriguing title "Misterium Cosmographium" published by Kepler in 1596 in the age of 25 years was his first astronomical work.

Reading this first Kepler's book it is impossible to be not surprised by his imaginations. A deep belief in existence of the Universe harmony imposed an impress on all Kepler's thinking.

The purpose of his researches is formulated by Kepler as the following:

"The kind reader! In this book I intended to demonstrate, that the all-good and almighty God at the creation of our moving world and at the arrangement of the celestial orbits used the five regular polyhedrons, which from Pythagor and Plato's times and up to now got so loud glory, and selected a number and proportions of celestial orbits, and also the relations between the planet motions pursuant to the nature of the regular polyhedrons.

Especially I interested by the nature of the three things: why the planets are arranged so but no otherwise, namely, a number, sizes and motions of celestial orbits".

So, already in the foreword to his first book the 25-year's Kepler put forward the problem being the main problem of the new time physics, the causes problem of natural phenomena. So natural today, this problem during Kepler's times sounded unusually. In Ptolomey's anf even in Copernicus astronomy this problem did not be formulated. Following to this old tradition, the astronomers considered a problem of the science only in possible precise description of planet's motions and prediction of celestial phenomena.

How Kepler answered the surprising problems? After check of numerous hypotheses connected with arrangement of planets Kepler came to the following geometrical model of the Solar system based on the "Platonic Solids":

"The Earth orbit is the measure of all orbits. Around of it we circumscribe the dodecahedron. The orbit circumscribed around of the dodecahedron is the Mars orbit. Around of the Mars orbit we circumscribe the tetrahedron. The orbit circumscribed around of the tetrahedron is the Jupiter orbit. Around of the Jupiter orbit we circumscribe the cube. The sphere circumscribed around of the cube is the Saturn orbit. In the Earth orbit the regular icosahedron is inserted. The orbit entered in it is the Venus orbit. In the Venus orbit the octahedron is inserted. The orbit entered in it is the Mercury orbit".

Kepler figured his model geometrically as the following:

The geometrical model of the Solar system

In Kepler's opinion, the secret of the Universe consists of the following: the Universe is arranged on the basis of the unified geometrical principle! But Kepler's joy was prematurely. In spite of his exaltation character Kepler had all capacities of serious scientist. Kepler perceived, that the theory should be coordinated with observations data. By constraining his delight Kepler undertakes to check his model.

The unified geometrical principle allowed to Kepler to give the answer on two of three problems put forward by him: (1) to explain a number of the known then planets (with the help of the five "Platonic Solids" it is possible to construct 6 orbits; it follows from here a conclusion about existence of 6 planets known in that period); (2) to give the answer to the problem about distances between planets.

The answer to the third problem (about motion of planets) appeared by most difficult and its solution was got by Kepler many years after.

Kepler's model was based on the supposition about spherical nature of planet's motion. By receiving to his disposal the data of perennial observations of the famous astronomer Brage and by making his own observations, Kepler made convinced of necessity to reject astronomical constructions as his forerunners, Ptolomey and Copernicus, and his own one's. Carefully observing the planet orbits he came to the following conclusion:

"The fact that the planet motions are circular is testified by their incessant repeatability. The mind extracting this true from experience at once concludes from here, that the planets are rotated on the "ideal" circles, wherefore among the plane figures the circle and among the spatial figures the celestial orbit are considered as perfect. However at the more close examination it appears that the experience learns a little bit other, namely: planet's orbits differ from simple circles".

The tireless search of the laws corresponding to the observational data ended by discovery of the three famous laws of planet's motion. The former two laws were stated by Kepler in the book "New Astronomy", published in 1609.

The first Kepler's law in contradictory with the astronomical tradition introduced the ellipse as geometric model of planet's motion. The first Kepler's Law asserts, that planets move on ellipsoidal orbits. But it keeps silent about a question how fast are moved the planers on their orbits. The answer this question is given by the second Kepler's Law, which asserts: "the areas covered for equal time by the segment, draw from the Sun to the planet are equal".

But one relevant problem remained unsolved. Under what law the distances from the Sun to planets change? The matter was complicated by the fact that the distances from the planets to the Sun are non-constant and Kepler attempts to grope for a new principle for the solution of this complicated problem. Here again the philosophical Kepler's beliefs ascending to Pythagor and Plato came on the aid. According to Kepler's deep belief the God created the nature on the basis not only mathematical but also harmonic principles. He believed in "music of spheres", which charming melodies are embodied not in sounds but in planet's motions capable to bear harmonic consonances. Following to this idea, Kepler by the way of surprising combinations of the mathematical and musical nature arguments came to the third law of planet's motion, which asserts: "If is a cycle time of the planet circulation around of the Sun, and D is its middle distance from the Sun, then we have:

T2 = kD3,

where k is a constant equal for all planets".

Kepler expressed his joy by the obtained result in the following words, which can be considered as the glory hymn to the Creator:

"The wisdom of the Creator is endless and his glory and power are borderless. You, the skies, glorify Praise to him! The Sun, the Moon and planets, glorify the God on their inexplicable language! You, celestial harmonies comprehended his wonderful creations, glorify Praise to him! And you, my soul, eulogize the Creator! Everything is built by him and everything is embodied in him. Everything best that is known to us is created in him and in ours bustling science. The Praise, the Honor and the Glory to him for all eternity!".

So the drama stage in astronomy development was finished. It was completed by discovery of the three major astronomical laws of planet's motion, Kepler's Laws. And this history began from the rather original model of the Solar system based on the "Platonic solids". Though his model, in the issue, appeared erroneous Kepler did not refuse from it and considered this model as one of his highest scientific achievements. Succumbing to the requests of his friends Kepler in the twilight of his life undertaken the second issuing of his first book "for benefit not only booksellers, but also scientists". Addressing to a new reader Kepler already at the end of his life path wrote with pride in his Dedication:

"Almost 25 years passed since I issued a small book "Misterium Cosmographium". And though in that time I was very young and this publication was my first astronomical work, nevertheless an success accompanying to it in the subsequent years testifies eloquently that never and anybody cannot to write the first book more considerable, successful and valuable for treated subject. As if oracle from skies dictated to me the chapters of this book, as all of them, on a common opinion, were excellent and corresponded to true. To me, during here 25 years working on by transformation of astronomy, the chapters of this book illuminated my path many times. Almost all astronomical works, which was published by me for this time, take the beginning in this or that chapter of my first book and therefore can be considered as more in-depth or more full presentation of these chapters. A reason of this is not in the fact, as if I acted so from my love to my discoveries but in the fact that the nature of things reinforced extremely precise observations of Brage resulted me to the conclusion that there is no other path to transformation of astronomy, reliability of computations, and to construction of the metaphysical part of astronomy called also as physics of skies, except for that path, which I described in this book in detail or I scheduled timidly (if I did not have some more steep confidence)".

But there came old age. The death (in 1630) interrupts Kepler's work under the last book "Somnium" ("Dreaming"), the first scientific-fantastic novel about flight on the Moon. But about harmony was not written any more word. There were no captious checks; there were no new hypotheses. The Kepler is tired: "My brain gets tired, when I attempt to understand, that I have written, and it is difficult to me already to reestablish connection between figures and text, which was found by me at one time have ...".

So the drama was finished. With Kepler's death his discoveries were forgotten. Even the wise Descartes does not know about Kepler's works. Galilei had not found necessary to read his books. Only for Newton the Kepler's Laws find a new life. But the harmony was not be interested for Newton. He had the Equations. There came new times.

Kepler terminates the epoch of "scientific romanticism", the epoch of harmony and golden section, that was inherent in the Renaissance epoch. But on the other hand, his scientific works became the beginning of the new science, which began to develop, since the works of Descartes, Galilei and Newton.

But with Kepler's death the golden section considered by him as one of the "geometry treasures" was forgotten. And this strange oblivion is continued almost two centuries. The interest in the golden section is revived again only in the 19th century. And we will tell about it on the next pages of our Museum. Follow us!