Kepler scientist. Johannes Kepler - the difficult fate of talent

Johannes Kepler (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. He invented a telescope in which the objective and eyepiece are biconvex lenses. Zodiac sign - Capricorn.

Soon after the death of Copernicus, based on his system of the world, astronomers compiled tables of planetary movements. These tables were in better agreement with observations than the previous tables compiled according to Ptolemy. But after some time, astronomers discovered a discrepancy between these tables and movement observation data celestial bodies.

It was clear to advanced scientists that the teachings of Copernicus were correct, but it was necessary to study more deeply and clarify the laws of planetary motion. This problem was solved by the great German scientist Kepler.

Johannes Kepler was born on December 27, 1571 in the small town of Weil near Stuttgart. Kepler was born in poor family, and therefore he with great difficulty managed to finish school and enter the University of Tübingen in 1589. Here he enthusiastically studied mathematics and astronomy. His teacher, Professor Mestlin, was secretly a follower of Copernicus. Of course, at the university Mestlin taught astronomy according to Ptolemy, but at home he introduced his student to the basics of the new teaching. And soon Kepler became an ardent and convinced supporter of the Copernican theory.

Unlike Maestlin, Johannes Kepler did not hide his views and beliefs. Open propaganda of the teachings of Copernicus very soon brought upon him the hatred of local theologians. Even before graduating from university, in 1594, Johann was sent to teach mathematics at the Protestant school in Graz, the capital of the Austrian province of Styria.

Already in 1596, Johann published the “Cosmographical Secret”, where, accepting Copernicus’s conclusion about central position Sun in planetary system, tries to find a connection between the distances of planetary orbits and the radii of the spheres in which in a certain order are inscribed and around which regular polyhedra are described. Despite the fact that this work of Kepler still remained an example of scholastic, quasi-scientific wisdom, it brought fame to the author. The famous Danish astronomer-observer Tycho Brahe, who was skeptical about the scheme itself, paid tribute to the young scientist’s independent thinking, his knowledge of astronomy, art and perseverance in calculations and expressed a desire to meet with him. The meeting that took place later was of exceptional importance for the further development of astronomy.

In 1600, Tycho Brahe, who arrived in Prague, offered Johann a job as his assistant for sky observations and astronomical calculations. Shortly before this, Brahe was forced to leave his homeland of Denmark and the observatory he had built there, where he conducted astronomical observations for a quarter of a century. This observatory was equipped with the best measuring instruments, and Brahe himself was a skilled observer.

When the Danish king deprived Brahe of funds to maintain the observatory, he left for Prague. Brahe was very interested in the teachings of Johannes Kepler, but was not a supporter of it. He put forward his explanation of the structure of the world; He recognized the planets as satellites of the Sun, and considered the Sun, Moon and stars to be bodies revolving around the Earth, which thus retained the position of the center of the entire Universe.

Brahe did not work with Kepler for long: he died in 1601. After his death, Johannes Kepler began to study the remaining materials with data from long-term astronomical observations. While working on them, especially on materials about the motion of Mars, Kepler made a remarkable discovery: he derived the laws of planetary motion, which became the basis of theoretical astronomy.

Philosophers Ancient Greece They thought that the circle was the most perfect geometric shape. And if so, then the planets should make their revolutions only in regular circles (circles).

Kepler came to the conclusion that the opinion that had been established since ancient times about the circular shape of planetary orbits was incorrect. Through calculations, he proved that the planets do not move in circles, but in ellipses - closed curves, the shape of which is slightly different from a circle. When solving this problem, Kepler had to encounter a case that, generally speaking, using the methods of mathematics constant values could not be resolved. The matter came down to calculating the area of ​​the sector of the eccentric circle. If this problem is translated into modern mathematical language, we arrive at the elliptic integral. Naturally, Johannes Kepler could not give a solution to the problem in quadratures, but he did not give up in the face of the difficulties that arose and solved the problem by summing infinitely large number"actualized" infinitesimals. In modern times, this approach to solving an important and complex practical problem represented the first step in the prehistory of mathematical analysis.

Johannes Kepler's first law suggests: The sun is not at the center of the ellipse, but at a special point called the focus. It follows from this 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: when approaching closer to the Sun, the planet moves faster, and moving further away from it, slower. This feature in the motion of planets constitutes Kepler's second law. At the same time, I. Kepler developed a fundamentally new mathematical apparatus, making an important step in the development of the mathematics of variable quantities.

Both of Kepler's laws have become the property of science since 1609, when his famous “New Astronomy” was published - a statement of the foundations of the new celestial mechanics. However, the publication of this remarkable work did not immediately attract due attention: even the great Galileo, apparently, did not accept Kepler’s laws until the end of his days.

The needs of astronomy stimulated further development computational means of mathematics and their popularization. In 1615, Johannes Kepler published a relatively small book, but very capacious in content, “The New Stereometry of Wine Barrels,” in which he continued to develop his integration methods and used them to find the volumes of more than 90 bodies of rotation, sometimes quite complex. There he also considered extremal problems, which led to another branch of infinitesimal mathematics - differential calculus.

The need to improve the means of astronomical calculations and the compilation of tables of planetary movements based on the Copernican system attracted Kepler to the theory and practice of logarithms. Inspired by the work of Napier, Johannes Kepler independently built a theory of logarithms on a purely arithmetic basis and, with its help, compiled ones close to Napier’s, but more accurate logarithmic tables, first published in 1624 and reprinted until 1700. Kepler was the first to use logarithmic calculations in astronomy. He was able to complete the “Rudolfin Tables” of planetary movements only thanks to a new means of calculation.

The scientist's interest in second-order curves and problems of astronomical optics led him to develop general principle continuity - a kind of heuristic technique that allows you to find the properties of one object from the properties of another, if the first is obtained by passing to the limit from the second. In the book “Supplements to Vitellius, or the Optical Part of Astronomy” (1604), Johannes Kepler, studying conic sections, interprets a parabola as a hyperbola or ellipse with a focus at infinity - this is the first case in the history of mathematics of the application of the general principle of continuity. By introducing the concept of a point at infinity, Kepler took an important step towards the creation of another branch of mathematics - projective geometry.

Kepler's entire life was devoted to open struggle for the teachings of Copernicus. In 1617-1621, at the height of Thirty Years' War, when Copernicus’s book had already been included in the Vatican’s “List of Prohibited Books”, and the scientist himself was going through a particularly difficult period in his life, he published Essays on Copernican Astronomy in three editions totaling approximately 1000 pages. The title of the book does not accurately reflect its content - the Sun there occupies the place indicated by Copernicus, and the planets, the Moon and the satellites of Jupiter, recently discovered by Galileo, orbit according to the laws discovered by Kepler. This was in fact the first textbook of new astronomy, and it was published during a period of particularly fierce struggle of the church against revolutionary teaching, when Kepler’s teacher Mestlin, a Copernican by conviction, published an astronomy textbook on Ptolemy!

During these same years, Kepler published Harmony of the World, where he formulated the third law of planetary motions. The scientist established a strict relationship between the time of revolution of the planets and their distance from the Sun. It turned out that the squares of the periods of revolution of any two planets are related to each other as the cubes of their average distances from the Sun. This is the third law of Johannes Kepler.

For many years, I. Kepler has been working on compiling new planetary tables, printed in 1627 under the title “Rudolfin Tables,” which for many years were reference book astronomers. Kepler also owns important results in other sciences, in particular in optics, the optical refractor scheme he developed had already become the main one in astronomical observations by 1640.

Kepler's work on the creation of celestial mechanics played a crucial role in the approval and development of the teachings of Copernicus. They prepared the ground for subsequent research, in particular for the discovery of the law by Isaac Newton universal gravity. Kepler's laws still retain their significance, 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, artificial ones, such as spaceships, the emergence and improvement of which our generation is witnessing.

The discovery of the laws of planetary rotation required the scientist many years of persistent and intense work. Kepler, who suffered persecution both from the Catholic rulers whom he served and from fellow Lutherans (Lutheranism is the largest branch of Protestantism. Founded by Martin Luther in the 16th century), not all of whose dogmas he could accept, has to move a lot. Prague, Linz, Ulm, Sagan - this is an incomplete list of cities in which he worked.

Johannes Kepler was not only involved in the study of planetary revolutions, he was also interested in other issues of astronomy. Comets especially attracted his attention. Noticing that the tails of comets always face away from the Sun, Kepler conjectured that the tails are formed under the influence of sun rays. At that time nothing was known about nature solar radiation and the structure of comets. Only in the second half of the 19th century and in the 20th century was it established that the formation of comet tails is actually associated with radiation from the Sun.

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

Kepler owes enormous credit for the development of our knowledge of the solar system. Scientists of subsequent generations, who appreciated the significance of Kepler’s works, called him “the legislator of the sky,” since it was he who discovered the laws by which the movement of celestial bodies in the solar system occurs. (Samin D.K. 100 great scientists. - M.: Veche, 2000)

More about Johannes Kepler:

Johann Kepler is one of the greatest astronomers of all centuries and peoples, the founder of modern theoretical astronomy.

Johannes Kepler was born near Weil in Württemberg from poor parents. Having lost his father early, Johann spent part of his childhood as a servant in a tavern and only thanks to the famous Maestlin, he ended up at the University of Tübingen and here he devoted himself entirely to the study of mathematics and astronomy. In 1594, Johannes Kepler was already a professor in Graetz and wrote here the essay “Prodromus dissertationem cosmographicarum”, in which he defends the Copernican system. This work attracted the general attention of scientists, and soon Kepler established active relations with Copernicus himself and other modern astronomers.

Religious persecution forced him, however, to leave Graz and in 1609 Johannes Kepler moved to Prague, at the invitation of the famous Tycho Brahe. After the death of the latter, Kepler was appointed imperial mathematician with a certain content and, more importantly, became the heir to the extensive collection of manuscripts left by Tycho and representing the latter’s observations at Uranieborg (in Denmark).

In Prague, Johannes Kepler published “Astronomia Nova” (1609), “Dioptrece” (1611), wrote about refraction, invented the simplest spotting scope, which still bears his name, observed a comet (Halley), etc. Immediately, processing Tycho’s systematic and very accurate observations, I. Kepler discovered the first two of his immortal laws of planetary motion around the sun (all planets rotate in ellipses, in one of the foci of which the sun is located and the areas described by radii vectors are proportional to times).

However, family misfortunes and delays in the payment of salaries often forced Kepler to compile calendars and horoscopes, in which he himself did not believe. After the death of his patron, Emperor Rudolph II, Johannes Kepler accepted a professorship in Linz and here he compiled his famous “Tabulae Rudolphinae”, which for a whole century served as the basis for calculating the positions of the planets.

Finally, in 1619 one of the last opus was published. Kepler: “Harmonia mundi”, in which, among deep and still interesting considerations about the secrets of the universe, the third law of planetary motion is stated (the squares of the revolution times of different planets are proportional to the cubes of the semi-major axes of their orbits).

Johannes Kepler spent the last years of his life in continuous travel, partly due to the political turmoil of the Thirty Years' War (at one time the scientist was in the service of Wallenstein as an astrologer), partly due to the trial of his mother, who was accused of witchcraft. He died on November 15, 1630, in Regensburg, where he was buried in the cemetery of St. Petra. Above his grave there is an inscription: “Mensus eram coelos nune terrae metior umbras; Mens coelestis erat, corporis umbra jacet." This epitaph, written by Johannes Kepler himself, translated means: “Before I measured the heavens, now I measure the darkness underground; my mind was a gift from heaven - and my body, transformed into a shadow, rests.” In Regensburg, in 1808, a monument to him was erected.

For the three-hundredth anniversary of the birth of Johannes Kepler, a complete collection of his works was published (“Opera omnia”, Frankfurt am M. and Erlangen 1758 - 71), in 8 volumes the astronomer Frisch devoted almost his entire life to the preparation of this publication and received an allowance from St. Petersburg. acd. Sci. Many of Kepler's manuscripts are now kept in the library of the Pulkovo Observatory; biography of Kepler in Russian and a generally understandable presentation of it scientific activity- in the biographical library of F. Pavlenkov. The biography was compiled, according to Frisch, by E. A. Predtechensky.

Johannes Kepler is an outstanding German scientist who achieved everything in his life thanks to his remarkable perseverance and determination. The heyday of the scientist’s activity occurred during the grueling Thirty Years’ War. But neither devastation nor poverty could prevent selfless service. Accepting the blows of fate, Kepler worked selflessly and gave the world discoveries 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 never appeared at home again. The boy's mother, Katarina, was the owner of the inn. She also did fortune telling.

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

Young Kepler's childhood was marred by poor health and lack of proper care. The parents did not care too much about the child’s education; at the age of 7, they assigned the boy to 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 physical work the young man could not due to health reasons. In such circumstances, the young man was virtually doomed to choose a spiritual career.

In 1584, Johann entered the lower seminary, which he graduated after 2 years, and immediately became a student at the higher seminary in Maulbronn. As a capable student, the city provided him with a monthly boarding school, which greatly helped Kepler to study in higher school- where he wanted. In 1591 he became a university student educational institution in the town of Tübingen, starting his studies at the Faculty of Arts (at that time these included mathematics and astronomy). There he learns about the existence of a world system developed by Nicolaus Copernicus.

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

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

A year later, Johann married Barbara Müller von Muhleck, for whom it was her second marriage. Her first husband died, leaving his wife a young widow. After unsuccessful attempts to acquire offspring (two children died in infancy) and the wave of persecution of Protestants, Kepler, who was included in 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 at the imperial court, who partly shared his ideas and sympathized with the young scientist. When Brahe passed away a year later, Kepler took his place. It seems as if after the death of his friend, Johann hit a “dark streak” in his life. Not only was the budget tight due to the unstable situation in the country, and the scientist received payment irregularly, but Tycho Brahe’s heirs also appeared. They claimed it scientific developments, and Johann had to part with a significant sum of money paid as compensation.

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

Still, Brahe was an excellent observer and left behind many manuscripts on astronomy, which Johann carefully analyzed over 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. Having scrupulously analyzed the notes of his late 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 children, but in 1611 a smallpox epidemic claimed the life of the eldest son, Frederick. Soon after a long illness, Johann’s faithful companion also passed away.

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

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

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

The year 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 throughout the area. When Kepler found himself in difficult situation- there was a catastrophic lack of money - he had to go to the emperor with a request for payment of the due salary. On the way to Regensburg, he caught a serious cold, which brought him to his grave. This happened in 1630, the scientist was not even sixty years old.

But even after his death, the misfortunes continued. After the 30-year war, the graveyard where his grave was located was completely destroyed. Not a trace remains of the burials. Even worse, after the fires, half of the scientist’s records disappeared without a trace. Everything that remained from his observations was bought by the St. Petersburg Academy of Sciences in 1774, and to this day Kepler’s legacy is located in St. Petersburg, the manuscripts can be viewed in the original.

The 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 said that their trajectory was 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. While 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.” Prior to this, this book, consisting of three volumes, remained banned for many years.

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

Also associated with the name of Johannes Kepler is the concept of “inertia,” used today in physics. It was he who proved that the body has the ability to resist 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 have not lost their significance centuries later.

Biography of Johannes Kepler - V the greatest mathematician, natural scientist and philosopher of the Middle Ages. Johannes Kepler was born on December 27, 1571 in the town of Weil der Stadt, in the territory of the modern German federal state of Baden-Württemberg. In the 16th century it was still the Holy Roman Empire.

Literally since childhood, watching wonderful celestial phenomena, little Johann became interested in astronomy. But independent observations were hampered by poor eyesight - a consequence of a serious illness.

The Art of Astronomy and Mathematics

In those distant years, such serious sciences as mathematics and astronomy were considered arts - philosophy and alchemy reigned supreme in the minds of people. Kepler showed an ability for such pseudosciences from childhood, after graduating from the monastery school of Maillebonne. In 1591 he was a student at the famous University of Tübingen. Of course, to the Faculty of Arts. Later, having chosen geology for further study, the young man first read the postulates of the heliocentric theory of the construction of the world, the author of which was Nicolaus Copernicus. The great Pole's monograph became Kepler's life guide to for many years scientific research.

Kepler's Mystery

After graduating from university, Kepler lectured in mathematics at the University of Graz for six years. This period marks the first scientific work young researcher, which he called “The Mystery of the Universe.” Subsequently, more significant discoveries pushed this work into the background.

"Kepler Cup" - a model of the solar system of five Platonic solids

Appreciating the young scientist’s aspirations to know the truth, the outstanding astronomers Galileo and Brahe, however, rejected its main postulates.

Later, Johannes Kepler and Tycho Brahe met in Prague. They spent the period from 1600 to 1610 in close scientific collaboration, which did not prevent them from looking at the theory of the universe differently.

Kepler's astronomical observations of those years were classified into a work on the supernova that erupted in 1604. Today in astrophysics it is named after him. The German followed in the footsteps of the excellent astronomer-observer Tycho Brahe. Studying the results of his work, Kepler drew his own conclusions.

Thus, critically assessing the results of Brahe’s stellar observations, he predicted the elliptical nature of the orbit of Mars. At the focal point of the red planet's orbit, the German absolutely accurately located the center of the system - the Sun. This is how Kepler's First Law was born. Consistent study of the problem even earlier led to the emergence of the Second Law, which proves that the speed of a planet’s motion slows down as it moves away from the Sun. In 1609, Kepler formulated these laws in a published monograph entitled The New Astronomy.

Kepler formulated the third law of his name in 1618 in the book “Harmony of the World” - the ratio of the cube of the average distance of a planet from the Sun to twice the period of revolution around the center of the system is a constant.

The simplicity of the formulation and application of Kepler's laws made them an indispensable tool for posterity in astronomical research. Finally revealed deepest meaning Kepler's discoveries were his great follower Isaac Newton.

Censor's Favorite

In 1613-1615, the Protestant community adopted, not least thanks to the efforts of Kepler, the Gregorian chronology system and calendar.

At the end of his life, from 1617 to 1622, Kepler worked hard to unify the astronomical teachings of Copernicus in a modern presentation. The book includes all the postulates of Keplerian astronomy. Medieval scientific censorship, the so-called “Index of Forbidden Books,” took great pleasure in introducing this work of Kepler into its annals.

In 1627, Kepler published completely new astronomical “Rudolph Tables”, calculated taking into account the latest scientific discoveries. During their preparation, the talented mathematician Johannes Kepler was the first European scientist to use logarithms.

In addition to the astronomical works of Kepler, in the medieval scientific world His very famous works on mathematics, optics, mechanics, physics:

• Author of the first integral mathematical calculus in the work “New Stereometry of Wine Barrels.”
• He introduced the term “arithmetic mean” into the mathematical lexicon.
• First explored the phenomenon of body resistance external influence, called inertia.
• He studied the properties and role of the eye lens, established the causes of myopia and farsightedness.

Johannes Kepler died of a cold on November 15, 1630 in Regensburg. Creative heritage - 27 published manuscripts, a huge number of works published after his death in a 22-volume collected works. It is noteworthy that during the reign of Empress Catherine II, part of Kepler’s works was purchased and exported to Russia. Since then it has been kept in the archives Russian Academy Sciences in St. Petersburg.

Johannes Kepler(German: Johannes Kepler; December 27, 1571, Weil der Stadt - November 15, 1630, Regensburg) - German mathematician, astronomer, mechanic, optician, discoverer of the laws of motion of the planets of the solar system.

Early years

Johannes Kepler was born in the imperial city of Weil der Stadt (30 kilometers from Stuttgart, now the federal state of Baden-Württemberg). His father, Heinrich Kepler, served as a mercenary in the Spanish Netherlands. When the young man was 18 years old, his father went on another hike and disappeared forever. Kepler's mother, Katharina Kepler, ran an inn and worked part-time as a fortune teller and herbalist.

Kepler's interest in astronomy began in his childhood, when his mother showed the impressionable boy a bright comet (1577), and later a lunar eclipse (1580). After suffering from smallpox in childhood, Kepler received a lifelong visual defect, which prevented him from making astronomical observations, but he retained his enthusiastic love for astronomy forever.

In 1589, Kepler graduated from school at the Maulbronn monastery, showing outstanding abilities. The city authorities awarded him a scholarship to help him further education. In 1591 he entered the university in Tübingen - first at the Faculty of Arts, which then included mathematics and astronomy, then moved to the Faculty of Theology. Here he first heard (from Michael Möstlin) about the heliocentric system of the world developed by Nicolaus Copernicus and immediately became its staunch supporter. Kepler's university friend was Christoph Bezold, a future jurist.

Initially, Kepler planned to become a Protestant priest, but thanks to the extraordinary mathematical abilities was invited in 1594 to lecture on mathematics at the University of Graz (now in Austria).

Kepler spent 6 years in Graz. Here his first book, “The Mystery of the Universe,” was published (1596). Mysterium Cosmographicum). In it, Kepler tried to find the secret harmony of the Universe, for which he compared various “Platonic solids” (regular polyhedra) to the orbits of the five then known planets (he especially singled out the sphere of the Earth). He presented the orbit of Saturn as a circle (not yet an ellipse) on the surface of a sphere circumscribed around a cube. The cube, in turn, was inscribed with a ball, which was supposed to represent the orbit of Jupiter. A tetrahedron was inscribed in this ball, circumscribed around a ball representing the orbit of Mars, etc. This work, after further discoveries by Kepler, lost its original meaning (if only because the orbits of the planets turned out to be non-circular); Nevertheless, Kepler believed in the existence 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.

Kepler sent the book “The Mystery of the Universe” to Galileo and Tycho Brahe. Galileo approved of Kepler's heliocentric approach, although he did not support mystical numerology. Subsequently, they carried on a lively correspondence, and this circumstance (communication with the “heretic” Protestant) at the trial of Galileo was especially emphasized as aggravating Galileo’s guilt.

Tycho Brahe, like Galileo, rejected Kepler’s far-fetched constructions, but highly appreciated his knowledge and originality of thought and invited Kepler to his place.

In 1597, Kepler married the widow Barbara Müller von Muleck. Their first two children died in infancy, and their wife developed epilepsy. To add insult to injury, persecution of Protestants began in Catholic Graz. Kepler, included in the list of expelled "heretics", was forced to leave the city and accept the invitation of Tycho Brahe. Brahe himself had by this time been evicted from his observatory and moved to Prague, where he served as a court astronomer and astrologer for Emperor Rudolf II.

Prague

In 1600, both exiles - Kepler and Brahe - met in Prague. The 10 years spent here were the most fruitful period of Kepler's life.

It soon became clear that Tycho Brahe only partly shared the views of Copernicus and Kepler on astronomy. To preserve geocentrism, Brahe proposed a compromise model: all planets except the Earth revolve around the Sun, and the Sun revolves around a stationary Earth (geo-heliocentric world system). This theory gained great popularity and for several decades was the main competitor to the Copernican world system.

After Brahe's death in 1601, Kepler succeeded him in office. The emperor's treasury was constantly empty due to endless wars, and Kepler's salary was paid rarely and meagerly. He was forced to earn extra money by drawing up horoscopes. Kepler also had to conduct many years of litigation with the heirs of Tycho Brahe, who tried to take away from him, among other property of the deceased, also the results of astronomical observations. In the end, we managed to pay them off.

Being an excellent observer, Tycho Brahe compiled a voluminous work over many years on the observation of planets and hundreds of stars, and the accuracy of his measurements was significantly higher than that of all his predecessors. To increase accuracy, Brahe used both technical improvements and a special technique for neutralizing observation errors. The systematic nature of the measurements was especially valuable.

For several years, Kepler carefully studied Brahe's data and, as a result of careful analysis, came to the conclusion that the trajectory of Mars is not a circle, but an ellipse, at one of the foci of which the Sun is located - a position known today as Kepler's first law. The analysis led to second law(in fact, the second law was even discovered earlier than first): the radius vector connecting the planet and the Sun describes equal areas at equal times. This meant that the further a planet is from the Sun, the slower it moves.

Kepler's laws were formulated by Kepler in 1609 in the book “New Astronomy”, and, for the sake of caution, he applied them only to Mars.

The new model of movement aroused great interest among Copernican scientists, although not all of them accepted it. Galileo resolutely rejected Keplerian ellipses. After Kepler's death, Galileo remarked in a letter: "I have always appreciated Kepler's mind - sharp and free, perhaps even too free, but our ways of thinking are completely different."

In 1610, Galileo informed Kepler of the discovery of the moons of Jupiter. Kepler greeted this message with incredulity and in his polemical work “Conversation with the Starry Messenger” he gave a somewhat humorous objection: “it is not clear why there should be [satellites] if there is no one on this planet who could admire this spectacle.” But later, having received his copy of the telescope, Kepler changed his mind, confirmed the observation of satellites and himself took up the theory of lenses. The result was an improved telescope and the fundamental work of the Dioptric.

In Prague, Kepler had two sons and a daughter. In 1611, the eldest son Frederick died of smallpox. At the same time, the mentally ill Emperor Rudolf II, having lost the war with his own brother Matthew, abdicated the Czech crown in his favor and soon died. Kepler began preparing to move to Linz, but then his wife Barbara died after a long illness.

Recent years

Portrait of Kepler, 1627

In 1612, having collected meager funds, Kepler moved to Linz, where he lived for 14 years. The position of court mathematician and astronomer was retained for him, but in terms of payment, the new emperor turned out to be no better than the old one. Teaching and horoscopes brought in some income.

In 1613, Kepler married the 24-year-old daughter of a carpenter, Susanna. They had seven children, four survived.

In 1615, Kepler receives news that his mother has been accused of witchcraft. The accusation is serious: last winter in Leonberg, where Katharina lived, 6 women were burned under the same article. The indictment contained 49 points: communication with the devil, blasphemy, corruption, necromancy, etc. Kepler writes to the city authorities; The mother is initially released, but then arrested again. The investigation lasted 5 years. Finally, in 1620, the trial began. Kepler himself acted as a defender, and a year later the exhausted woman was finally released. IN next year she passed away.

Meanwhile, Kepler continued his astronomical research and in 1618 discovered third law: the ratio of the cube of the average distance of a planet from the Sun to the square of its period of revolution around the Sun is a constant value for all planets: a³/T² = const. Kepler published this result in his final book, “The Harmony of the World,” and applied it not only to Mars, but also to all other planets (including, naturally, the Earth), as well as to the Galilean satellites.

Let us note that the book, along with the most valuable scientific discoveries, also contains philosophical discussions about the “music of the spheres” and the Platonic solids, which, according to the scientist, constitute the aesthetic essence of the highest project of the universe.

In 1626, during the Thirty Years' War, Linz was besieged and soon captured. Looting and fires began; Among others, the printing house burned down. Kepler moved to Ulm and in 1628 entered the service of Wallenstein.

In 1630, Kepler went to the emperor in Regensburg to receive at least part of his salary. On the way he caught a bad cold and soon died.

After Kepler's death, the heirs received: second-hand clothes, 22 florins in cash, 29,000 florins in unpaid salary, 27 published manuscripts and many unpublished ones; they were later published in a 22-volume collection.

Kepler's death did not end his misadventures. At the end of the Thirty Years' War, the cemetery where he was buried was completely destroyed, and nothing remained of his grave. Part of Kepler's archive has disappeared. In 1774, most of the archive (18 out of 22 volumes), on the recommendation of Leonhard Euler, was acquired by the St. Petersburg Academy of Sciences, and is now stored in the St. Petersburg branch of the RAS archive.

Scientific activities

Albert Einstein called Kepler “an incomparable man” and wrote about his fate:

He lived in an era when there was still no certainty about the existence of some general pattern for all natural phenomena. How deep was his faith in such a pattern, if, working alone, not supported or understood by anyone, for many decades he drew strength from it for difficult and painstaking work? empirical research the movements of the planets and the mathematical laws of this movement!

Today, when this scientific act has already been accomplished, no one can fully appreciate how much ingenuity, how much hard work and patience was required to discover these laws and express them so accurately.

Astronomy

IN late XVI centuries in astronomy there was still a struggle between the geocentric system of Ptolemy and the heliocentric system of Copernicus. Opponents of the Copernican system argued that in terms of calculation errors it was no better than the Ptolemaic system. Let us recall that in the Copernican model the planets move uniformly in circular orbits: in order to reconcile this assumption with the apparent unevenness of the planets’ motion, Copernicus had to introduce additional movements by epicycles. Although Copernicus had fewer epicycles than Ptolemy, his astronomical tables, initially more accurate than Ptolemy’s, soon diverged significantly from observations, which puzzled and cooled the enthusiastic Copernicans a lot.

The three laws of planetary motion discovered by Kepler fully and with excellent accuracy explained the apparent unevenness of these movements. Instead of numerous contrived epicycles, Kepler's model includes only one curve - an ellipse. The second law established how the speed of the planet changes as it moves away or approaches the Sun, and the third allows us to calculate this speed and the period of revolution around the Sun.

Although historically the Keplerian world system is based on the Copernican model, in fact they have very little in common (only the daily rotation of the Earth). Disappeared circular movements spheres carrying planets, the concept of planetary orbit appeared. In the Copernican system, the Earth still occupied a somewhat special position, since Copernicus declared the center of the world earth's orbit. According to Kepler, the Earth is an ordinary planet, the movement of which is subject to three general laws. All orbits of celestial bodies are ellipses (movement along a hyperbolic trajectory was discovered later by Newton), the common focus of the orbits is the Sun.

Kepler also derived the “Kepler equation,” which is used in astronomy to determine the positions of celestial bodies.

The laws of planetary kinematics, discovered by Kepler, later served as the basis for Newton to create the theory of gravitation. Newton mathematically proved that all Kepler's laws are direct consequences of the law of gravity.

Kepler's views on the structure of the Universe beyond the solar system stemmed from his mystical philosophy. He believed the sun to be motionless, and considered the sphere of stars to be the boundary of the world. Kepler did not believe in the infinity of the Universe and, as an argument, proposed (1610) what was later called photometric paradox: If the number of stars is infinite, then in any direction the gaze would encounter a star, and there would be no dark areas in the sky.

Strictly speaking, Kepler’s world system claimed not only to identify the laws of planetary motion, but also to do much more. Like the Pythagoreans, Kepler considered the world to be the realization of a certain numerical harmony, both geometric and musical; revealing the structure of this harmony would provide answers to the most profound questions:

I found out that everything celestial movements, both in their entirety and in all in some cases, imbued general harmony- true, not the one I expected, but even more perfect.

For example, Kepler explains why there are exactly six planets (by that time only six planets of the Solar System were known) and they are located in space in this way and not in any other way: it turns out that the orbits of the planets are inscribed in regular polyhedra. Interestingly, based on these unscientific considerations, Kepler predicted the existence of two moons of Mars and an intermediate planet between Mars and Jupiter.

Kepler's laws combined clarity, simplicity and computational power, but the mystical form of his world system thoroughly clogged the real essence Kepler's great discoveries. Nevertheless, Kepler's contemporaries were already convinced of the accuracy of the new laws, although their deep meaning remained unclear until Newton. No further attempts were made to revive Ptolemy's model or to propose a system of motion other than the heliocentric one.

Kepler did a lot to get Protestants to accept Gregorian calendar(at the Diet in Regensburg, 1613, and in Aachen, 1615).

Kepler became the author of the first extensive (in three volumes) expositions of Copernican astronomy ( Epitome Astronomiae Copernicanae, 1617-1622), which immediately received the honor of being included in the “Index of Prohibited Books”. In this book, your main work, Kepler included a description of all his discoveries in astronomy.

In the summer of 1627, after 22 years of work, Kepler published (at his own expense) astronomical tables, which he named “Rudolph” in honor of the emperor. The demand for them was enormous, since all the previous tables had long since diverged from the observations. It is important that for the first time the work included tables of logarithms convenient for calculations. Keplerian tables served astronomers and sailors until the beginning of the 19th century.

A year after Kepler's death, Gassendi observed the passage of Mercury across the disk of the Sun, which he predicted. In 1665, Italian physicist and astronomer Giovanni Alfonso Borelli published a book confirming Kepler's laws for discovered by Galileo satellites of Jupiter.

Mathematics

Kepler found a way to determine the volumes of various bodies of rotation, which he described in the book “New Stereometry of Wine Barrels” (1615). The method he proposed contained the first elements of integral calculus. Cavalieri later used the same approach to develop the extremely fruitful “method of indivisibles.” The completion of this process was the discovery of mathematical analysis.

In addition, Kepler analyzed the symmetry of snowflakes in great detail. Research on symmetry led him to hypothesize about dense packing of balls, according to which the highest packing density is achieved when the balls are arranged pyramidally on top of each other. It was not possible to prove this fact mathematically for 400 years - the first report on the proof of the Kepler hypothesis appeared only in 1998 in the work of mathematician Thomas Hales. Kepler's pioneering work in the field of symmetry later found application in crystallography and coding theory.

During his astronomical research, Kepler contributed to the theory conic sections. He compiled one of the first tables of logarithms.

Kepler first used the term “arithmetic mean.”

Kepler also entered the history of projective geometry: he first introduced the most important concept endlessly remote point . He also introduced the concept of the focus of a conic section and considered projective transformations conic sections, including those changing their type - for example, converting an ellipse into a hyperbola.

Mechanics and physics

It was Kepler who introduced the term inertia into physics as the innate property of bodies to resist an applied external force. At the same time, like Galileo, he clearly formulated the first law of mechanics: every body that is not acted upon by other bodies is at rest or undergoes uniform linear motion.

Kepler came close to discovering the law of gravitation, although he did not try to express it mathematically. He wrote in the book “New Astronomy” that in nature there is “a mutual bodily desire of similar (related) bodies for unity or connection.” The source of this force, in his opinion, is magnetism combined with the rotation of the Sun and planets around their axis.

In another book, Kepler clarified:

I define gravity as a force similar to magnetism - mutual attraction. The greater the force of attraction, the closer both bodies are to one another.

True, Kepler mistakenly believed that this force extends only in the ecliptic plane. Apparently he believed that the force of gravity was inversely proportional to distance (not the square of the distance); however, its formulations are not clear enough.

Kepler was the first, almost a hundred years before Newton, to hypothesize that the cause of tides is the influence of the Moon on the upper layers of the oceans.

Optics

In 1604, Kepler published a comprehensive treatise on optics, Additions to Vitellius, and in 1611 another book, Dioptrics. The history of optics as a science begins with these works. In these writings, Kepler describes in detail both geometric and physiological optics. It describes the refraction of light, refraction and the concept of optical image, general theory lenses and their systems. Introduces the terms “optical axis” and “meniscus”, and for the first time formulates the law of illumination falling inversely proportional to the square of the distance to the light source. For the first time he describes the phenomenon of total internal reflection of light upon transition to a less dense medium.

Described by him physiological mechanism view, from modern positions, is fundamentally correct. Kepler figured out the role of the lens and correctly described the causes of myopia and farsightedness.

Kepler's deep insight into the laws of optics led him to design a telescopic telescope (Kepler telescope), made in 1613 by Christoph Scheiner. By the 1640s, such telescopes had replaced Galileo's less advanced telescope in astronomy.

Kepler and astrology

Kepler's attitude towards astrology was ambivalent. On the one hand, he assumed that the earthly and the heavenly are in some kind of harmonious unity and interconnection. On the other hand, he was skeptical about the possibility of using this harmony to predict specific events.

Kepler said: “People are mistaken in thinking that earthly affairs depend on the heavenly bodies.” Another of his frank statements is also widely known:

Of course, this astrology is a stupid daughter, but, my God, where would her mother, the highly wise astronomy, go if she didn’t have a stupid daughter! The world is even much more stupid and so stupid that for the benefit of this old reasonable mother, the stupid daughter must chat and lie. And the salary of mathematicians is so insignificant that the mother would probably starve if her daughter did not earn anything.

Nevertheless, Kepler never broke with astrology. Moreover, he had his own view on the nature of astrology, which made him stand out among contemporary astrologers. In his work “Harmony of the World,” he states that “there are no luminaries in the heavens that bring misfortune,” but human soul capable of “resonating” with rays of light emanating from celestial bodies, she imprints in her memory the configuration of these rays at the moment of her birth. The planets themselves, in Kepler’s view, were living beings endowed with an individual soul.

Thanks to some successful predictions, Kepler earned a reputation as a skilled astrologer. In Prague, one of his duties was to draw up horoscopes for the emperor. It should be noted, however, that Kepler did not engage in astrology solely for the sake of earning money and compiled horoscopes for himself and his loved ones. Thus, in his work “About Myself,” he describes his own horoscope, and when his son, Heinrich, was born in January 1598, Kepler compiled a horoscope for him as well. In his opinion, the next year when his son’s life was in danger was 1601, but his son died in April 1598.

Kepler's attempts to cast a horoscope for the general Wallenstein also failed. In 1608, Kepler compiled a horoscope for the commander, in which he predicted marriage at the age of 33, called the years 1613, 1625 and the 70th year of Wallenstein’s life dangerous, and also described a number of other events. But from the very beginning the predictions failed. Wallenstein returned the horoscope to Kepler, who, having corrected the time of birth in it by half an hour, obtained an exact correspondence between the prediction and the course of life. However, this option also contained mistakes. Thus, Kepler believed that the period from 1632 to 1634 would be prosperous for the commander and did not promise danger. But in February 1634 Wallenstein was killed.

Perpetuating the memory of Kepler

Monument to Kepler and Tycho Brahe, Prague

Monument to Kepler in Linz

Kepler crater on the Moon. Photo from the Apollo 12 spacecraft

Named in honor of the scientist:

• Craters on the Moon and Mars.
• Asteroid (1134) Kepler.
• Supernova 1604, described by him.
• NASA orbital observatory, launched into orbit in March 2009. Main task: search and study of planets outside the solar system.
• University in Linz.
• Vienna metro station.
• European cargo spacecraft"Johanns Kepler" (2011).

There are Kepler museums in Weil der Stadt, Prague, Graz and Regensburg.

Other events in memory of Kepler:

• In 1971, for the 400th anniversary of Kepler's birth, a commemorative coin worth 5 marks was issued in the GDR.
• In 2009, for the 400th anniversary of the discovery of Kepler's laws, a commemorative silver coin worth 10 euros was issued in Germany.

The following works of art are dedicated to the life of the scientist:

• Opera and symphony “Harmony of the World” by composer Paul Hindemith (1956).
• Historical story by Yuri Medvedev “Captain of the Starry Ocean (Kepler)”, Young Guard, 1972.
• Feature film “Johannes Kepler” directed by Frank Vogel (GDR, 1974).
• Novel by John Banville Kepler, translated into Russian in 2008.
• Opera "Kepler" by composer Philip Glass (2009).
• Feature film “The Astronomer's Eye” directed by Stan Neumann (France, 2012).
• Opera "Kepler's Judgment" by composer Tim Watts (2016).

Stamps in honor of Kepler's 400th anniversary (1971)

1971, GDR

1971, Romania

1971, UAE

1971, Germany

Appearance heliocentric system Nicolaus Copernicus is the most important component of the process that historians called the scientific revolution of the 16th-17th centuries. In the preface to his book, where he outlined this theory, the great Pole carefully pointed out its absurdity, proposing that his work be considered only an attempt to find a way to alleviate mathematical calculations in astronomy.

The credit for transforming the Copernican model of the universe into one belongs to the great German scientist named Kepler. Johann, among other great contemporaries, did more: he announced the arrival of a new type of man in the world - a scientist who actively cognizes nature.

Comet is a harbinger of great destiny

The future astronomer, mathematician, mechanic, optician was born on December 27, 1571 into a poor family, in the town of Weil, in the Duchy of Württemberg, in the Swabian part of Germany. When he was 5 years old, the head of the family, the mercenary soldier Heinrich Kepler, went to war in Holland. Johann never saw him again. His mother, Katarina, was the daughter of an innkeeper, practiced herbal medicine and fortune telling, for which she later almost paid with her head. Having a small income, she did everything to ensure that her son received a decent education.

An interesting fact, perhaps one that determined his entire fate, is contained in the biography of Johannes Kepler at its very beginning. Katharina Kepler showed six-year-old Johann a comet, and three years later - in 1580 - an eclipse of the Moon. The star moving across the night sky and the Moon changing shape before our eyes made a strong impression on the inquisitive boy. Maybe then his desire to get to the bottom of what was happening was born?

Theologian, supporter of Copernicus

IN early childhood Johann suffered from smallpox, which weakened his vision. Therefore, he grew up physically weak and sickly. Because of this, it took him longer than his peers to complete his secondary education. At the same time, Kepler’s admission to the University of Tübingen was facilitated by the city authorities, who noted the outstanding abilities that Johann Kepler possessed. Brief biography scholar from 1591 to 1594 represents an intense absorption of knowledge in one of the best European universities.

Kepler was a deeply religious man and a staunch Protestant all his life. Therefore, he prepared to become a priest and entered the theological faculty. True, before this he took a course in mathematics and astronomy, becoming a Master of Arts - that is what these were called at that time. Among his teachers was a proponent of the heliocentric system, Michael Möstlin. Under the influence of his lectures, Kepler also became a convinced preacher of this theory. Johann tried to creatively comprehend the ideas of Copernicus, but did not always draw the right conclusions.

Kepler Cup

Johann's plans to become a priest were prevented by his invitation to the position of teacher of mathematics at the University of Graz (1594). Although his conviction in his commitment to the path of serving God was complete, the biography of Johannes Kepler becomes the biography of a research scientist standing on the platform of teaching that denied the Ptolemaic (geostationary) model of the world.

In Harz, he searched for mathematical harmony in the structure of the solar system and published the book “The Mystery of the Universe” (1596). The “Kepler Cup” became a visual expression of the ideas proclaimed by the scientist in this book. It was a volumetric one in which the luminary is located in the center in Copernican style, but Kepler endows the orbits of the planets revolving around with the properties of Platonic solids - cubes, spheres and regular polyhedra. It was not for nothing that mathematics was considered an art at that time - this model was very beautiful, although absolutely incorrect.

A timely invitation

Kepler sent his book to the most advanced scientists in Europe, including Galileo and the Dane Tycho Brahe, who served as court astronomer in Prague. Denying the harmony of orbital forms proposed by Kepler, both scientists highly appreciate the work of the young mathematician and astronomer. True, from different positions. Galileo approved of the heliocentric approach, and Brahe liked the boldness and originality of his thinking. The Dane invited Kepler to Prague.

Several circumstances contributed to Johann's departure to Prague. Among them are Kepler’s difficult financial and moral situation (he got married, but his young wife fell ill with epilepsy and soon died) and the beginning of the persecution of Protestants by the Catholic Church, which declared Johannes Kepler an apostate. Brief biography of the scientist in last period His stay in the Harz is full of threats and pressure on him as a supporter of heretical theories.

Kepler arrives in Prague, where the most fruitful stage of his life begins.

Kepler in Prague. Heritage

Soon after the start collaboration Brahe died unexpectedly, leaving Kepler his archives and the position of court astronomer and astrologer. The decade Kepler spent in Prague underlies all his main scientific achievements made in astronomy, physics, mathematics.

In astronomy, Kepler brought final order to the idea of ​​​​the movement of the planets of the solar system. His contemporaries could understand what discovery belonged to Johannes Kepler from the scientist’s main book, “New Astronomy” (1609). In it and in the final work, “The Harmony of the World” (1618), three laws of celestial kinematics were formulated. The first spoke about the shape of the orbit of the planets in the form of an ellipse with the Sun at one of the focuses, the second and third described the speed of the planet’s movement in orbit and methods for measuring it. In addition, Kepler described and compiled precise astronomical tables that served to guide sailors and astronomers by the stars.

Mathematics was the main tool Kepler used in his work. Johann, in his book “New Stereometry of Wine Barrels” (1615), shows ways of finding volume for bodies of rotation, lays the foundations of mathematical analysis and integral calculus. Among Kepler's mathematical discoveries was a table of logarithms, new concepts - "arithmetic mean" and "point at infinity".

Kepler introduced the concept of “inertia” into scientific use, speaking about the existence in nature of the desire of related bodies to unite, and came close to the discovery of the law of universal gravitation. For the first time he explained the cause of sea ebbs and flows by the influence of the Moon, described the causes of myopia, and developed a more advanced telescope.

Recent years. Memory

In 1615, Kepler was forced to become a lawyer for his mother, who was accused of witchcraft. She was threatened with burning at the stake, but Johann managed to secure her release.

Kepler was forced to spend his last years searching for a reliable source to provide for his family, and during a trip to the emperor, who owed him a salary, in the city of Rigensburg in 1630, he died.

Kepler's name today is in line greatest minds, whose ideas underlie both current scientific and technical achievements. An asteroid and a crater on the Moon are named after him. space truck and an orbital space observatory, with the help of which it was discovered new planet, similar in conditions to Earth and also named after Kepler.