(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 and his heliocentric system of the world and immediately became their adherent.
Thanks to his 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. The emperor's treasury was constantly empty due to endless wars. 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 of careful analysis, came to the conclusion that the trajectory of Mars is not a circle, but an ellipse, at one of the focuses of which is the Sun - a position known today as the first law Kepler.
As a result of further analysis, Kepler discovered the second law: the radius vector connecting the planet and the Sun describes equal areas in equal times. 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 marked a turning point in Kepler's life and scientific career.
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. Kepler's last major work was the planetary tables conceived by Tycho Brahe, 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 of sunlight. 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.
Kepler's work on the creation of celestial mechanics played a vital role in the establishment and development of the teachings of Copernicus. He paved the way for subsequent research, in particular for Newton’s discovery of the law of universal gravitation.
Kepler's laws still 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 is credited with enormous credit for developing our knowledge of the 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 apply equally 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
Biography Johannes Kepler (1571-1630)
Short biography:
Education: University of Tübingen
Place of Birth: Weil der Stadt, Holy Roman Empire
A place of death: Regensburg
– German astronomer, mathematician: biography with photos, discoveries and contributions to astronomy, laws of planetary motion, Brahe’s receiver, influence on Newton.
Johannes Kepler was born ahead of schedule on December 27, 1571. His short biography started in Weil der Stadt (Germany). He was a sickly child and suffered from smallpox at an early age. Kepler went to study at the University of Tübingen, a Protestant institution, where he studied theology and philosophy, as well as mathematics and astronomy. After completing his education, he was hired as a teacher of mathematics and astronomy in Graz, Germany. In 1596, at the age of 24, Kepler published the Mysterium Cosmographicum (Cosmographic Mystery). In this work he defended the theories of Copernicus, who argued that the Sun, not the Earth, was at the center of the Solar System. was heavily influenced by the Pythagoreans, believing that the Universe is governed by geometric relationships that correspond to the incircle and circumcircle of five regular polygons.
In 1598, Kepler's school in Graz was closed on the initiative of Ferdinand of Habsburg. Kepler wanted to return to Tübingen, but they did not want to let him go, thanks to his well-known belief in Copernicanism. The astronomer Brahe secretly invited Johannes Kepler to come to Prague to be his assistant. Faced with Catholic persecution of Protestant minorities in Graz, Kepler accepted Brahe's offer and left for Prague on 1 January 1600. When Brahe died the following year, Kepler was appointed as his successor. Kepler inherited from Brahe knowledge of many of the exact locations of certain planets, in particular Mars. Kepler used this data to study the orbits of the planets. He abandoned the claim that the planet moved in a circle and proved that the orbit of Mars is actually an ellipse. This, the first of Kepler's laws of planetary motion, appeared in the Astronomia Nova (New Astronomy), which he published in 1609. His second law of planetary motion, also published in 1609, describes the concept of planetary speed. His third law, published in 1619, describes the relationship between the orbital distance of orbiting planets and their distance from the Sun.
In short, Johannes Kepler’s three laws of planetary motion sound like this:
- Each planet of the solar system rotates in an ellipse, the Sun is located at one of the foci of such a planet;
- Each planet moves in a plane that passes through the center of the Sun, and over equal periods of time, the radius vector connecting the Sun and the planet describes equal areas.
- The squares of the periods of revolution of the planets around the Sun are related like the cubes of the semi-major axes of the planets' orbits.
Johannes Kepler died in Regensburg (Germany) on November 15, 1630 after a short illness. His important work would later lay the foundation for Isaac Newton and the theory of gravity. In the biography of astronomers, Johannes Kepler was the link between the thoughts of Copernicus and Newton, and is seen as a particularly important figure in the scientific revolution of the 17th century.
rendered great services to astronomy not only with his immortal laws, but the fruit of deep, brilliant considerations and persistent, constant work that overcame all obstacles. If in his writings great ideas were not mixed with systematic ideas that he borrowed from contemporary philosophy; then his proposals would be assessed much more accurately than that science cannot move forward without proposals; without suggestions it is impossible to come up with a single useful experience; you just need to be conscientious and only after experiments and calculations that confirm the proposal, allow it into science.Kepler adhered to this rule as much as he could; Without hesitation or stubbornness, he abandoned his most beloved hypotheses if they were destroyed by experience.
Kepler always lived in poverty, and therefore was forced to work for booksellers, who demanded almost daily news from him; he had no time to think about his thoughts; he presented them as they were born in his mind; he thought out loud. How many wise men are there who have endured such torture?
Although in numerous works of Kepler we find ideas that cannot be justified by his constrained circumstances, we cannot help but be lenient towards him if we fully understand his difficult life and take into account the misfortunes of his family.
We extracted this opinion about the causes of many of Kepler’s paradoxes from the writings of Breischvert, who in 1831 examined the unpublished works of the great astronomer, who completed the transformation of ancient astronomy.
Johannes Kepler was born on December 27, 1571 in Magstadt, in the Wirtemberg village, located one mile from the imperial city of Weil (in Swabia). He was born premature and very weak. His father, Heinrich Kepler, was the son of the burgomaster of this city; his poor family considered themselves to be nobility; because one of the Keplers was made a knight under the emperor Sigismund. His mother, Katerina Guldenman, the daughter of an innkeeper, was a woman without any education; she could neither read nor write, and spent her childhood with her aunt, who was burned for witchcraft.
Kepler's father was a soldier who fought against Belgium under the command of the Duke of Alba.
At the age of six, Kepler suffered from severe smallpox; He had barely escaped death when in 1577 he was sent to the Leonberg school; but his father, returning from the army, found his family completely ruined by one bankrupt, for whom he had the imprudence to vouch for; then he opened a tavern in Emerdinger, took his son from school and forced him to serve the visitors of his establishment. Kepler corrected this position until he was twelve years old.
And so the one who was destined to glorify both his name and his fatherland began life as a tavern servant.
At the age of thirteen, Kepler again became very ill and his parents did not hope for his recovery.
Meanwhile, his father’s affairs were going badly, and therefore he again joined the Austrian army, which was going against Turkey. Since that time, Kepler's father has been missing; and his mother, a rude and quarrelsome woman, spent the last property of the family, which amounted to 4 thousand florins.
Johannes Kepler had two brothers who resembled his mother; one was a tin smith, the other a soldier, and both were complete scoundrels. Thus, the future astronomer found nothing in his family except burning grief, which completely destroyed him if it were not for the comfort of his sister Margarita, who married a Protestant pastor; but this relative also later became his enemy.
When Kepler's father left the army, he was forced to work in the fields; but the weak and skinny young man could not endure hard work; he was appointed a theologian, and at the age of eighteen (1589) he entered the Tubinham seminary and was supported there at public expense. During the examination for his bachelor's degree he was not recognized as excellent; this title went to John Hippolytus Brencius, whose name you will not find in any historical dictionary, although the publishers of such collections are very lenient and put all sorts of rubbish in them. However, in our biographies we will often encounter such cases that prove the absurdity of school pedantry.
Kepler failed for more than one reason: while still at school, he took an active part in Protestant theological disputes, and since his opinions were contrary to the Wirtemberg orthodoxy, they decided that he was not worthy of promotion to the clergy.
Fortunately for Kepler, Maestlin, summoned (1584) from Heidelberg to Tübingen to the department of mathematics, gave his mind a different direction. Kepler left theology, but did not completely free himself from the mysticism rooted in him by his initial upbringing. At this time, Kepler saw the immortal book of Copernicus for the first time.
“When I,” says Kepler, “appreciated the delights of philosophy, then I ardently occupied myself with all its parts; but did not pay much attention to astronomy, although he well understood everything that was taught from it at school. I was brought up at the expense of the Duke of Wirtemberg, and seeing that my comrades entered his service not entirely according to their inclinations, I also decided to accept the first position offered to me.”
He was offered the position of professor of mathematics.
In 1593, twenty-two-year-old Kepler was appointed professor of mathematics and moral philosophy at Graetz. He began by publishing a calendar according to the Gregorian reformation.
In 1600 religious persecution began in Styria; all Protestant professors were expelled from Graetz, including Kepler, although he was already, as it were, a permanent citizen of this city, having married (1597) a noble and beautiful woman, Barbara Muller. Kepler was the third husband, and when marrying him, she demanded evidence of his nobility: Kepler went to Wirtemberg to take care of this. The marriage was unhappy.
After historical details of the discovery of the new star in Ophiuchus and theoretical considerations about its brilliance, Kepler examines observations made in various places and proves that the star had neither proper motion nor annual parallax.
Although in his book Kepler apparently shows contempt for astrology. However, after a long refutation of Pic de la Mirandole's criticism, he admits the influence of the planets on the Earth when they are located among themselves in a certain way. By the way, one cannot read without being surprised that Mercury can produce storms.
Tycho argued that the star of 1572 was formed from matter in the Milky Way; the star of 1604 was also near this light belt; but Kepler did not consider such star formation possible, because since the time of Ptolemy the Milky Way had not changed at all. But how did he become convinced of the immutability of the Milky Way? “However,” says Kepler, “the appearance of a new star destroys Aristotle’s opinion that the sky cannot deteriorate.”
Kepler considers whether the appearance of a new star had any relationship with the conjunction of planets that was nearby to its place? But, unable to find a physical cause for the formation of a star, he concludes: “God, constantly caring for the world, can command a new star to appear in any place and at any time.”
There was a proverb in Germany: a new star is a new king. “It is amazing,” says Kepler, “that not a single ambitious person has taken advantage of popular prejudice.”
Regarding Kepler's discussion of the new star in Cygnus, we note that the author used all his learning to prove that the star really appeared again and does not belong to the number of variable stars.
Kepler immediately proves that the time of the Nativity of Christ is not precisely determined and that the beginning of this era must be pushed back by four or five years, so that 1606 must be considered either 1610 or 1611.
Astronomia nova sive physica caelestis, tradita commetaris de motibus stellae Martis ex observationibus Tycho Brahe. — Prague, 1609
In his first studies to improve Rudolf's tables, Kepler did not yet dare to reject the eccentrics and epicycles of the Almagest, also accepted by Copernicus and Tycho, for reasons borrowed from metaphysics and physics; he only argued that planetary conjunctions should be attributed to the true, and not to the average Sun. But extremely difficult and long-term calculations did not satisfy him: the differences between calculations and observations extended to 5 and 6 minutes of a degree; He wanted to free himself from these differences and finally discovered the true system of the world. Then Kepler decided against the movement of the planets in circles around the eccentric, that is, around an imaginary, immaterial point. Along with such circles, epicycles were destroyed. He suggested that the Sun is the center of the movement of planets moving along an ellipse, at one of the foci of which this center is located. To raise this assumption to the level of a theory, Kepler performed calculations that were surprising in their difficulty and in their duration. He showed unprecedented tireless constancy in work and insurmountable perseverance in achieving the proposed goal.
Such work was rewarded by the fact that calculations regarding Mars, based on his assumption, led to conclusions completely consistent with Tycho's observations.
Kepler's theory consists of two provisions: 1) the planet rotates in an ellipse, at one of the foci of which the center of the Sun is located, and 2) the planet moves at such a speed that the radius vectors describe the areas of the cuts, proportional to the times of movement. From the numerous observations at Uraniburg, Kepler had to select those most capable of solving questions related to the main task and invent new methods of calculation. By this judicious choice, without any supposition, he proved that the lines in which the planes of the orbits of all the planets intersect the ecliptic pass through the center of the sun, and that these planes are inclined to the ecliptic at almost constant angles.
We have already noticed that Kepler performed calculations that were extremely lengthy and extremely burdensome, because in his time logarithms were not yet known. On this subject in Bailly’s “History of Astronomy” we find the following statistical assessment of Kepler’s work: “Kepler’s efforts are incredible. Each of his calculations takes up 10 pages per sheet; he repeated each calculation 70 times; 70 repetitions equal 700 pages. Calculators know how many mistakes can be made and how many times it was necessary to perform calculations that took up 700 pages: how much time should it have taken? Kepler was an amazing man; he was not afraid of such work and the work did not tire his mental and physical strength.”
To this we must add that Kepler understood the enormity of his enterprise at its very beginning. He says that Rheticus, an excellent student of Copernicus, wanted to transform astronomy; but could not explain the movements of Mars. “Rhaeticus,” continues Kepler, “called on his domestic genius for help, but the genius, probably angry at the disturbance of his peace, grabbed the astronomer by the hair, lifted him to the ceiling and, lowering him to the floor, said: this is the movement of Mars.”
This joke by Kepler proves the difficulty of the problem, and therefore one can judge his pleasure when he was convinced that the planets really rotate according to the two laws mentioned above. Kepler expressed his pleasure in words addressed to the memory of the unfortunate Ramus.
If the Earth and the Moon, assuming that they were equally dense, were not held in their orbits by animal or some other force, then the Earth would approach the Moon to the 54th part of the distance separating them, and the moon would travel the remaining 53 parts and they would connect.
If the Earth stopped attracting its waters, then all the seas would rise and unite with the Moon. If the attractive force of the Moon extends to the Earth, then, conversely, the same force of the Earth reaches the Moon and spreads further. And so everything similar to the Earth cannot but be subject to its attractive force.
There is no substance that is absolutely light; one body is lighter than another because one body is rarer than the other. “I,” says Kepler, “call rare a body which, given its volume, has little substance.”
One should not imagine that light bodies rise and are not attracted: they attract less than heavy bodies and the heavy bodies displace them.
The driving force of the planets is in the Sun and weakens with increasing distance from this body.
When Kepler admitted that the Sun is the cause of the revolution of the planets, then he had to assume that it rotates on its axis in the direction of the translational motion of the planets. This consequence of Kepler's theory was subsequently proven by sunspots; but Kepler added circumstances to his theory that were not justified by observations.
Dioptrica, etc. - Frankfurt, 1611; reprinted in London 1653
It seems that in order to write a diopter, it was necessary to know the law according to which light is refracted when it passes from a rare substance (medium) to a dense one - a law discovered Descartes; But as at small angles of incidence, the angles of refraction are almost proportional to the first: then Kepler, on the basis of his research, accepted these approximate relationships and studied the properties of plane-spherical glasses, as well as spherical ones, the surfaces of which have equal radii. Here we find formulas for calculating the distances with the focus of the mentioned glasses. These formulas are still used today.
In the same book we find that he was the first to give the concept of telescopes made of two convex glasses. Galileo always used pipes made up of one convex glass and another concave glass. And so with Kepler we must begin the history of astronomical tubes, the only ones capable of projectiles with graduations designed to measure angles. As for the rule that determines the magnification of a telescope and consists in dividing the focal distance of a glass slide by the focal distance of an eye glass, it was discovered not by Kepler, but by Huygens.
Kepler, when compiling his diopter, already knew that Galileo discovered Jupiter's satellites: from their short-term rotations, he concluded that the planet must also rotate on its axis, moreover, in less than 24 hours. This conclusion was not justified soon after Kepler.
Nova stereometria doliorum vinariorum. — Linz, 1615
This book is purely geometric; in it the author especially considers bodies arising from the rotation of an ellipse about its various axes. It also proposes a method for measuring the capacity of barrels.
<>bHarmonicces mundi libri quinque, etc. - Linz, 1619
Here Kepler reports the discovery of his third law, namely: the squares of the rotation times of the planets are proportional to the cubes of their distances from the Sun.
On March 18, 1618, he decided to compare the squares of rotation times with the cubes of distances: but, due to a calculation error, he found that the law was incorrect; On May 15, he redid the calculations again, and the law was justified. But even here Kepler doubted him, because there could also be an error in the second calculation. “However,” says Kepler, “after all the checks I was convinced that the law completely agreed with Tycho’s observations. And so the discovery is beyond doubt.”
Surprisingly, Kepler added many strange and completely false ideas to this great discovery. The law he discovered attracted his imagination to Pythagorean harmonies.
“In the music of the celestial bodies,” says Kepler, “Saturn and Jupiter correspond to the bass, Mars to the tenor, Earth and Venus to the contralto, and Mercury to the falsetto.”
The same great discovery is disfigured by Kepler's belief in astrological nonsense. For example, he argued that planetary conjunctions always disturb our atmosphere, etc.
De cometis libelli tres, etc. - Augsburg, 1619
After reading three chapters of this work, one cannot help but be surprised that Kepler, who discovered the laws of planetary motion around the Sun, argued that comets move in straight lines. “Observations of the course of these luminaries,” he says, “are not worthy of attention, because they do not return.” This conclusion is surprising because it refers to the comet of 1607, which then appeared for the third time. And what is even more surprising is that from an incorrect assumption he drew the correct conclusions about the enormous distance of the comet from the Earth.
“Water, especially salty water, produces fish; ether produces comets. The Creator did not want the immeasurable seas to be without inhabitants; He also wanted to populate the heavenly space. The number of comets must be extremely large; We don’t see many comets because they don’t come close to the Earth and are destroyed very quickly.”
Near such nonsense of Kepler's deluded imagination we find ideas that have entered science. For example, the sun's rays, penetrating into comets, constantly tear off particles of their matter from them and form their tails.
According to Ephorus, Seneca, having mentioned a comet splitting into two parts, which took different paths, considered this observation to be completely false. Kepler strongly condemned the Roman philosopher. Kepler's severity is hardly fair, although almost all astronomers are on Seneca's side: in our time, astronomers witnessed a similar event in celestial space; they saw two parts of the same comet, taking different paths. One should never neglect the foresight or fortune telling of brilliant people.
The book about comets was published in 1619, that is, after the great discoveries of Kepler; but its last chapter is especially filled with astrological nonsense about the influence of comets on the events of the sublunary world, from which they are at great distances. I say: at distances, because a comet can produce diseases, even plague, when its tail covers the Earth, for who knows the essence of the substance of comets?
Epitome astronomiae copernicanae, and etc .
This work consists of two volumes, published in Aenz in different years: 1618, 1621 and 1622. They contain the following discoveries that expanded the field of science:
The sun is a fixed star; it seems to us more than all other stars, because it is closest to the Earth.
It is known that the Sun rotates on its axis (this was shown by observations of sunspots); Consequently, the planets must rotate in the same way.
Comets are made of matter that can expand and contract, matter that the sun's rays can carry over long distances.
The radius of the sphere of stars is at least two thousand times the distance of Saturn.
Sunspots are clouds or thick smoke rising from the depths of the Sun and burning on its surface.
The sun rotates, and therefore its attractive force is directed in different directions of the sky: when the Sun takes possession of any planet, then it will force it to rotate with itself.
The center of planetary motion is at the center of the Sun.
The light that surrounds the Moon during a total solar eclipse comes from the Sun's atmosphere. In addition, Kepler thought that this atmosphere was sometimes visible after the sun had set. From this remark one might think that Kepler was the first to discover the zodiacal light; but he says nothing about the form of light; therefore, we do not have the right to deprive D. Cassini and Shaldrey of the honor of their discoveries.
Jo. Kepleri tabulae Rudolphinae, etc. - Ulm, 1627
These tables were started by Tycho, and finished by Kepler, having worked on them for 26 years. They received their name from the name of Emperor Rudolf, who was the patron of both astronomers, but did not give them the promised salary.
The same book contains the history of the discovery of logarithms, which, however, cannot be taken away from Napier, their first inventor. The right to an invention belongs to the one who first published it.
The Prussian tables, so called because they are dedicated to Albert of Brandeburg, Duke of Prussia, were published by Reinhold in 1551. They were not based on observations Ptolemy And Copernicus. Compared to the “Rudolph tables” compiled based on Tycho’s observations and the new theory, in the Rheingold tables the errors extend to many degrees.
This posthumous work by Kepler, published by his son in 1634, contains a description of astronomical phenomena for an observer on the Moon. Some authors of astronomical textbooks also dealt with similar descriptions, transferring observers to different planets. Such descriptions are useful for beginners, and fairness demands that Kepler was the first to open the way to this.
Here are the titles of other works by Kepler, showing what a hardworking life the great astronomer led:
Nova dissertatiuncula de fundamentis astrologiae certioribus, etc. - Prague, 1602.
Epistola ad rerum coelestium amatores universos, etc. - Prague, 1605.
Sylva chronologica. — Frankfurt, 1606
Detailed history of the new comet 1607, etc. In German; in Halle, 1608
Phenomenon singulare, seu Mercurius in Sole, etc. Leipzig, 1609
Dissertatio cum Nuncio sidereo nuper ad mortales misso a Galileo. - Prague, 1610; in the same year it was reprinted in Florence, and in 1611 in Frankfurt.
Narration de observatis a se quatuor Jovis satellitibus erronibus quos Galilaeus medica sidera nuncupavit. Prague, 1610
Jo. Kepleri strena, seu de nive sexangula. Frankfurt, 1611
Kepleri eclogae chronicae ex epistolis doctissimorum aliquot virorum et suis mutuis. Frankfurt, 1615
Ephtmerides novae, etc. - Keplerian ephemerides were published until 1628 and always a year in advance; but were published after a year. After Kepler, they were continued by Barchiy, Kepler's son-in-law. News of disasters for the government and churches, especially comets and earthquakes in 1618 and 1619. In German, 1619.
Eclipses of 1620 and 1621 in German, at Ulm, 1621
Kepleri apologia pro suo opere Harmonices mundi, etc. Frankfurt, 1622
Discursus conjuctionis Saturni et Joves in Leone. Linz, 1623
Jo. Kepleri chilias logarithmorum. Marburg, 1624
Jo. Kepleri hyperaspistes Tychonis contra anti-Tychonem Scipionis Claramonti, etc. Frakfurt, 1625
Jo. Kepleri supplementum chiliadis logaritmorum. Acnypr, 1625 r.
Admonitio ad astronomos rerumque coelestium studiosos de miris rarisque anni 1631 phoenomenis, Veneris puta et Mercurii in Solem incursu. Leipzig, 1629
Responsio ad epistolum jac. Bartschii praefixam ephemeridi anni 1629, etc. Sagan, 1629.
Sportula genethliacis missa de Tab. Rudolphi usu in computationibus astrologicis, cum modo dirigendi novo et naturali. Sagan, 1529
Gansch in 1718 published one volume containing part of the manuscripts left after Kepler; The second volume he promised was not published due to lack of funds. Another eighteen notebooks of unpublished manuscripts were purchased by the Imperial St. Petersburg Academy of Sciences in 1775.
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.
