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 then mathematical sciences, which 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 in early XVII 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 insoluble before him, and the path was paved for the discovery 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 put correct basis theories of telescope operation. 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 an accident; 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 facts to explain them. This phase, through which all branches of natural science have passed or must eventually pass, consists in finding the basic 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 true form 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 a planet's orbital motion in different parts 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 of the scientist, called “Harmony of the Universe”, and is expressed in the words: squares of revolution times different planets are in the same proportion to each other as the cubes of those lines of their orbits, which are called the semimajor 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 job required huge amount 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 in it extraordinary strength 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 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 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 - moon 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 at 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 Secret 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 regular 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 he passed away and faithful companion Johanna.
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 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 shortage 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 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, discovered by the researcher Newton took the laws of planetary kinematics as a basis for his theory of gravitation. In addition, Johannes Kepler is the author of the very first exposition of “Copernican astronomy”. Before 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 property of resisting 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 everyone modern mathematicians, physicists and astronomers, and scientific achievements centuries later they have not lost their significance.
(German: Johannes Kepler) - an outstanding German mathematician, astronomer, optician and astrologer. Discovered the laws of planetary motion.
Johannes Kepler was born on December 27, 1571 in Weil der Stadt, a suburb of Stuttgart (Baden-Württemberg). His father served as a mercenary in 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.
In 1589, Kepler graduated from school at the Maulbronn monastery, where he showed outstanding abilities. The city authorities awarded him a scholarship to help him further his studies.
In 1591 he entered the university in Tübingen - first at the Faculty of Arts, which then included mathematics and astronomy, then moved to the Faculty of Theology. Here he first heard about the ideas of Nicolaus Copernicus heliocentric system world and immediately became their adherent.
Thanks to the extraordinary mathematical abilities Johannes Kepler was invited in 1594 to lecture on mathematics at the University of Graz (now in Austria).
Kepler spent 6 years in Graz. Here his first book, “The Mystery of the World” (Mysterium Cosmographicum), was published (1596). In it, Kepler tried to find the secret harmony of the Universe. This work, after further discoveries by Kepler, lost its original significance, 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.
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 begins in Catholic Graz. Kepler is included in the list of expelled "heretics" and is forced to leave the city.
Johannes Kepler accepted the invitation of the famous Danish astronomer Tycho Brahe, who by this time had moved to Prague and served as court astronomer and astrologer for Emperor Rudolf II. In 1600, Kepler arrives in Prague. The 10 years spent here were the most fruitful period of his life.
After Brahe's death in 1601, Kepler succeeded him in office. Emperor's treasury due to endless wars was constantly empty. Kepler's salary was paid rarely and meagerly. He is forced to earn extra money by drawing up horoscopes.
For several years, Johannes Kepler carefully studied the data of the astronomer Tycho Brahe and, as a result, thorough analysis comes 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.
As a result of further analysis, Kepler discovered the second law: the radius vector connecting the planet and the Sun describes in equal time equal areas. This meant that the further a planet is from the Sun, the slower it moves.
Both laws were formulated by Kepler in 1609 in the book “New Astronomy”, and, for the sake of caution, he applied them only to Mars.
The publication of the New Astronomy and the almost simultaneous invention of the telescope marked the advent of a new era. These events became a turning point in life and scientific career Kepler.
After the death of Emperor Rudolf II, Johannes Kepler's position in Prague became increasingly uncertain. He turned to the new emperor for permission to temporarily take up the post of mathematician of the province of Upper Austria in Linz, where he spent the next 15 years.
In 1618, the scientist discovered Kepler's third law - the ratio of the cube of the average distance of 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. Thus, the great German astronomer Johannes Kepler discovered the law of planetary motion.
For the next 9 years, Kepler worked on compiling tables of planetary positions based on new laws of their motion. The events of the Thirty Years' War and religious persecution forced Kepler to flee to Ulm in 1626. Having no means of subsistence, in 1628 he entered the service of the imperial commander Wallenstein as an astrologer. Last major work Kepler's planetary tables, conceived by Tycho Brahe, were published in Ulm in 1629 under the title Rudolf's Tables.
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 guessed that tails are formed under the influence 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.
The scientist died during a trip to Regensburg on November 15, 1630, when he tried in vain to get at least part of the salary that the imperial treasury owed him for many years.
Kepler's work on the creation celestial mechanics played vital role in the approval and development of the teachings of Copernicus. He paved the way for subsequent research, in particular for Newton's discovery of the law 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.
Kepler owes enormous credit for the development of our knowledge about solar system . Scientists of subsequent generations who appreciated the significance of Kepler’s works They called him "the lawgiver of heaven", since it was he who found out the laws by which the movement of celestial bodies occurs in the solar system.
Kepler's laws equally applicable to any planetary system anywhere in the Universe. Astronomers searching for new planetary systems in outer space time after time, as a matter of course, Kepler's equations are used to calculate the parameters of the orbits of distant planets, although they cannot observe them directly.
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 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 of the Sun in the 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 inscribed and around which are described regular polyhedra. 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. Accomplished meeting 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 thought that a 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, using the methods of mathematics constant values could not be decided. 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 an 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 shortly before discovered by Galileo Jupiter's satellites rotate 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 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 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 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. There is an inscription above his grave: “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 underground darkness; 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.
Published for the tercentenary anniversary of the birth of Johannes Kepler full meeting his works (“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.
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Johannes Kepler (German: Johannes Kepler, December 27, 1571, Weil der Stadt - November 15, 1630, Regensburg) was a German mathematician, astronomer, mechanic, optician, discoverer of the laws of motion of the planets of the solar system.
After graduating church school in Alderberg, in 1586 he entered the higher theological school at the Maulborn Monastery. In 1589 he was admitted to the University of Tübingen, where he studied theology, mathematics and philosophy for three years. Astronomy at the university was taught by M. Mestlin, who gave private lessons to Kepler and introduced him to the theory of Copernicus. In 1591 Kepler defended master's thesis, graduated from the university in 1593 and was recommended for the position of professor of mathematics at the Graz gymnasium (Upper Styria). Here from 1594 he lectured on astronomy. In 1596, his first work, The Mystery of the Universe (Prodromus dissertationum mathematicarum continens mysterium cosmographicum, 1596), was published, in which Kepler tried to find relationships between the elements of planetary orbits. This work attracted the attention of Tycho Brahe, who invited Kepler as an assistant to process the results of observations of the planets. The collaboration between astronomers lasted about two years, until the death of Tycho Brahe on October 24, 1601. Soon, Emperor Rudolf II appointed Kepler to the position of court mathematician, which he held until the end of his life.
During Tycho Brahe's lifetime, Kepler attempted mathematical description patterns of movement of the planet Mars within the framework of the then existing theories (Ptolemy, Tycho Brahe, Copernicus). As a result of much thought, Kepler came to the empirical laws of planetary motion (Kepler's laws). According to the first two, the planets revolve around the Sun in elliptical orbits, the focus of which is the luminary; The radius vector of each planet sweeps out equal areas in equal periods of time. These results were published in the book New Astronomy (Astronomia Nova, 1609), which ranked alongside Copernicus's De Revolutionibus and Newton's Principia.
The publication of the New Astronomy and the almost simultaneous invention of the telescope marked the advent of a new era. These events marked a turning point in Kepler's life and scientific career. After the death of Rudolf II, the position of the scientist at the court in Prague became increasingly uncertain. He therefore turned to the new emperor for permission to temporarily take up the post of mathematician of the province of Upper Austria in Linz, where he spent the next 15 years. Kepler's main achievement during this period was the discovery of the third law of planetary motion: the squares of the planets' periods of revolution are related as the cubes of the semimajor axes of their elliptical orbits. This law was formulated in the work Harmony of the World (De Harmonice Mundi, 1619). For the next 9 years, Kepler worked on compiling tables of planetary positions based on new laws of their motion.
The events of the Thirty Years' War and religious persecution forced Kepler to flee to Ulm in 1626. Having no means of subsistence, in 1628 he entered the service of the imperial commander Wallenstein as an astrologer. Kepler's last major work was the planetary tables conceived by Tycho Brahe, published in Ulm in 1629 under the name Rudolph's Tables (Tabulae Rudolphianae).
