Since time immemorial, man has been interested in the starry sky. Not only bewitching beauty and curiosity directed human eyes to the starry sky, but also interest in studying the movement of celestial objects.

Great scientist. Johannes Kepler (1571-1630)

The study of movements and changes in the starry sky allowed people to draw up the first calendars, as well as predict phenomena such as solar and lunar eclipses. Navigators could accurately plot their course by the stars, and travelers could find directions on land. One of the great German scientists who was interested in the movement of celestial objects was the astronomer Johannes Kepler.

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Background.

Even ancient astronomers studied the visible path of the Sun and Moon. They found that the sun describes a semicircle in the sky, moving from west to east. It was also found that there are 365 days in a year. Ancient observers of the sky found that the path of the Sun is not changed, and it appears where it is needed and disappears where it is supposed to. They called this circle the ecliptic, which sounds in Greek - Clipce. The Greeks associated the ecliptic with solar and lunar eclipses. The apparent revolution of the Sun along the ecliptic is the basis of the earth's calendar year.

Ancient astronomers also established that the moon moves from west to east, while making a full circle in 27 days. The most interesting thing is that the motion of the moon is not uniform. It can speed up or slow down the movement to a small extent. The period of apparent movement of the Moon became the basis of the earth's calendar month.

If you look at the starry sky, then it seems that the stars are stationary relative to each other. The starry firmament makes a complete rotation in a certain time, which is called a sidereal day.
Next to the stars, ancient people considered five celestial objects that look like stars, but have a brighter glow. These objects take an integral part in the movement of the starry sky. Their trajectories seemed to ancient astronomers confusing and complex. If we translate the word "planet" from Greek, it means "wandering". AT ancient rome the planets were given names that have survived to this day: Mars, Venus, Saturn, Mercury and Jupiter.

Ancient scientists considered the Sun and Moon to be planets as well, as they also took a walk in the starry sky.

Ancient scientists found that planets located near the ecliptic can change their direction of motion after a certain time. But this was not observed in the trajectories of the Moon and the Sun. These objects made a direct movement of the planets. But at one of the moments the planet reduces the speed of movement, stops in place and begins to move backward, that is, in reverse direction(from east to west). Next in certain moment the planet reverses and returns to its original direct motion. If observations are made visible part the starry sky, it is difficult to understand the patterns of planetary motion. For modern astronomers, there are no longer any secrets of planetary motion, because the gift of knowledge came to them with a centuries-old history of astronomy. Some discoveries were made by the German scientist Johannes Kepler, who discovered in the first half XVII century laws of planetary motion.

Modern knowledge about the solar system was formed in the course of developments and studies of the starry sky over thousands of years. Many ancient scientists contributed to the evolution of astronomy. These are Pythagoras, Plato, Ptolemy, Archimedes and others. Some of them also had misconceptions that have long been proven. Much can be said about ancient scientists and their achievements, but let's return to Johannes Kepler (1571-1630).

Johannes Kepler was fortunate enough to live at the same time as a no less famous scientist - the Italian Galileo Galilei (1564-1642). These two scientists were adherents of the heliocentric system of the world, which Copernicus once proposed.

Heliocentric system of the world of Copernicus.

Johannes Kepler with student years was a supporter of the teachings of Copernicus. Although at the University of Tübingen, where he studied from 1589 to 1592, astronomy was interpreted according to the teachings of Ptolemy.

In 1596, Kepler publishes his first book, The Mystery of the World, in which he reveals the secret harmony of the universe. Kepler's fantasy made it possible to draw the orbits of each of the five planets of the solar system in the form of circles that are inscribed in various polyhedra. correct form- cubes and tetrahedra.

Galileo, having read Kepler's book "Secrets of the Worlds", did not agree with some aspects of the fantastic geometric construction. And 25 years later, Kepler made corrections in his book "Secrets of the Worlds" and republished it in a new way.

The well-known astronomer from Denmark Tycho Brahe (1546-1601) also appreciated the work of Kepler, who read The Secrets of the World and said that its author had good knowledge in the field of astronomy. He liked Johann's thinking and the fact that he produced a large amount of mathematical calculations. In the future, these two scientists met, and Brahe offered the 24-year-old Kepler a job in Prague as an assistant for astronomical observations and calculations. They worked together for several years, and their collaboration was interrupted by the death of Tycho Brahe in 1601. Then Kepler was offered the position of court astronomer at the court of Rudolf II. Kepler left a lot of developments in the field of astronomy from Tycho Brahe, which, with the help of mathematical calculations, made it possible to give the world famous laws Kepler.

Kepler's laws.

Law 1. This law states that all the planets in our solar system revolve in elliptical orbits around the sun. In this case, the coordinates of the center of the Sun are not located in the central part of the ellipse, but at one of its foci. This explains the temporary change in distance between the Sun and the moving planets.

Law 2. The segment that connects the centers of the planets and the Sun is called the radius or vector of the planet. He is able to describe equal areas for the same time intervals. This suggests that the planets, when moving in an elliptical orbit, do not always move at the same speed. As they approach the Sun, their movement speeds up, and as they move away, they slow down. This law is called the "law of areas".

Law 3. This law at one time was published in the book "The Harmony of the World" (published in parts 1618 - 1621 onwards). The squares of the orbital periods of a pair of planets are related to each other as the cubic value of their average distances from the Sun.

At the time, not all scientists agreed with Kepler. Galileo could not measure that the planets do not move uniformly. But over time, the ideality of Kepler's laws was proven. Kepler's laws helped Newton discover the law gravity and before today they are the basis of celestial mechanics.

There is another major work of Kepler, which has the name "Rudolf Tables". This work on astronomy, which deals with the motions of the planets, was published in 1627. The basis of the tables was laid by Tycho Brahe, and Kepler worked on them for 22 years. table data are more accurate than previous work in astronomy" Prussian tables”, which were compiled by the astronomer Reinhold in 1551. I would like to say that the "Rudolf Tables" served good help for astronomers, sailors and travelers for several centuries.

I would also like to say that Kepler's attention was attracted not only by planets, but also by comets. He was the first to suggest that the visibility of comet tails is possible under the influence of sunlight. Therefore, the tail of a comet always points towards opposite side from the sun.

Kepler also made contributions to the field of mathematics. He created the theory of logarithms on an arithmetic basis and reduced it to a very precise tables which were published in 1624.

Thanks to Kepler, humanity received certain knowledge in the field of optics. He even wrote the book Dioptika. His work in the field of optics was the basis for the creation of the optical scheme of the telescope, since he was able to study the action physiological mechanism vision. He first announced such physiological phenomena person as nearsightedness and farsightedness.

Kepler gave the world the basics of calculating volumes various bodies rotation, and areas flat figures, which are formed by curves of the second order - an oval, an ellipse, a section of a cone, etc. These methods were the beginning of the era of differential and integral calculus.

Much more can be said about Kepler's achievements. This scientist, who laid the foundations, both in astronomy and in mathematics. Johannes Kepler died on November 15, 1630 in Regensberg from a cold.

Johannes Kepler is an outstanding German scientist who achieved everything in his life thanks to remarkable perseverance and determination. The heyday of the scientist's activity fell on the exhausting Thirty Years' War. But neither devastation nor poverty could prevent selfless service. Accepting the blows of fate, Kepler worked selflessly and gave discoveries to the world despite the unfavorable circumstances that accompanied him throughout his short life.

Johannes Kepler was born on December 27, 1571 in the small town of Weil der Stadt. His father had the position of burgomaster in Holland, often traveled around the world and was rarely at home. When the son reached the age of eighteen, the father left on official business and did not appear at home again. The boy's mother, Katharina, was the mistress of the tavern. She also did fortune telling.

Johann became interested in astronomy since childhood, more precisely - from the age of 6. Since I saw the fall of a comet, and a little later, in 1580 - moon eclipse, an inquisitive boy realized that he wanted to connect his life with the study of the stars.

The childhood of young Kepler was overshadowed by poor health and lack of proper care. Parents did not care too much about the education of the child, at the age of 7 they identified the boy in primary school, and only after its completion the question arose of where to send my son for further education. By that time, the father no longer lived with them, the family had no money, and the young man could not do physical work for health reasons. In such circumstances, the young man was actually doomed to choose a spiritual career.

In 1584, Johann enters the lower seminary, which he graduates in 2 years, and immediately becomes a student of the higher seminary in Maulbronn. As an able student, the city gave him a monthly boarding school, which greatly helped Kepler to study in high school- where he wanted. In 1591, he became a student at a higher educational institution in the town of Tübingen, starting his studies at the Faculty of Arts (at that time they included both mathematics and astronomy). There he learns about the existence of the system of the world, which was developed by Nicolaus Copernicus.

At first, Kepler planned to be a priest, but in 1594 he was invited to teach mathematics at the University of Graz, Austria, and for the next 6 years he worked there.

In 1596, Johann's first book was published, which he called "The Secret of the World." In this curious work, the author demonstrates non-trivial thinking when trying to discover the harmony of the universe by “setting” 5 planets into polyhedra. In the author's mind planetary orbits correspond to geometrically correct figures built into each other. For example, he presented Saturn in the form of a ball, Jupiter corresponded to a cube, a tetrahedron became the figure of Mars.

A year later, Johann married Barbara Müller von Mulek, for whom this was the second marriage. Her first husband died, leaving his wife a young widow. After unsuccessful attempts to acquire offspring (two babies died in infancy) and a wave of persecution of Protestants, Kepler, who was on the list of heretics, hastily left Austria.

In 1600, the astronomer settled in Prague. The city was not chosen by chance, Tycho Brahe lived here (the same Tycho Brahe to whom Kepler sent his first work) - an astrologer with imperial court, who partly shared his ideas and sympathized with the young scientist. When Brahe passes away a year later, Kepler takes his place. It seems that after the death of a friend, Johann had a “black streak” in his life. Not only was the budget scarce due to the unstable situation in the country, and the scientist received payment irregularly, Tycho Brahe's heirs also appeared. They claimed his scientific developments, and Johann had to part with a significant amount of money paid as compensation.

In 1604, the scientist published his observations of a supernova, which today bears his name.

Yet Brahe was an excellent observer and left behind many manuscripts on astronomy, which Johann carefully sorts through the next few years. Now it seems to him that in his work "The Secret of the World" he made mistakes, for example, Mars corresponds not to a circle, but to an ellipse. After scrupulously analyzing the notes of the deceased comrade, Kepler formulated astronomical laws and published them in 1609 in the book New Astronomy.

During the decade spent in Prague, the couple had three babies, but in 1611 a smallpox epidemic claimed the life of the eldest of the sons, Frederick. Soon after a long illness, Johann's faithful companion also dies.

In 1612, Kepler moved to Linz and took the position of astrologer under the emperor, but the means of subsistence were still not enough. A year later, he marries the daughter of a carpenter, who at that time was barely 24 years old. During their life together they had four children.

In 1615, terrible information reaches Kepler - his mother is accused of witchcraft. The accusation at that time is very serious, then for this reason many women were executed by burning. Johann stands up for his mother. The investigation lasts for several years, at the trial he himself acts as a defender, and soon the tired and exhausted woman is nevertheless released. She died after a year.

In 1816, Kepler formulated the third law and published it in an amended version of his book.

1626 was marked by the siege and capture of the city of Linz, where the scientist lived, and he moved to Ulm. Due to the hardships of wartime, devastation and desolation reigned everywhere in the district. When Kepler found himself in a difficult situation - there was a catastrophic shortage of money - he had to go to the emperor with a request for payment of his due salary. On the way to Regensburg, he caught a serious cold that brought him to his grave. It happened in 1630, the scientist was not even sixty years old.

But even after his death, the misadventures continued. After a 30-year war, the churchyard on which his grave was located was completely destroyed. Not a trace remains of the graves. Even worse, after the fires, half of the scientist's records disappeared without a trace. Everything that was left of his observations was bought by the St. Petersburg Academy of Sciences in 1774, and to this day Kepler's legacy is in St. Petersburg, the manuscripts can be found in the original.

A talented visionary Johannes Kepler, a European mathematician of the Middle Ages, a famous mechanic and astronomer who was interested in optics and passionate about astrology, gave many ideas and discoveries to his descendants.

Kepler formulated three laws of planetary motion. The first one said that their trajectory is an ellipse. The second law proved that when approaching the sun, the speed of celestial bodies changes, the third law helped to calculate this speed. Studying the system of the world, Johann took the Copernican model as a basis, but in the course of his work he almost completely moved away from it, which is why these concepts have so little in common.

The “Kepler equation” he derived is still used in astronomy to determine the position of celestial bodies. Subsequently, the laws of planetary kinematics discovered by the researcher were taken as a basis by Newton for his theory of gravitation. In addition, Johannes Kepler is the author of the very first exposition of "Copernican astronomy". Until then, this book, consisting of three volumes remained banned for many years.

In addition to the study of celestial bodies, he paid much attention to mathematics and formulated a method for determining the volume of rotating bodies, describing it in the work “New stereometry of wine barrels”. The book was published in 1615. It already contained the first elements of the integral calculus. In addition to the above, Kepler was the first to present his contemporaries with a table of logarithms. He was the first to use the term "arithmetic mean".

Also, the concept of "inertia", used today in physics, is associated with the name of Johannes Kepler. It was he who proved that the body has the property of resisting the applied external force. Despite the fact that part of the interests of the medieval scientist extended to astrology, his name and ideas are known to all modern mathematicians, physicists and astronomers, and scientific achievements Centuries later, they have not lost their significance.

(German Johannes Kepler) - an outstanding German mathematician, astronomer, optician and astrologer. Discovered the laws of planetary motion.

Johannes Kepler was born on December 27, 1571 in Weil der Stadt, a suburb of Stuttgart (Baden-Württemberg). His father served as a mercenary in Spanish Netherlands. When the young man was 18 years old, his father went on another campaign and disappeared forever. Kepler's mother, Katharina Kepler, kept a tavern, moonlighted as divination and herbal medicine.

In 1589, Kepler graduated from school at the Maulbronn monastery, where he showed outstanding abilities. The city authorities awarded him a scholarship to help him further his studies.

In 1591 he entered the university in Tübingen - first at the faculty of arts, which then included mathematics and astronomy, then moved to the theological faculty. Here he first heard about the ideas of Nicolaus Copernicus and his heliocentric system of the world and immediately became their adherent.

Thanks to outstanding mathematical ability Johannes Kepler was invited in 1594 to lecture on mathematics at the University of Graz (now in Austria).

Kepler spent 6 years in Graz. Here was published (1596) his first book "The Secret of the World" (Mysterium Cosmographicum). In it, Kepler tried to find the secret harmony of the Universe. This work, after further discoveries by Kepler, lost its original meaning, if only because the orbits of the planets were not circular. Nevertheless, Kepler believed in the presence of a hidden mathematical harmony of the Universe until the end of his life, and in 1621 he republished The Secret of the World, making numerous changes and additions to it.

In 1597, Kepler married the widow Barbara Müller von Mulek. Their first two children died in infancy, and their wife fell ill with epilepsy. To top it off, persecution of Protestants begins in Catholic Graz. Kepler is put on the list of "heretics" to be expelled and is forced to leave the city.

Johannes Kepler accepted the invitation of the famous Danish astronomer Tycho Brahe, who by this time had moved to Prague and served as court astronomer and astrologer for Emperor Rudolf II. In 1600 Kepler arrives in Prague. 10 years spent here is the most fruitful period of his life.

After Brahe's death in 1601, Kepler succeeded him in office. The treasury of the emperor was constantly empty because of the endless wars. Kepler's salary was rare and meager. He is forced to earn extra money by compiling horoscopes.

For several years, Johannes Kepler carefully studied the data of the astronomer Tycho Brahe and, as a result of careful analysis, comes to the conclusion that the trajectory of Mars is not a circle, but an ellipse, in one of the focuses of which is the Sun - a position known today as the first law Kepler.

As a result of further analysis, Kepler discovered the second law: the radius vector connecting the planet and the Sun describes equal areas in equal time. This meant that what further planet away from the Sun, the slower it moves.

Both laws were formulated by Kepler in 1609 in the book "New Astronomy", and, for the sake of caution, he referred them only to Mars.

The publication of the New Astronomy and the almost simultaneous invention of the telescope ushered in a new era. These events marked a turning point in Kepler's life and scientific career.

After the death of Emperor Rudolph II, Johannes Kepler's position in Prague became increasingly uncertain. He applied to the new emperor for permission to temporarily take the post of mathematician of the province of Upper Austria in Linz, where he spent the next 15 years.

In 1618, the scientist discovered Kepler's third law - the ratio of the cube of the average distance of the planet from the Sun to the square of the period of its revolution around the Sun is a constant value for all planets: a³/T² = const. Kepler publishes this result in the final book "Harmony of the World", and applies it not only to Mars, but also to all other planets (including, of course, the Earth), as well as to the Galilean satellites. Thus, the great German astronomer Johannes Kepler discovered the law of planetary motion.

For the next 9 years, Kepler worked on compiling tables of the positions of the planets based on the new laws of their motion. The events of the Thirty Years' War and religious persecution forced Kepler to flee to Ulm in 1626. Having no means of subsistence, in 1628 he entered the service of the imperial commander Wallenstein as an astrologer. Last major work Kepler were the planetary tables conceived by Tycho Brahe, published in Ulm in 1629 under the title "Rudolf Tables".

Johannes Kepler was engaged not only in the study of the circulation of the planets, he was also interested in other issues of astronomy. Comets especially attracted his attention. Noticing that the tails of comets always point away from the Sun, Kepler conjectured that tails are formed by the action of sunlight. At that time, nothing was known about nature solar radiation and structure of comets. It was only in the second half of the 19th century and in the 20th century that it was established that the formation of comet tails is really connected with the radiation of the Sun.

The scientist died during a trip to Regensburg on November 15, 1630, when he tried in vain to get at least part of the salary that the imperial treasury owed him for many years.

Kepler's work on the creation of celestial mechanics played essential role in the approval and development of the teachings of Copernicus. He paved the way for subsequent research, in particular for Newton's discovery of the law of universal gravitation.

Kepler's laws still hold their value. Having learned to take into account the interaction of celestial bodies, scientists use them not only to calculate the movements of natural celestial bodies, but, most importantly, also artificial ones, such as spaceships witnesses of the emergence and improvement of which our generation is.

Kepler belongs great merit in developing our knowledge of the solar system. Scientists of subsequent generations, who appreciated the significance of Kepler's works, called him the "legislator of heaven", since it was he who found out the laws according to which the movement of celestial bodies in the solar system takes place.

Kepler's laws apply equally to any planetary system anywhere in the universe. Astronomers who are looking for new planetary systems in space, time after time, as a matter of course, apply Kepler's equations to calculate the parameters of the orbits of distant planets, although they cannot observe them directly.

rendered great services to astronomy not only by his immortal laws, the fruit of deep, ingenious considerations and hard, constant work, overcoming all obstacles. If in his writings great ideas were not mixed with systematic ideas, which he borrowed from contemporary philosophy; then his proposals would be much more appreciated than as saying that science without proposals cannot move forward; without suggestions it is impossible to come up with a single useful experience; you just have to be conscientious and only after experiments and calculations that have confirmed the proposal, admit it to science.

Kepler, as far as he could, was faithful to this rule; without hesitation and stubbornness, he abandoned his most beloved hypotheses, if they were destroyed by experience.

Kepler always lived in poverty, and therefore was forced to work for booksellers who demanded almost daily news from him; he had no time to ponder his thoughts; he expounded them as they were born in his mind; he thought aloud. Are there many wise men who endured such torture?

Although in numerous writings of Kepler we find ideas that cannot be justified by his straitened circumstances, we cannot but be indulgent towards him if we fully understand his hard life and take into account the misfortunes of his family.

Such an opinion about the causes of many of Kepler's paradoxes we have taken from the writings of Breishwert, who reviewed in 1831 the unpublished works of the great astronomer, who completed the transformations of ancient astronomy.

Johannes Kepler was born on December 27, 1571 in Magstadt, in the village of Wiertemberg, located one mile from the imperial city of Weil (in Swabia). He was born premature and very weak. His father, Heinrich Kepler, was the son of the burgomaster of this city; his poor family considered themselves to be nobility; because one of the Keplers was made a knight under the emperor Sigismund. His mother, Katerina Guldenman, the daughter of an innkeeper, was a woman without any education; she could neither read nor write, and spent her childhood with an aunt who was burned for witchcraft.

Kepler's father was a soldier who fought against Belgium under the command of the Duke of Alba.

At the age of six, Kepler suffered from severe smallpox; as soon as he got rid of death, in 1577 he was sent to the Leonberg school; but his father, returning from the army, found his family completely ruined by one bankrupt, for whom it had the imprudence to guarantee; then he opened a tavern in Emerdinger, took his son out of school and forced him to serve the visitors of his establishment. This position was corrected by Kepler until the age of twelve.

And so the one who was destined to glorify both his name and his fatherland began life as a tavern servant.

At the age of thirteen, Kepler fell seriously ill again and his parents did not hope for his recovery.

Meanwhile, his father's affairs were going badly, and therefore he again joined the Austrian army, which was marching against Turkey. Since that time, Kepler's father has gone missing; and his mother, a rude and quarrelsome woman, spent the last property of the family, which amounted to 4,000 florins.

Johannes Kepler had two brothers who looked like his mother; one was a tin-man, the other a soldier, and both were complete scoundrels. Thus, the future astronomer found nothing in his family, except for burning grief, which completely destroyed him, if his sister Margaret, who married a Protestant pastor, had not consoled him; but this relative later became his enemy.

When Kepler's father left the army, then he was forced to work in the field; but the weak and skinny youth could not endure hard work; he was appointed a theologian, and at the age of eighteen (1589) he entered the Tubingham Seminary and was kept there at public expense. In the examination for a bachelor's degree, he was not recognized as the most excellent; this title went to John-Hippolytus Brentius, whose name you will not find in any historical dictionary, although the publishers of such collections are very lenient and put all sorts of rubbish in them. However, in our biographies we will meet with such cases more than once, proving the absurdity of school pedantry.

Kepler failed for more than one reason: while still sitting on school bench, he took an active part in Protestant theological disputes, and since his opinions were contrary to the Wirtemberg orthodoxy, it was decided that he was not worthy of promotion in the clergy.

Fortunately for Kepler, Mestlin, called (1584) from Heidelberg to Tübingen to the chair of mathematics, gave his mind a different direction. Kepler abandoned theology, but did not completely free himself from the mysticism rooted in him by his original upbringing. At this time, Kepler saw the immortal book of Copernicus for the first time.

“When I,” says Kepler, “appreciated the charms of philosophy, then I ardently occupied myself with all its parts; but did not pay special attention to astronomy, although he understood well everything that was taught from it at school. I was brought up at the expense of the Duke of Wirtemberg, and seeing that my comrades enter his service not entirely according to their inclinations, I also decided to accept the first post offered to me.

He was offered the position of professor of mathematics.

In 1593, the twenty-two-year-old Kepler was appointed professor of mathematics and moral philosophy in Graetz. He began by publishing a Gregorian calendar.

In 1600 religious persecution began in Styria; all Protestant professors were expelled from Graetz, including Kepler, although he was already, as it were, a permanent citizen of this city, having married (1597) a noble and beautiful woman, Barbara Müller. Kepler was the third husband, and when she married him, she demanded evidence of his nobility: Kepler went to Wirtemberg to inquire about it. The marriage was unhappy.

After the historical details of the discovery of a new star in Ophiuchus and theoretical considerations about its sparkle, Kepler analyzes the observations made in various places and proves that the star had no own movement, no annual parallax.

Although in his book Kepler seems to have a contempt for astrology. However, after a long refutation of Pic de la Mirandole's criticism, he admits the influence of the planets on the Earth when they are located among themselves in a certain way. By the way, one cannot read without surprise that Mercury can produce storms.

Tycho claimed that the star of 1572 was formed from matter milky way; the star of 1604 was also near this bright belt; but Kepler did not consider such a formation of stars possible, because the milky way had not changed in the least since the time of Ptolemy. But how did he become convinced of the immutability of the Milky Way? “However,” says Kepler, “the appearance of a new star destroys Aristotle’s opinion that the sky cannot be spoiled.”

Kepler considers whether the appearance of a new star had anything to do with the conjunction of the planets that was close to its place? But, being unable to find the physical reason for the formation of a star, he concludes: "God, who constantly cares about the world, can command a new luminary to appear in any place and at any time."

There was a proverb in Germany: a new star - a new king. “It is amazing,” says Kepler, “that not a single ambitious man took advantage of popular prejudice.”

Regarding Kepler's reasoning about the new star in Cygnus, we note that the author used all his scholarship to prove that the star really appeared again and does not belong to the number of variable stars.

Immediately, Kepler proves that the time of the Nativity of Christ is not precisely determined and that the beginning of this era must be pushed back four or five years, so that 1606 must be considered either 1610 or 1611.

Astronomia nova sive physica caelestis, tradita commetaris de motibus stellae Martis ex observationibus Tycho Brahe. – Prague, 1609

In his first studies to improve the Rudolphian tables, Kepler did not yet dare to reject the eccentrics and epicycles of the Almagest, also accepted by Copernicus and Tycho, for reasons borrowed from metaphysics and physics; he only asserted that the conjunctions of the planets should be attributed to the true, and not to the average Sun. But extremely difficult and long-term calculations did not satisfy him: the difference between calculations and observations extended up to 5 and 6 minutes of a degree; from these differences he wanted to free himself and finally discovered the true system of the world. Then Kepler decided against the motion of the planets in circles near the eccentric, i.e., near an imaginary, immaterial point. Along with such circles, epicycles were also destroyed. He suggested that the Sun is the center of the motion of the planets, which move along an ellipse, in one of the focuses of which this center is located. To raise such an assumption to the level of a theory, Kepler performed calculations surprising in their difficulty and duration. He showed unparalleled indefatigable constancy in work and irresistible perseverance in achieving the proposed goal.

Such work was rewarded by the fact that the calculations on Mars, based on his assumption, led to conclusions that are in perfect agreement with Tycho's observations.

Kepler's theory consists of two propositions: 1) the planet revolves in an ellipse, in one of the foci of which is the center of the Sun, and 2) the planet moves at such a speed that the radius vectors describe the areas of the cutouts proportional to the times of motion. From the numerous observations in Uraniburg, Kepler had to choose the most capable ones for solving problems connected with the main problem and invent new methods of calculation. By such a prudent choice, without any assumption, he proved that the lines in which the planes of the orbits of all the planets intersect the ecliptic pass through the center of the Sun, and that these planes are inclined to the ecliptic at almost constant angles.

We have already noted that Kepler made extremely lengthy and extremely burdensome calculations, because in his time logarithms were not yet known. On this subject, in Bagli's History of Astronomy we find the following statistical evaluation Kepler's work: “Kepler's efforts are incredible. Each of his calculations takes up 10 pages per sheet; he repeated each calculation 70 times; 70 repetitions give 700 pages. Calculators know how many mistakes can be made and how many times it was necessary to do calculations that take up 700 pages: how much time should have been used? Kepler was an amazing person; he was not afraid of such work and the work did not tire his mental and physical strength.

To this it must be added that Kepler understood the enormity of his undertaking from the very beginning. He relates that Rheticus, an excellent student of Copernicus, wished to transform astronomy; but could not explain the movements of Mars. “Rhethik,” Kepler continues, “summoned his domestic genius to help, but the genius, probably angry at disturbing his peace, grabbed the astronomer by the hair, lifted him to the ceiling and, lowering him to the floor, said: here is the movement of Mars.”

This joke of Kepler proves the difficulty of the task, and therefore one can judge his pleasure when he was convinced that the planets really circulate according to the two laws mentioned above. Kepler expressed his pleasure in words addressed to the memory of the unfortunate Ramus.

If the Earth and the Moon, assuming that they are equally dense, were not held in their orbits by animal or some other force: then the Earth would approach the Moon at the 54th part of the distance separating them, and the moon would pass the remaining 53 parts and they would join.

If the Earth ceased to attract its waters, then all the seas would rise and unite with the Moon. If the attractive force of the Moon extends to the Earth, then, conversely, the same force of the Earth reaches the Moon and spreads further. And so everything like the Earth cannot but be subject to its attractive force.

There is no absolutely light substance; one body is lighter than another because one body is rarer than the other. “I,” says Kepler, “call rare that body which, given its volume, has little substance.”

It is not necessary to imagine that light bodies rise and are not attracted: they are attracted less than heavy bodies and heavy bodies displace them.

The driving force of the planets is in the Sun and weakens with increasing distance from this star.

When Kepler admitted that the Sun is the cause of the revolution of the planets, then he had to admit that it rotates on its axis in the direction of the translational motion of the planets. This consequence of Kepler's theory was proved later. sunspots; but to his theory Kepler added circumstances that were not justified by observations.

Dioptrica, etc. - Frankfurt, 1611; reprinted in London 1653

It seems that in order to write a diopter, one had to know the law according to which light is refracted when it passes from a rare substance (medium) into a dense one - the law discovered by Descartes; but as at small angles of incidence, the angles of refraction are almost proportional to the first: then Kepler, in the basis of his research, accepted these approximate ratios and studied the properties of flat-spherical glasses, as well as spherical glasses, the surfaces of which have equal radii. Here we find formulas for calculating the focus distances of the glasses mentioned. These formulas are still in use today.

In the same book we find that he was the first to give the concept of spyglasses made of two convex glasses. Galileo always used pipes made up of one convex glass and another concave eye glass. And so, with Kepler, one must begin the history of astronomical tubes, the only ones capable of projectiles with divisions designed to measure angles. As for the rule that determines the magnification of a telescope and consists in dividing the focus distance of an object glass by the focus distance of an eye glass, it was discovered not by Kepler, but by Huygens.

Kepler, compiling his dioptrics, already knew that Galileo had discovered Jupiter's satellites: from their short-term rotations, he concluded that the planet must also rotate on its axis, moreover, in less than 24 hours. This conclusion was justified not soon after Kepler.

Nova stereometria doliorum vinariorum. — Linz, 1615

This book is purely geometric; in it the author especially considers the bodies resulting from the rotation of an ellipse around its various axes. It also proposes a method for measuring the capacity of barrels.

<>bHarmonicces mundi libri quinque, etc. - Linz, 1619

Here Kepler gives an account of the discovery of his third law, namely: the squares of the times of rotation of the planets are proportional to the cubes of their distances from the Sun.

On March 18, 1618, he thought of comparing the squares of the times of rotations with the cubes of distances: but, due to a calculation error, he found that the law was wrong; On May 15, he again redid the calculations, and the law was justified. But even here Kepler doubted it, because there could also be an error in the second calculation. “However,” says Kepler, “after all the tests, I was convinced that the law is in perfect agreement with Tycho's observations. And so the discovery is not in doubt.

Surprisingly, Kepler mixed in a lot of strange and completely false ideas with this great discovery. The law he discovered led his imagination to the Pythagorean harmonies.

“In the music of the heavenly bodies,” says Kepler, “Saturn and Jupiter correspond to the bass, Mars to the tenor, Earth and Venus to the contralto, and Mercury to the falsetto.”

The same great discovery is disfigured by Kepler's belief in astrological nonsense. For example, he argued that planetary conjunctions always perturb our atmosphere, and so on.

De cometis libelli tres, etc. - Augsburg, 1619

After reading the three chapters of this work, one cannot help but be surprised that Kepler, who discovered the laws of motion of the planets around the Sun, argued that comets move in straight lines. “Observations on the course of these luminaries,” he says, “are not worthy of attention, because they do not return.” This conclusion is surprising because it refers to the comet of 1607, which then appeared for the third time. And even more surprising is that from an incorrect assumption, he deduced the correct consequences about the huge distance of the comet from the Earth.

“Water, especially salty water, produces fish; ether produces comets. The Creator did not want the immeasurable seas to be without inhabitants; He also wanted to inhabit the celestial space. The number of comets must be extremely large; we do not see many comets because they do not approach the Earth and are destroyed very soon.

Near such delusions of Kepler's deluded imagination, we find ideas that have entered science. For example, Sun rays, penetrating into comets, they constantly tear off particles of their substance from them and form their tails.

According to Efor, Seneca, mentioning the comet, divided into two parts, which took different ways, considered this observation to be completely false. Kepler strongly condemned the Roman philosopher. The severity of Kepler is hardly fair, although almost all astronomers are on the side of Seneca: in our time, astronomers have witnessed a similar event in celestial space; they saw two parts of the same comet taking different paths. One should never neglect the predictions or fortune-telling of brilliant people.

The book on comets was published in 1619, that is, after the great discoveries of Kepler; but her final chapter especially filled with astrological nonsense about the influence of comets on events sublunar world from which they are at a great distance. I say: in distances, because a comet can produce diseases, even a plague, when its tail covers the Earth, for who knows the essence of the substance of comets?

Epitome astronomiae copernicanae, and etc .

This work consists of two volumes, published in Aenz in different years: 1618, 1621 and 1622. They contain next discoveries who spread the field of science:

The sun is a fixed star; it seems to us more than all other stars, because it is closest to the Earth.

It is known that the Sun rotates on its axis (observations over spots showed this); consequently the planets must rotate in the same way.

Comets are made up of matter that can expand and contract—matter that the sun's rays can carry over long distances.

The radius of the sphere of stars at least two thousand times the distance of Saturn.

Sunspots are clouds or thick smoke that rises from the depths of the Sun and burns on its surface.

The sun rotates, and therefore its attractive force is directed to different sides of the sky: when the Sun takes possession of a planet, then it will make it rotate with it.

The center of planetary motion is at the center of the sun.

The light that surrounds the Moon during a total solar eclipse comes from the Sun's atmosphere. In addition, Kepler thought that this atmosphere was sometimes visible after the sun had set. From this remark one might think that Kepler was the first to discover the zodiacal light; but he says nothing about the form of the light; therefore, we do not have the right of D. Cassini and Shaldrei to deprive their discoveries of honor.

Jo. Kepleri tabulae Rudolphinae, etc. - Ulm, 1627

These tables were started by Tycho, and finished by Kepler, after working on them for 26 years. They got their name from the name of Emperor Rudolf, who was the patron of both astronomers, but did not give them the promised salary.

The same book contains the history of the discovery of logarithms, which, however, cannot be taken away from Napier, their first inventor. The right of invention belongs to the one who first published it.

Prussian tables, so named because they are dedicated to Albert of Brandenburg, Duke of Prussia, were published by Reingold in 1551. They were based on the observations of Ptolemy and Copernicus. Compared with the "Rudolf tables" compiled from Tycho's observations and from new theory, in the Rheingold tables the errors extend to many degrees.

This posthumous work by Kepler, published by his son in 1634, contains a description of astronomical phenomena for an observer on the moon. Some writers of astronomical textbooks also engaged in similar descriptions, transferring observers to different planets. Such descriptions are useful for beginners, and it is fair to say that Kepler was the first to open the way to this.

Here are the titles of other works by Kepler, showing what a hardworking life the great astronomer led:

Nova dissertatiuncula de fundamentis astrologiae certioribus, etc. - Prague, 1602
Epistola ad rerum coelestium amatores universos, etc. - Prague, 1605
Sylva chronologica. — Frankfurt, 1606
Detailed history new comet 1607, etc. In German; at Halle, 1608
Phoenomenon singulare, seu Mercurius in Sole, etc. Leipzig, 1609
Dissertatio cum Nuncio sidereo nuper ad mortales misso a Galileo. - Prague, 1610; in the same year it was reprinted in Florence, and in 1611 in Frankfurt.
Narration de observatis a se quatuor Jovis satellitibus erronibus quos Galilaeus medica sidera nuncupavit. Prague, 1610
Jo. Kepleri strena, seu de nive sexangula. Frankfurt, 1611
Kepleri eclogae chronicae ex epistolis doctissimorum aliquot virorum et suis mutuis. Frankfurt, 1615
Ephtmerides novae, etc. - Keplerian ephemerides were published until 1628 and always a year ahead; but published after a year. After Kepler, they were continued by Barchiy, Kepler's son-in-law. News of disasters for government and churches, especially comets and earthquakes in 1618 and 1619. In German, 1619.
Eclipses of 1620 and 1621 in German, at Ulm, 1621
Kepleri apologia pro suo opere Harmonices mundi, etc. Frankfurt, 1622
Discursus conjuctionis Saturni et Joves in Leone. Linz, 1623
Jo. Kepleri chilias logarithmorum. Marburg, 1624
Jo. Kepleri hyperaspistes Tychonis contra anti-Tychonem Scipionis Claramonti, et pr. Frankfurt, 1625
Jo. Kepleri supplementum chiliadis logaritmorum. Acnypr, 1625 r.
Admonitio ad astronomos rerumque coelestium studiosos de miris rarisque anni 1631 phoenomenis, Veneris puta et Mercurii in Solem incursu. Leipzig, 1629
Responsio ad epistolum jac. Bartschii praefixam ephemeridi anni 1629, etc. Sagan, 1629.
Sportula genethliacis missa de Tab. Rudolphi usu in computationibus astrologicis, cum modo dirigendi novo et naturali. Sagan, 1529

Ganche in 1718 published one volume containing part of the manuscripts left after Kepler; the second volume promised by him was not published due to lack of funds. Eighteen more notebooks of unpublished manuscripts were bought by the Imperial St. Petersburg Academy of Sciences in 1775.

Johannes Kepler.
Based on the original in the Royal Observatory in Berlin.

Kepler (Kepler) Johannes (1571-1630), German astronomer, one of the creators of modern astronomy. He discovered the laws of planetary motion (Kepler's laws), on the basis of which he compiled planetary tables (the so-called Rudolf tables). Laid the foundations of the theory of eclipses. Invented a telescope in which the objective and eyepiece are biconvex lenses.

Kepler (Kepler) Johann (December 27, 1571, Weilder Stadt - November 15, 1630, Regensburg) - German astronomer and mathematician. In search of the mathematical harmony of the world created by God, he undertook a mathematical systematization of the ideas of Copernicus. He studied at the University of Tübingen, taught mathematics and ethics in Graz, compiled calendars and astrological forecasts. In the work "The Harbinger, or Cosmographic Mystery" (Prodromus sive Mysterium cosmographicum, 1596), he expounded the divine mathematical order heavens: six planets define five gaps corresponding to the five "Platonic" polyhedra. He was a court mathematician in Prague, an assistant to Tycho Brahe; processing his precise observations on the movements of Mars, he established the first two laws of planetary circulation: the planets do not move in circular orbits, but in ellipses, in one of the focuses of which is the Sun; the planets move at a speed at which the radius vectors describe the same areas in equal times ("New Astronomy" - Astronomia nova, Pragae, 1609). Later these laws were extended to all planets and satellites. The third law - the squares of the periods of revolution of the planets are related as the cubes of their average distances from the Sun - is set forth in the Pythagorean-inspired "Harmony of the World" (Harmonices mundi, 1619). For mathematics, the study “Stereometry of wine barrels” (1615) was of particular importance, in which Kepler calculated the volumes of bodies obtained by rotating conic sections around an axis lying in the same plane with them. He also applied logarithms to the construction of new tables of planetary motions (1627). His " Brief essay Copernican astronomy" (Epitome astronomiae Copernicanae, 1621) was the best textbook astronomy of that era. Kepler's discoveries were of great importance for the philosophical and scientific development New time.

L. A. Mikeshina

New Philosophical Encyclopedia. In four volumes. / Institute of Philosophy RAS. Scientific ed. advice: V.S. Stepin, A.A. Huseynov, G.Yu. Semigin. M., Thought, 2010, vol. II, E - M, p. 242.

Johannes Kepler was born on December 27, 1571 in the town of Weil near Stuttgart in Germany. Kepler was born into a poor family, and therefore, with great difficulty, he managed to finish school and enter the University of Tübingen in 1589. Here he studied mathematics and astronomy. His teacher Professor Mestlin was secretly a follower of Copernicus. Soon Kepler also became a supporter of the Copernican theory.

Already in 1596, he published the "Cosmographic Secret" where, accepting the conclusion of Copernicus about the central position of the Sun in the planetary system, he tries to find a connection between the distances of planetary orbits and the radii of spheres, in which regular polyhedra are inscribed in a certain order and around which are described. Despite the fact that this work of Kepler was still a model of scholastic, quasi-scientific sophistication, it brought fame to the author.

In 1600, the famous Danish astronomer Tycho Brahe, who came to Prague, offered Johann a job as his assistant for sky observations and astronomical calculations. After Brahe's death in 1601, Kepler began to study the remaining materials with data from long-term observations. Kepler came to the conclusion that the opinion about the circular shape of planetary orbits was incorrect. By calculations, he proved that the planets do not move in circles, but in ellipses. Kepler's first law suggests that the sun is not at the center of the ellipse, but at a special point called the focus. From this it follows that the distance of the planet from the Sun is not always the same. Kepler found that the speed at which a planet moves around the Sun is also not always the same: approaching closer to the Sun, the planet moves faster, and moving further away from it, slower. This feature in the motion of the planets constitutes Kepler's second law.

Both Kepler's laws have become the property of science since 1609, when his "New Astronomy" was published - a presentation of the foundations of new celestial mechanics.

The need to improve the means of astronomical calculations, the compilation of tables of planetary movements based on the Copernican system attracted Kepler to questions of the theory and practice of logarithms. He built the theory of logarithms on an arithmetic base and with its help compiled logarithmic tables, first published in 1624 and republished until 1700.

In the book "Additions to Vitellius, or the Optical Part of Astronomy" (1604), Kepler, studying conic sections, interprets the parabola as a hyperbola or ellipse with an infinitely distant focus - this is the first case in the history of mathematics of applying general principle continuity.

In 1617-1621, at the height of the Thirty Years' War, when the book of Copernicus was already on the Vatican's "List of Forbidden Books". Kepler publishes Essays on Copernican Astronomy in three volumes. The title of the book inaccurately reflects its content - the Sun there takes the place indicated by Copernicus, and the planets, the Moon and shortly before discovered by Galileo Jupiter's satellites circulate according to the laws discovered by Kepler. In the same years, Kepler also published "Harmony of the World", where he formulates the third law of planetary motions: the squares of the periods of revolution of two planets are related to each other as the cubes of their average distances from the Sun.

For many years he has been working on compiling new planetary tables, printed in 1627 under the title "Rudolphin Tables", which for many years were the reference book of astronomers. Kepler also owns important results in other sciences, in particular in optics. The optical scheme of the refractor developed by him already by 1640 became the main one in astronomical observations.

Kepler was engaged not only in the study of the circulation of the planets, he was also interested in other issues of astronomy. Comets especially attracted his attention. Noticing that the tails of comets always point away from the Sun, Kepler conjectured that the tails are formed under the action of the sun's rays. At that time, nothing was yet known about the nature of solar radiation and the structure of comets. It was only in the second half of the 19th century and in the 20th century that it was established that the formation of comet tails is really connected with the radiation of the Sun.

The scientist died during a trip to Regensburg on November 15, 1630, when he tried in vain to get at least part of the salary that the imperial treasury owed him for many years.

Reprinted from http://100top.ru/encyclopedia/

Read further:

World-famous scientists (biographical guide).

Three laws of Kepler. In the book: Gurtovtsev A.L. Think or believe? Ode to human donkey. Minsk, 2015.

Compositions:

Gesammelte Werke, Bd. 1 - 18 hrsg. W. Van Dyckund M. Caspar. Munch., 1937-63; in Russian per.: New stereometry of wine barrels. M,-L., 1935:

About hexagonal snowflakes. M., 1982.

Literature:

Kirsanov V.S. Scientific revolution of the 17th century. M., 1987;

Reale J., Antiseri D. Western philosophy from the origins to the present day, v. 3. New time. SPb., 1996.