Kepler's discoveries in mathematics and optics. Johann Kepler: biography, photos and interesting facts. In what year was Johann Kepler born?

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 observational data on the movement of 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 into a poor family, and therefore with great difficulty he managed to graduate from 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 Cosmographic Secret”, where, accepting Copernicus’ conclusion about the central position of the Sun in the planetary system, he tried to find a connection between the distances of planetary orbits and the radii of the spheres into which regular polyhedra were inscribed in a certain order and around which they were 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.

The philosophers of Ancient Greece 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 somewhat different from a circle. When solving this problem, Kepler had to encounter a case that, generally speaking, could not be solved using the methods of mathematics of constant quantities. The matter came down to calculating the area of ​​the sector of the eccentric circle. If we translate this problem into modern mathematical language, we arrive at an 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 an infinitely large number of “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 the further development of computational tools in 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 applied 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 Napier's work, Johannes Kepler independently constructed the theory of logarithms on a purely arithmetic basis and, with its help, compiled logarithmic tables close to Napier's, but more accurate, 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 in the problems of astronomical optics led him to the development of the general principle of continuity - a kind of heuristic technique that allows one 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 an infinitely distant focus - 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 an open struggle for the teachings of Copernicus. In 1617-1621, at the height of the Thirty Years' War, when Copernicus's book was already on 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 1,000 pages. The title of the book does not accurately reflect its content - the Sun occupies the place indicated by Copernicus, and the planets, the Moon and the satellites of Jupiter discovered by Galileo shortly before revolve 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, published in 1627 under the title “Rudolfin Tables,” which for many years were a reference book for astronomers. Kepler was also responsible for 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 establishment and development of the teachings of Copernicus. They prepared the ground for subsequent research, in particular for Isaac Newton's discovery of the law of universal gravitation. 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 solar rays. At that time, nothing was known about the nature of 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 ages 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 telescope, which still bears his name, observed a comet (Halley), etc. Immediately, processing systematic and very accurate observations Tycho, I. Kepler discovered the first two of his immortal laws of planetary motion around the sun (all planets revolve in ellipses, at one of the foci of which the sun is located and the areas described by radius 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 Rudolf II, Johannes Kepler accepted a professorship in Linz and here 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; in Russian, a biography of Kepler and a generally understandable presentation of his scientific activities are in the biographical library of F. Pavlenkov. The biography was compiled, according to Frisch, by E. A. Predtechensky.

Johannes Kepler was born on December 27, 1571 in the German state of Stuttgart in the family of Heinrich Kepler and Katharina Guldenmann. It was believed that the Kelpers were rich, however, by the time the boy was born, the wealth in the family had decreased significantly. Heinrich Kepler made his living as a trader. When Johann was 5 years old, his father left the family. The boy's mother, Katharina Guldenmann, was a herbalist and healer, and later, in order to feed herself and her child, she even attempted witchcraft. According to rumors, Kepler was a sickly boy, frail in body and weak in mind.

However, from an early age he showed interest in mathematics, often surprising those around him with his abilities in this science. Even as a child, Kepler became acquainted with astronomy, and he would carry his love for this science throughout his life. Occasionally, he and his family observe eclipses and the appearance of comets, but poor eyesight and smallpox-affected hands do not allow him to seriously engage in astronomical observations.

Education

In 1589, after graduating from high school and Latin school, Kepler entered the Tübingen Theological Seminary at the University of Tübingen. It was here that he first showed himself as a competent mathematician and a skilled astrologer. At the seminary he also studied philosophy and theology under the guidance of outstanding personalities of his time - Vitus Müller and Jacob Heerbrand. At the University of Tübingen, Kepler became acquainted with the planetary systems of Copernicus and Ptolemy. Leaning towards the Copernican system, Kepler takes the Sun as the main source of driving force in the Universe. After graduating from university, he dreams of getting a government position, however, after being offered the post of professor of mathematics and astronomy at the Protestant School of Graz, he immediately abandons his political ambitions. Kepler took up the post of professor in 1594, when he was only 23 years old.

Scientific activity

While teaching at a Protestant school, Kepler, in his own words, “had a vision” of the cosmic plan for the structure of the Universe. In defense of his Copernican views, Kepler presents a periodic relationship of the planets, Saturn and Jupiter, in the zodiac. He also directs his efforts to determine the relationship between the distances of the planets from the Sun and the sizes of regular polyhedra, claiming that the geometry of the Universe was revealed to him.
Most of Kepler's theories, based on the Copernican system, stemmed from his belief in the interconnection of scientific and theological views of the Universe. As a result of this approach, in 1596 the scientist wrote his first, and perhaps the most controversial of his works on astronomy, “The Secret of the Universe.” With this work he gained a reputation as a skilled astronomer. In the future, Kepler would make only minor amendments to his work, and would take it as the basis for a number of his future works. The second edition of “The Secret” will appear in 1621, with a number of amendments and additions from the author.

The publication increases the scientist’s ambitions, and he decides to expand his field of activity. He begins four more scientific works: on the immutability of the Universe, on the influence of the heavens on the Earth, on the movements of the planets and on the physical nature of stellar bodies. He sends his works and assumptions to many astronomers, whose views he supports, and whose works serve as an example for him, in order to obtain their approval. One of these letters turns into a friendship with Tycho Brahe, with whom Kepler will discuss many questions regarding astronomical and celestial phenomena.

Meanwhile, a religious conflict is brewing in the Protestant school in Graz, which threatens his further teaching at the school, and therefore he leaves the educational institution and joins Tycho’s astronomical works. January 1, 1600 Kepler leaves Graz and goes to work for Tycho. The result of their joint work will be the outstanding works “Astronomy from the Point of View of Optics”, “Rudolph's Tables” and “Prussian Tables”. The Rudolphian and Prussian tables were presented to the Holy Roman Emperor Rudolf II. But in 1601, Tycho suddenly dies, and Copernicus is appointed imperial mathematician, who is entrusted with the responsibility of finishing the work Tycho began. Under the emperor, Kepler rose to the rank of chief astrological adviser. He also helped the ruler during political unrest, without forgetting his works on astronomy. In 1610, Kepler began joint work with Galileo Galilei, and even published his own telescopic observations of the satellites of various planets. In 1611, Kepler constructed a telescope for astronomical observations of his own invention, which he called the “Keplerian telescope.”

Supernova observations

In 1604, a scientist observes a new bright evening star in the starry sky, and, not believing his eyes, notices a nebula around it. A supernova like this can only be observed once every 800 years! It is believed that such a star appeared in the sky at the birth of Christ and at the beginning of the reign of Charlemagne. After such a unique spectacle, Kepler checks the astronomical properties of the star and even begins to study the celestial spheres. His calculations of parallax in astronomy bring him to the forefront of that science and strengthen his reputation.

Personal life

During his life, Kepler had to endure many emotional upheavals. On 27 April 1597 he married Barbara Müller, by then twice a widow, who already had a young daughter, Gemma. In the first year of their married life, the Keplers had two daughters.
Both girls die in infancy. In subsequent years, three more children would be born into the family. However, Barbara's health deteriorated, and in 1612 she died.

October 30, 1613 Kepler marries again. After reviewing eleven games, he chooses 24-year-old Susanne Reuttingen. The first three children born from this union die in infancy. Apparently, the second marriage turned out to be happier than the first. To add insult to injury, Kepler's mother is accused of witchcraft and imprisoned for fourteen months. According to eyewitnesses, the son did not leave his mother during the entire process.

Death and legacy

Kepler died just before he was to observe the transits of Mercury and Venus, which he had been eagerly awaiting. He died on November 15, 1630, in Regensburg, Germany, after a short illness. For many years, Kepler's laws were viewed with skepticism. However, after some time, scientists began to test Kepler's theories, and, gradually, began to agree with his discoveries. The Reduction of Copernican Astronomy, the main vehicle of Kepler's ideas, served as a guide to astronomers for many years. Famous scientists, such as Newton, built their theories on the work of Kepler.

Kepler is also known for his philosophical and mathematical works. A number of famous composers dedicated musical compositions and operas to Kepler, Harmony of the World being one of them.
In 2009, to commemorate Kepler's contributions to astronomy, NASA launched the Kepler mission.

Major works

• "New Astronomy"
• "Astronomy from the point of view of optics"
• "The Secret of the Universe"
• "Dream"
• "New Year's gift, or About hexagonal snowflakes"
• "Kepler's Conjectures"
• "Law of Continuity"
• "Keplerian laws of planetary motion"
• "Copernican Astronomy Reduced"
• "Harmony of the World"
• "Rudolph's Tables"

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There was a strong poetic imagination, as we see from the hypotheses that he makes in his great astronomical creations. But he distinguished his assumptions from the positive truths he discovered. There is not a single department of the mathematical sciences of that time that he would not have advanced. Kepler lovingly accepted every discovery, every new sensible thought of other scientists, and was excellent at separating truth from error. He correctly appreciated the importance of logarithms, invented at the beginning of the 17th century by the Scottish mathematician Lord Napier. He realized that with their help it was easy to make calculations that without them would have been difficult due to their complexity; therefore I made a new edition of logarithms with an explanatory introduction; Thanks to this, logarithms quickly came into general use. In geometry, Kepler made discoveries that moved it forward a lot. He developed concepts and methods that solved many problems that had been unsolvable before him, and the path was paved for the discovery of differential calculus. He saw the need to investigate certain issues of optics in order to clear astronomical observations from the inaccuracy introduced into them by the refraction of light rays in the atmosphere, and to clarify the laws of operation of the then invented telescope. Kepler gave solutions to these questions in the optical part of his astronomical treatise and in Dioptrics. He discovered the true course of the vision process of our eye. He laid the correct foundation for the theory of the operation of the telescope. He was unable to find the exact law of refraction of rays, but he found a concept about it so close to the truth that it was sufficient to explain the action of optical instruments. Based on these studies, Johannes Kepler proposed a new telescope device, which, according to his considerations, should have been the best for astronomical observations. The telescope of this device, called a Keplerian, remained in use until the beginning of the 20th century. (The invention of the telescope was, in all likelihood, the result of chance; stories about it vary, but everyone agrees that it was made in Middelburg, in Holland. Galileo was the first to use the telescope for astronomical observations, but the laws of operation of this instrument became clear only thanks to Kepler's research.)

Portrait of Johannes Kepler, 1610

Kepler's laws

The greatest of the immortal discoveries of this scientist is the one the essence of which was formulated by him in conclusions called after his name Kepler's laws. They revealed the idea Copernicus in its full meaning and showed its thoroughness; they constituted a phase of transition in the history of astronomy from simple knowledge of facts to their explanation. This phase, through which all branches of natural science have passed or must eventually pass, consists of finding the main common features in the intricate course of phenomena. Copernicus gave a true concept of the structure of the solar system; Kepler discovered the basic laws of planetary rotation.

Copernicus already noticed that there are irregularities in the motion of the planets that cannot be explained by the adoption of planetary orbits as circles, in the center of which is the sun; but he considered it necessary to take a circular line as the shape of the orbits, and explained the inequalities in the motion of the planets in their orbits by the assumption that the sun is not in the center of these circles. Kepler by observation Tycho Brahe I saw that the inequalities in motion were especially great on Mars. He began to study them, and found that Copernicus’s assumption did not fully explain them. Through a series of deep studies and ingenious considerations, he finally made the discovery that the true shape of the orbit of Mars is an ellipse. This discovery, which turned out to be true for all other planets, is called Kepler's first law. It is expressed by the formula: the planets revolve around the sun in an ellipse, at one of the foci of which the sun is located. Kepler's second law determines the differences in the speed of the planet's orbital motion in different parts of this path; he says that the areas described by the rotation of the line going from the sun to the planet, and called the radius vector in an ellipse, are equal at equal times. Thus, the further the planet is from the focus in which the sun stands, the shorter will be the length of the path traveled by it during a certain time, for example an hour, because the longer the triangle, the smaller its width compared to a triangle with the same surface area at shorter length. The third law, discovered by Johannes Kepler, determines the proportion between the times of revolution of the planets around the sun and their distances from it. It is set out in another work by the scientist, called “Harmony of the Universe,” and is expressed in the words: the squares of the times of revolution of different planets are in the same proportion to each other as the cubes of those lines of their orbits, which are called the semi-major axes of these ellipses.

Kepler and the discovery of the law of universal gravitation

That part of astronomy, which consists in calculating observations, was also greatly advanced by the works of Kepler; he did this by compiling the so-called Rudolf tables, published by him in 1627 and named Rudolf in honor of the then reigning emperor. These tables are a compilation of observations made by Tycho Brahe and Kepler himself, and calculations made by Kepler from them; this work required a huge amount of time and iron will for its execution.

Johannes Kepler's ideas about the reason that causes the planets to move according to the laws he discovered are amazing in their genius. He had already foreseen what was later proven by Newton, and explained the rotation of the planets by the combination of the force of their tangent motion with the force that attracts them to the sun, and reached the conviction that this centripetal force is identical with what is called gravity. Thus, he only did not have the materials to find the law of action of the force of universal gravity, and to confirm his opinion with accurate evidence, as was later done by Newton; but he had already found that the reason for the rotation of the planets is the force of universal gravity. Kepler says: “Gravity is only the mutual attraction of bodies to approach each other. Heavy bodies on the earth tend to the center of the spherical body of which they form parts, and if the earth were not spherical, then the bodies would not fall vertically towards its surface. If the moon and the earth were not kept at their present distance by the moon's tendency to move along the tangent of its orbit, they would fall on each other; “The moon would travel about three-fourths of this distance, and the earth a fourth of this distance, assuming both were of the same density.” – Kepler also figured out that the cause of the ebb and flow of the tides is the attraction of the moon, which changes the level of the ocean. These discoveries show his extraordinary strength of mind.

Romance and mysticism in Kepler

Despite the extremely high scientific merit of Kepler's works, a breath of poetic spirit also runs through them. Kepler loves, like the Pythagoreans and Plato, to combine the results of serious research with fantastic thoughts about the harmony of numbers and distances. This tendency sometimes involved him in opinions that turned out to be incompatible with the truth, but serves as new proof of the creative power of his imagination. He developed fantastic thoughts especially in those works called “On the Mystery of the Structure of the Universe,” “Harmony of the Universe,” and “Kepler’s Dream.”

Job responsibilities forced Kepler to engage in astrological calculations. As a professor of mathematics in Graz, he was required to draw up a calendar annually; and the calendar, according to the custom of that time, was supposed to give astrological predictions about the weather, war and peace. Kepler performed this duty very cleverly: he studied the rules of astrology well, so that he could give his predictions the form required of them, and he made predictions by careful consideration of probabilities and, with the insight of his mind, often predicted successfully. This brought him great fame as an astrologer, and many of the most important people in Austria commissioned him to make their horoscopes. At the end of his life, Kepler was an astrologer under Wallenstein, who believed in astrology. However, he himself spoke about the unreliability of his predictions, and in his letters there are many places showing that he correctly thought about the astrological superstition that prevailed in his time. For example, he says: “Lord God, what would have happened to reasonable astronomy if it had not had its stupid daughter astrology with it. The salaries of mathematicians are so small that the mother would probably suffer hunger if her daughter did not acquire anything.”

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

Kepler Johann (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.

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, and compiled calendars and astrological forecasts. In the work “The Harbinger, or the Cosmographic Mystery” (Prodromus sive Mysterium cosmographicum, 1596), he set out the divine mathematical order of the heavens: six planets determine five intervals, corresponding to the five “Platonic” polyhedra. He was a court mathematician in Prague, an assistant to Tycho Brahe; processing his precise observations of the movements of Mars, he established the first two laws of planetary rotation: the planets do not move in circular orbits, but in ellipses, at one of the focuses of which is the Sun; planets move at a speed at which radius vectors describe equal 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 planets' periods of revolution are related to the cubes of their average distances from the Sun - is set out 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 "Short Essay on Copernican Astronomy" (Epitome astronomiae Copernicanae, 1621) was the best astronomy textbook of that era. Kepler's discoveries were of enormous importance for the philosophical and scientific development of modern times.

L. A. Mikeshina

New philosophical encyclopedia. In four volumes. / Institute of Philosophy RAS. Scientific ed. advice: V.S. Stepin, A.A. Guseinov, G.Yu. Semigin. M., Mysl, 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 graduate from school and enter the University of Tübingen in 1589. Here he studied mathematics and astronomy. His teacher Professor Mestlin was secretly a follower Copernicus. Soon Kepler also became a supporter of the Copernican theory.

Already in 1596, he published “The Cosmographic Secret” where, accepting Copernicus’ conclusion about the central position of the Sun in the planetary system, he tried to find a connection between the distances of planetary orbits and the radii of the spheres into which regular polyhedra were inscribed in a certain order and around which they were described. Despite the fact that this work of Kepler still remained an example of scholastic, quasi-scientific wisdom, it brought fame to the author.

In 1600, the famous Danish astronomer-observer 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 long-term observational data. Kepler came to the conclusion that the opinion about the circular shape of planetary orbits was incorrect. Through calculations, he proved that the planets do not move in circles, but in ellipses. 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.

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

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. He built the theory of logarithms on an arithmetic basis and, with its help, compiled logarithmic tables, first published in 1624 and reprinted until 1700.

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

In 1617-1621, at the height of the Thirty Years' War, when Copernicus' book was already on the Vatican's "List of Prohibited Books." Kepler publishes Essays on Copernican Astronomy in three editions. 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 discovered by Galileo shortly before revolve according to the laws discovered by Kepler. During these same years, Kepler published Harmony of the World, where he formulated 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 name “Rudolfin Tables,” which for many years were a reference book for astronomers. Kepler also contributed 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 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 solar rays. At that time, nothing was known about the nature of 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.

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 the site http://100top.ru/encyclopedia/

Read further:

World-famous scientists (biographical reference book).

Kepler's three laws. In the book: Gurtovtsev A.L. Think or believe? Ode to Human Asinineness. Minsk, 2015.

Essays:

Gesammelte Werke, Bd. 1 - 18, hrsg. W. Van Dyckund M. Caspar. Munch., 1937-63; in Russian Transl.: 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 its origins to the present day, vol. 3. Modern times. St. Petersburg, 1996.

German mathematician, astronomer, mechanic, optician, discoverer of the laws of motion of the planets of the solar system

short biography

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 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 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 his extraordinary mathematical abilities, he 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 ball 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 discovered even before the first): the radius vector connecting the planet and the Sun describes equal areas in equal time. 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 Star 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 Dioptricus.

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.

Last 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. The following year she died.

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 volumes out of 22), 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 activity

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

He lived in an era when there was still no confidence in 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 a difficult and painstaking empirical study of the movement of 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

At the end of the 16th century, there was still a struggle in astronomy 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 Copernicus’ 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 along 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). The circular motions of spheres carrying planets disappeared, and the concept of a planetary orbit appeared. In the Copernican system, the Earth still occupied a somewhat special position, since Copernicus declared the center of the earth's orbit to be the center of the world. 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,” 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 all celestial movements, both in their entirety and in all individual cases, are imbued with a general harmony - not the one I expected, however, 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 polluted the real essence of 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 for the adoption of the Gregorian calendar by Protestants (at the Diet in Regensburg, 1613, and in Aachen, 1615).

Kepler became the author of the first extensive (in three volumes) presentation 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, his 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, the Italian physicist and astronomer Giovanni Alfonso Borelli published a book in which Kepler's laws were confirmed for the moons of Jupiter discovered by Galileo.

Mathematics

Kepler found a way to determine the volumes of various bodies of revolution, 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 the assumptions 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 of 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 point at infinity. He also introduced the concept of the focus of a conic section and considered projective transformations of conic sections, including those that change their type - for example, transforming 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. He describes the refraction of light, refraction and the concept of optical image, the general theory of 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.

The physiological mechanism of vision described by him, from a modern point of view, 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 of the nature of astrology, which made him stand out among contemporary astrologers. In his work “The Harmony of the World,” he states that “there are no luminaries in the heavens that bring misfortune,” but the human soul is capable of “resonating” with the rays of light emanating from celestial bodies; it imprints in memory the configuration of these rays at the moment of its birth. The planets themselves, in Kepler’s view, were living beings endowed with an individual soul.