Johannes Kepler

Johannes Kepler

Overview
Johannes Kepler (ˈkɛplɐ; December 27, 1571 – November 15, 1630) was a German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....

 mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

 and astrologer
Astrologer
An astrologer practices one or more forms of astrology. Typically an astrologer draws a horoscope for the time of an event, such as a person's birth, and interprets celestial points and their placements at the time of the event to better understand someone, determine the auspiciousness of an...

. A key figure in the 17th century scientific revolution
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

, he is best known for his eponym
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...

ous laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

, codified by later astronomers, based on his works Astronomia nova
Astronomia nova
The Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year long investigation of the motion of Mars...

, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's theory of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

.

During his career, Kepler was a mathematics teacher at a seminary
Seminary
A seminary, theological college, or divinity school is an institution of secondary or post-secondary education for educating students in theology, generally to prepare them for ordination as clergy or for other ministry...

 school in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...

, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg was an Austrian statesman, a son of Seyfried von Eggenberg and great-grandson of Balthasar Eggenberger of the House of Eggenberg.- Biography :...

.
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Quotations

Discover the force of the heavens O Men: once recognised it can be put to use.

De Fundamentis [On the more Certain Fundamentals of Astrology or On Giving Astrology Sounder Foundations] (1601)

He who will please the crowd and for the sake of the most ephemeral renown will either proclaim those things which nature does not display or even will publish genuine miracles of nature without regard to deeper causes is a spiritually corrupt person… With the best of intentions I publicly speak to the crowd (which is eager for things new) on the subject of what is to come.

De Fundamentis (1601)

Nature uses as little as possible of anything.

Viking Book of Aphorisms: A Personal Selection (1920) by W. H. Auden and Louis Kronenberger, p. 98; also in The Infinite Cosmos: Questions from the Frontiers of Cosmology (2006) by Joseph Silk

We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens. The diversity of the phenomena of nature is so great and the treasures hidden in the heavens so rich precisely in order that the human mind shall never be lacking in fresh nourishment.

As quoted in Cosmos (1980) by Carl Sagan.

In Terra inest virtus, quae Lunam del.

There is a force in the earth which causes the moon to move.

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

As quoted in The Golden Ratio : The Story of Phi, the World's Most Astonishing Number (2003) by Mario Livio, p. 62

I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.

As quoted in (K)new Words: Redefine Your Communication (2005) by Gloria Pierre, p. 147

I used to measure the heavens, now I measure the shadows of Earth. Although my mind was heaven-bound, the shadow of my body lies here.

Epitaph he composed for himself a few months before he died, as quoted in Calculus. Multivariable (2006) by Steven G. Krantz and Brian E. Blank. p. 126
Encyclopedia
Johannes Kepler (ˈkɛplɐ; December 27, 1571 – November 15, 1630) was a German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....

 mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

 and astrologer
Astrologer
An astrologer practices one or more forms of astrology. Typically an astrologer draws a horoscope for the time of an event, such as a person's birth, and interprets celestial points and their placements at the time of the event to better understand someone, determine the auspiciousness of an...

. A key figure in the 17th century scientific revolution
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

, he is best known for his eponym
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...

ous laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

, codified by later astronomers, based on his works Astronomia nova
Astronomia nova
The Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year long investigation of the motion of Mars...

, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's theory of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

.

During his career, Kepler was a mathematics teacher at a seminary
Seminary
A seminary, theological college, or divinity school is an institution of secondary or post-secondary education for educating students in theology, generally to prepare them for ordination as clergy or for other ministry...

 school in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...

, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg was an Austrian statesman, a son of Seyfried von Eggenberg and great-grandson of Balthasar Eggenberger of the House of Eggenberg.- Biography :...

. Later he became an assistant to astronomer Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

, and eventually the imperial mathematician to Emperor Rudolf II
Rudolf II, Holy Roman Emperor
Rudolf II was Holy Roman Emperor , King of Hungary and Croatia , King of Bohemia and Archduke of Austria...

 and his two successors Matthias
Matthias, Holy Roman Emperor
Matthias of Austria was Holy Roman Emperor from 1612, King of Hungary and Croatia from 1608 and King of Bohemia from 1611...

 and Ferdinand II
Ferdinand II, Holy Roman Emperor
Ferdinand II , a member of the House of Habsburg, was Holy Roman Emperor , King of Bohemia , and King of Hungary . His rule coincided with the Thirty Years' War.- Life :...

. He was also a mathematics teacher in Linz
Linz
Linz is the third-largest city of Austria and capital of the state of Upper Austria . It is located in the north centre of Austria, approximately south of the Czech border, on both sides of the river Danube. The population of the city is , and that of the Greater Linz conurbation is about...

, Austria, and an adviser to General Wallenstein
Albrecht von Wallenstein
Albrecht Wenzel Eusebius von Wallenstein , actually von Waldstein, was a Bohemian soldier and politician, who offered his services, and an army of 30,000 to 100,000 men during the Danish period of the Thirty Years' War , to the Holy Roman Emperor Ferdinand II...

. Additionally, he did fundamental work in the field of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, invented an improved version of the refracting telescope
Refracting telescope
A refracting or refractor telescope is a type of optical telescope that uses a lens as its objective to form an image . The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses...

 (the Keplerian Telescope), and mentioned the telescopic
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

 discoveries of his contemporary Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics
Quadrivium
The quadrivium comprised the four subjects, or arts, taught in medieval universities, after teaching the trivium. The word is Latin, meaning "the four ways" , and its use for the 4 subjects has been attributed to Boethius or Cassiodorus in the 6th century...

 within the liberal arts
Liberal arts
The term liberal arts refers to those subjects which in classical antiquity were considered essential for a free citizen to study. Grammar, Rhetoric and Logic were the core liberal arts. In medieval times these subjects were extended to include mathematics, geometry, music and astronomy...

) and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 (a branch of natural philosophy
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...

). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason
Reason
Reason is a term that refers to the capacity human beings have to make sense of things, to establish and verify facts, and to change or justify practices, institutions, and beliefs. It is closely associated with such characteristically human activities as philosophy, science, language, ...

. Kepler described his new astronomy as "celestial physics", as "an excursion into Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

's Metaphysics
Metaphysics (Aristotle)
Metaphysics is one of the principal works of Aristotle and the first major work of the branch of philosophy with the same name. The principal subject is "being qua being", or being understood as being. It examines what can be asserted about anything that exists just because of its existence and...

", and as "a supplement to Aristotle's On the Heavens
On the Heavens
On the Heavens is Aristotle's chief cosmological treatise: it contains his astronomical theory and his ideas on the concrete workings of the terrestrial world...

", transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.

Early years


Johannes Kepler was born on December 27, 1571, at the Free Imperial City
Free Imperial City
In the Holy Roman Empire, a free imperial city was a city formally ruled by the emperor only — as opposed to the majority of cities in the Empire, which were governed by one of the many princes of the Empire, such as dukes or prince-bishops...

 of Weil der Stadt
Weil der Stadt
Weil der Stadt is a small town of about 19,000 inhabitants, located in the Stuttgart Region of the German state of Baden-Württemberg. It is about west of Stuttgart city center, and is often called "Gate to the Black Forest"...

 (now part of the Stuttgart Region
Stuttgart Region
Stuttgart Region is a metropolitan area in Germany and consists of the city of Stuttgart and the surrounding districts of Ludwigsburg, Esslingen, Böblingen, Rems-Murr and Göppingen . About 2.7 million inhabitants live in that area...

 in the German state of Baden-Württemberg
Baden-Württemberg
Baden-Württemberg is one of the 16 states of Germany. Baden-Württemberg is in the southwestern part of the country to the east of the Upper Rhine, and is the third largest in both area and population of Germany's sixteen states, with an area of and 10.7 million inhabitants...

, 30 km west of Stuttgart's center). His grandfather, Sebald Kepler, had been Lord Mayor of that town but, by the time Johannes was born, he had two brothers and one sister and the Kepler family fortune was in decline. His father, Heinrich Kepler, earned a precarious living as a mercenary
Mercenary
A mercenary, is a person who takes part in an armed conflict based on the promise of material compensation rather than having a direct interest in, or a legal obligation to, the conflict itself. A non-conscript professional member of a regular army is not considered to be a mercenary although he...

, and he left the family when Johannes was five years old. He was believed to have died in the Eighty Years' War in the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

. His mother Katharina Guldenmann, an inn-keeper's daughter, was a healer and herbalist
Herbalist
An herbalist is:#A person whose life is dedicated to the economic or medicinal uses of plants.#One skilled in the harvesting and collection of medicinal plants ....

 who was later tried for witchcraft
Witchcraft
Witchcraft, in historical, anthropological, religious, and mythological contexts, is the alleged use of supernatural or magical powers. A witch is a practitioner of witchcraft...

. Born prematurely, Johannes claimed to have been a weak and sickly child. He was, however, a brilliant child; he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty.

He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577
Great Comet of 1577
The Great Comet of 1577 was a comet that passed close to Earth during the year 1577 AD. It was viewed by people all over Europe, including famous Danish astronomer Tycho Brahe. From his observations of the comet, Brahe was able to discover that comets and similar objects travel above the Earth's...

, writing that he "was taken by [his] mother to a high place to look at it." At age nine, he observed another astronomical event, a lunar eclipse
Lunar eclipse
A lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...

 in 1580, recording that he remembered being "called outdoors" to see it and that the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 "appeared quite red". However, childhood smallpox
Smallpox
Smallpox was an infectious disease unique to humans, caused by either of two virus variants, Variola major and Variola minor. The disease is also known by the Latin names Variola or Variola vera, which is a derivative of the Latin varius, meaning "spotted", or varus, meaning "pimple"...

 left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy.

In 1589, after moving through grammar school, Latin school, and seminary at Maulbronn
Evangelical Seminaries of Maulbronn and Blaubeuren
The Protestant Seminaries of Maulbronn and Blaubeuren in Baden-Württemberg, Germany are two Gymnasiums and Protestant boarding schools in the Württemberg tradition....

, Kepler attended Tübinger Stift
Tübinger Stift
The Tübinger Stift is a hall of residence and teaching; it is owned and supported by the Evangelical-Lutheran Church in Württemberg, and located in the university city of Tübingen, in South West Germany. The Stift was originally founded as an Augustinian monastery in the Middle Ages...

 at the University of Tübingen. There, he studied philosophy under Vitus Müller and theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...

 under Jacob Heerbrand
Jacob Heerbrand
Jacob Heerbrand was a German Protestant theologian and controversialist.-Life:He was born at Giengen in Swabia on August 12, 1521. He was educated at the school at...

 (a student of Philipp Melanchthon
Philipp Melanchthon
Philipp Melanchthon , born Philipp Schwartzerdt, was a German reformer, collaborator with Martin Luther, the first systematic theologian of the Protestant Reformation, intellectual leader of the Lutheran Reformation, and an influential designer of educational systems...

 at Wittenberg), who also taught Michael Maestlin
Michael Maestlin
Michael Maestlin was a German astronomer and mathematician, known for being the mentor of Johannes Kepler.-Career:...

 while he was a student, until he became Chancellor at Tübingen in 1590. He proved himself to be a superb mathematician and earned a reputation as a skillful astrologer, casting horoscope
Horoscope
In astrology, a horoscope is a chart or diagram representing the positions of the Sun, Moon, planets, the astrological aspects, and sensitive angles at the time of an event, such as the moment of a person's birth. The word horoscope is derived from Greek words meaning "a look at the hours" In...

s for fellow students. Under the instruction of Michael Maestlin, Tübingen's professor of mathematics from 1583 to 1631, he learned both the Ptolemaic system and the Copernican system
Copernican heliocentrism
Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets rotating around it in circular paths modified by epicycles and at uniform...

 of planetary motion. He became a Copernican at that time. In a student disputation, he defended heliocentrism
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...

 from both a theoretical and theological perspective, maintaining that the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 was the principal source of motive power in the universe. Despite his desire to become a minister, near the end of his studies Kepler was recommended for a position as teacher of mathematics and astronomy at the Protestant school in Graz (later the University of Graz
University of Graz
The University of Graz , a university located in Graz, Austria, is the second-largest and second-oldest university in Austria....

). He accepted the position in April 1594, at the age of 23.

Mysterium Cosmographicum


Johannes Kepler's first major astronomical work, Mysterium Cosmographicum
Mysterium Cosmographicum
Mysterium Cosmographicum, is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621...

(The Cosmographic Mystery), was the first published defense of the Copernican system. Kepler claimed to have had an epiphany
Epiphany (feeling)
An epiphany is the sudden realization or comprehension of the essence or meaning of something...

 on July 19, 1595, while teaching in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...

, demonstrating the periodic conjunction of Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

 and Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

 in the zodiac
Zodiac
In astronomy, the zodiac is a circle of twelve 30° divisions of celestial longitude which are centred upon the ecliptic: the apparent path of the Sun across the celestial sphere over the course of the year...

; he realized that regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...

s bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

. He found that each of the five Platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

s could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

, Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

, Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

, Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

, and Saturn. By ordering the solids correctly—octahedron
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

, icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....

, dodecahedron, tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

, cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

—Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough.

As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual
Spirituality
Spirituality can refer to an ultimate or an alleged immaterial reality; an inner path enabling a person to discover the essence of his/her being; or the “deepest values and meanings by which people live.” Spiritual practices, including meditation, prayer and contemplation, are intended to develop...

; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son
Jesus
Jesus of Nazareth , commonly referred to as Jesus Christ or simply as Jesus or Christ, is the central figure of Christianity...

, and the intervening space between to the Holy Spirit
Holy Spirit
Holy Spirit is a term introduced in English translations of the Hebrew Bible, but understood differently in the main Abrahamic religions.While the general concept of a "Spirit" that permeates the cosmos has been used in various religions Holy Spirit is a term introduced in English translations of...

. His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism.

With the support of his mentor Michael Maestlin
Michael Maestlin
Michael Maestlin was a German astronomer and mathematician, known for being the mentor of Johannes Kepler.-Career:...

, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible exegesis
Exegesis
Exegesis is a critical explanation or interpretation of a text, especially a religious text. Traditionally the term was used primarily for exegesis of the Bible; however, in contemporary usage it has broadened to mean a critical explanation of any text, and the term "Biblical exegesis" is used...

 and the addition of a simpler, more understandable description of the Copernican system as well as Kepler’s new ideas. Mysterium was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler’s reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system
Patronage
Patronage is the support, encouragement, privilege, or financial aid that an organization or individual bestows to another. In the history of art, arts patronage refers to the support that kings or popes have provided to musicians, painters, and sculptors...

.

Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621 Kepler published an expanded second edition of Mysterium, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.

In terms of the impact of Mysterium, it can be seen as an important first step in modernizing Copernicus' theory. There is no doubt that Copernicus' "De Revolutionibus" seeks to advance a sun-centered system, but in this book he had to resort to Ptolemaic devices (viz., epicycles and eccentric circles) in order to explain the change in planets' orbital speed. Furthermore, Copernicus continued to use as a point of reference the center of the earth's orbit rather than that of the sun, as he says, "as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy." Therefore, although the thesis of the "Mysterium Cosmographicum" was in error, modern astronomy owes much to this work "since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it."

Marriage to Barbara Müller


In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter, Gemma van Dvijneveldt, and he began courting her. Müller, heiress to the estates of her late husbands, was also the daughter of a successful mill owner. Her father Jobst initially opposed a marriage despite Kepler's nobility; though he had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. Jobst relented after Kepler completed work on Mysterium, but the engagement nearly fell apart while Kepler was away tending to the details of publication. However, church officials—who had helped set up the match—pressured the Müllers to honor their agreement. Barbara and Johannes were married on April 27, 1597.

In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); and in 1607, another son (Ludwig).

Other research


Following the publication of Mysterium and with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work. He planned four additional books: one on the stationary aspects of the universe (the Sun and the fixed stars); one on the planets and their motions; one on the physical nature of planets and the formation of geographical features (focused especially on Earth); and one on the effects of the heavens on the Earth, to include atmospheric optics, meteorology and astrology.

He also sought the opinions of many of the astronomers to whom he had sent Mysterium, among them Reimarus Ursus
Reimarus Ursus
Nicolaus Reimers Baer , also Reimarus Ursus, Nicolaus Reimers Bär or Nicolaus Reymers Baer was an astronomer and imperial mathematician to Emperor Rudolf II...

 (Nicolaus Reimers Bär)—the imperial mathematician to Rudolph II
Rudolf II, Holy Roman Emperor
Rudolf II was Holy Roman Emperor , King of Hungary and Croatia , King of Bohemia and Archduke of Austria...

 and a bitter rival of Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

. Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over (what is now called) the Tychonic system
Tychonic system
The Tychonic system was a model of the solar system published by Tycho Brahe in the late 16th century which combined what he saw as the mathematical benefits of the Copernican system with the philosophical and "physical" benefits of the Ptolemaic system...

 with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....

. Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory (particularly its theological viability). But without the significantly more accurate data of Tycho's observatory, Kepler had no way to address many of these issues.

Instead, he turned his attention to chronology
Chronology
Chronology is the science of arranging events in their order of occurrence in time, such as the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".Chronology is part of periodization...

 and "harmony," the numerological
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...

 relationships among music, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and the physical world, and their astrological
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...

 consequences. By assuming the Earth to possess a soul (a property he would later invoke to explain how the sun causes the motion of planets), he established a speculative system connecting astrological aspects and astronomical distances to weather
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

 and other earthly phenomena. By 1599, however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague
Prague
Prague is the capital and largest city of the Czech Republic. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of over 2.3 million...

; on January 1, 1600 (before he even received the invitation), Kepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones.

Work for Tycho Brahe


On February 4, 1600, Kepler met Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

 and his assistants Franz Tengnagel
Franz Tengnagel
Frans Gansneb Tengnagel van Kamp was a Dutch nobleman from the western edge of the modern Westphalian region. He was the son-in-law and assistant of astronomer Tycho Brahe. Tengnagel wrote a brief prefatory note to Johannes Kepler's astronomical treatise Astronomia Nova....

 and Longomontanus at Benátky nad Jizerou
Benátky nad Jizerou
Benátky nad Jizerou is a town on the Jizera river in the Central Bohemian Region of the Czech Republic, between the cities Stará Boleslav and Mladá Boleslav.The city was the site of a castle and observatory built by astronomer Tycho Brahe.-External links:...

 (35 km from Prague), the site where Tycho's new observatory was being constructed. Over the next two months he stayed as a guest, analyzing some of Tycho's observations of Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

; Tycho guarded his data closely, but was impressed by Kepler's theoretical ideas and soon allowed him more access. Kepler planned to test his theory from Mysterium Cosmographicum based on the Mars data, but he estimated that the work would take up to two years (since he was not allowed to simply copy the data for his own use). With the help of Johannes Jessenius, Kepler attempted to negotiate a more formal employment arrangement with Tycho, but negotiations broke down in an angry argument and Kepler left for Prague on April 6. Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June, Kepler returned home to Graz to collect his family.

Political and religious difficulties in Graz dashed his hopes of returning immediately to Tycho; in hopes of continuing his astronomical studies, Kepler sought an appointment as mathematician to Archduke Ferdinand
Ferdinand II, Holy Roman Emperor
Ferdinand II , a member of the House of Habsburg, was Holy Roman Emperor , King of Bohemia , and King of Hungary . His rule coincided with the Thirty Years' War.- Life :...

. To that end, Kepler composed an essay—dedicated to Ferdinand—in which he proposed a force-based theory of lunar motion: "In Terra inest virtus, quae Lunam ciet" ("There is a force in the earth which causes the moon to move"). Though the essay did not earn him a place in Ferdinand's court, it did detail a new method for measuring lunar eclipse
Lunar eclipse
A lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...

s, which he applied during the July 10 eclipse in Graz. These observations formed the basis of his explorations of the laws of optics that would culminate in Astronomiae Pars Optica.

On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were banished from Graz. Several months later, Kepler returned, now with the rest of his household, to Prague. Through most of 1601, he was supported directly by Tycho, who assigned him to analyzing planetary observations and writing a tract against Tycho's (by then deceased) rival, Ursus. In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: the Rudolphine Tables
Rudolphine Tables
The Rudolphine Tables consist of a star catalogue and planetary tables published by Johannes Kepler in 1627 using data from Tycho Brahe's observations.-Previous tables:...

that should replace the Prutenic Tables
Prutenic Tables
The Prutenic Tables , were an ephemeris by the astronomer Erasmus Reinhold published in 1551. They are sometimes called the Prussian Tables after Albert I, Duke of Prussia, who supported Reinhold and financed the printing...

of Erasmus Reinhold
Erasmus Reinhold
Erasmus Reinhold was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony....

. Two days after Tycho's unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician with the responsibility to complete his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life.

Advisor to Emperor Rudolph II


Kepler's primary obligation as imperial mathematician was to provide astrological advice to the emperor. Though Kepler took a dim view of the attempts of contemporary astrologers to precisely predict the future or divine specific events, he had been casting well-received detailed horoscope
Horoscope
In astrology, a horoscope is a chart or diagram representing the positions of the Sun, Moon, planets, the astrological aspects, and sensitive angles at the time of an event, such as the moment of a person's birth. The word horoscope is derived from Greek words meaning "a look at the hours" In...

s for friends, family and patrons since his time as a student in Tübingen. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble (though Kepler's recommendations were based more on common sense than the stars). Rudolph was actively interested in the work of many of his court scholars (including numerous alchemists
Alchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...

) and kept up with Kepler's work in physical astronomy as well.

Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquist, but Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. Court life, however, brought Kepler into contact with other prominent scholars (Johannes Matthäus Wackher von Wackhenfels, Jost Bürgi, David Fabricius
David Fabricius
David Fabricius , was a German theologian who made two major discoveries in the early days of telescopic astronomy, jointly with his eldest son, Johannes Fabricius ....

, Martin Bachazek, and Johannes Brengger, among others) and astronomical work proceeded rapidly.

Astronomiae Pars Optica


As he slowly continued analyzing Tycho's Mars observations—now available to him in their entirety—and began the slow process of tabulating the Rudolphine Tables, Kepler also picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and solar eclipse
Solar eclipse
As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...

s presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction
Atmospheric refraction
Atmospheric refraction is the deviation of light or other things like humanelectromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of altitude...

 applied to all astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published as Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole camera
Pinhole camera
A pinhole camera is a simple camera without a lens and with a single small aperture – effectively a light-proof box with a small hole in one side. Light from a scene passes through this single point and projects an inverted image on the opposite side of the box...

s, as well as the astronomical implications of optics such as parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

 and the apparent sizes of heavenly bodies. He also extended his study of optics to the human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye's lens
Lens (anatomy)
The crystalline lens is a transparent, biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina. The lens, by changing shape, functions to change the focal distance of the eye so that it can focus on objects at various distances, thus allowing a...

 onto the retina
Retina
The vertebrate retina is a light-sensitive tissue lining the inner surface of the eye. The optics of the eye create an image of the visual world on the retina, which serves much the same function as the film in a camera. Light striking the retina initiates a cascade of chemical and electrical...

. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul." Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).

The Supernova of 1604


In October 1604, a bright new evening star (SN 1604
SN 1604
Supernova 1604, also known as Kepler's Supernova, Kepler's Nova or Kepler's Star, was a supernova that occurred in the Milky Way, in the constellation Ophiuchus. , it is the last supernova to have been unquestionably observed in our own galaxy, occurring no farther than 6 kiloparsecs or about...

) appeared, but Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the star. Astrologically, the end of 1603 marked the beginning of a fiery trigon, the start of the ca. 800-year cycle of great conjunction
Great conjunction
A Great Conjunction is a conjunction of the planets Jupiter and Saturn. The last Great Conjunction took place on May 31, 2000, while the next one will be in late December 2020. Great Conjunctions take place regularly, every 18–20 years, as a result of the combined ~12-year orbital period of Jupiter...

s; astrologers associated the two previous such periods with the rise of Charlemagne
Charlemagne
Charlemagne was King of the Franks from 768 and Emperor of the Romans from 800 to his death in 814. He expanded the Frankish kingdom into an empire that incorporated much of Western and Central Europe. During his reign, he conquered Italy and was crowned by Pope Leo III on 25 December 800...

 (ca. 800 years earlier) and the birth of Christ
Christ
Christ is the English term for the Greek meaning "the anointed one". It is a translation of the Hebrew , usually transliterated into English as Messiah or Mashiach...

 (ca. 1600 years earlier), and thus expected events of great portent, especially regarding the emperor. It was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his De Stella Nova. In it, Kepler addressed the star's astronomical properties while taking a skeptical approach to the many astrological interpretations then circulating. He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

 to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens (the idea accepted since Aristotle that the celestial spheres
Celestial spheres
The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others...

 were perfect and unchanging). The birth of a new star implied the variability of the heavens. In an appendix, Kepler also discussed the recent chronology
Chronology
Chronology is the science of arranging events in their order of occurrence in time, such as the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".Chronology is part of periodization...

 work of the Polish historian Laurentius Suslyga
Laurentius Suslyga
Laurentius Suslyga or Laurence Suslyga , was a Polish Jesuit historian, chronologist, and an author of Baroque visual poetry. He was the first person to claim that Jesus Christ was in fact born around 4 BC, not in AD 1, as the Christian era would imply...

; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem
Star of Bethlehem
In Christian tradition, the Star of Bethlehem, also called the Christmas Star, revealed the birth of Jesus to the magi, or "wise men", and later led them to Bethlehem. The star appears in the nativity story of the Gospel of Matthew, where magi "from the east" are inspired by the star to travel to...

—analogous to the present new star—would have coincided with the first great conjunction of the earlier 800-year cycle.

Astronomia nova


The extended line of research that culminated in Astronomia nova
Astronomia nova
The Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year long investigation of the motion of Mars...

(A New Astronomy)—including the first two laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

—began with the analysis, under Tycho's direction, of Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

' orbit. Kepler calculated and recalculated various approximations of Mars' orbit using an equant
Equant
Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of heavenly bodies....

 (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data.

Within Kepler's religious view of the cosmos, the Sun (a symbol of God the Father
God the Father
God the Father is a gendered title given to God in many monotheistic religions, particularly patriarchal, Abrahamic ones. In Judaism, God is called Father because he is the creator, life-giver, law-giver, and protector...

) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from De Magnete
De Magnete
De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure is a scientific work published in 1600 by the English physician and scientist William Gilbert and his partner Aaron Dowling...

(1600) and on his own work on optics. Kepler supposed that the motive power (or motive species) radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle, however, required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times—Kepler's second law of planetary motion.

He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After approximately 40 failed attempts, in early 1605 he at last hit upon the idea of an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fit the Mars data, he immediately concluded that all planets move in ellipses, with the sun at one focus—Kepler's first law of planetary motion. Because he employed no calculating assistants, however, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the property of his heirs.

Dioptrice, Somnium manuscript and other work


In the years following the completion of Astronomia Nova, most of Kepler's research was focused on preparations for the Rudolphine Tables and a comprehensive set of ephemerides (specific predictions of planet and star positions) based on the table (though neither would be completed for many years). He also attempted (unsuccessfully) to begin a collaboration with Italian astronomer Giovanni Antonio Magini
Giovanni Antonio Magini
Giovanni Antonio Magini was an Italian astronomer, astrologer, cartographer, and mathematician.-Life:...

. Some of his other work dealt with chronology
Chronology
Chronology is the science of arranging events in their order of occurrence in time, such as the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".Chronology is part of periodization...

, especially the dating of events in the life of Jesus
Chronology of Jesus
The chronology of Jesus aims to establish a historical order for some of the events of the life of Jesus in the four canonical gospels. The Christian gospels were primarily written as theological documents rather than historical chronicles and their authors showed little interest in an absolute...

, and with astrology, especially criticism of dramatic predictions of catastrophe such as those of Helisaeus Roeslin
Helisaeus Roeslin
Helisaeus Roeslin was a German physician and astrologer who adopted a geoheliocentric model of the universe. He was one of five observers who concluded that the Great Comet of 1577 was located beyond the moon...

.

Kepler and Roeslin engaged in series of published attacks and counter-attacks, while physician Philip Feselius published a work dismissing astrology altogether (and Roeslin's work in particular). In response to what Kepler saw as the excesses of astrology on the one hand and overzealous rejection of it on the other, Kepler prepared Tertius Interveniens (Third-party Interventions). Nominally this work—presented to the common patron of Roeslin and Feselius—was a neutral mediation between the feuding scholars, but it also set out Kepler's general views on the value of astrology, including some hypothesized mechanisms of interaction between planets and individual souls. While Kepler considered most traditional rules and methods of astrology to be the "evil-smelling dung" in which "an industrious hen" scrapes, there was "also perhaps a good little grain" to be found by the conscientious scientific astrologer.
In the first months of 1610, Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

—using his powerful new telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

—discovered four satellites orbiting Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

. Upon publishing his account as Sidereus Nuncius
Sidereus Nuncius
Sidereus Nuncius is a short treatise published in New Latin by Galileo Galilei in March 1610. It was the first scientific treatise based on observations made through a telescope...

(Starry Messenger), Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger). He endorsed Galileo's observations and offered a range of speculations about the meaning and implications of Galileo's discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons in Narratio de Jovis Satellitibus, providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) to Astronomia Nova.

After hearing of Galileo's telescopic discoveries, Kepler also started a theoretical and experimental investigation of telescopic optics using a telescope borrowed from Duke Ernest of Cologne. The resulting manuscript was completed in September 1610 and published as Dioptrice in 1611. In it, Kepler set out the theoretical basis of double-convex converging lenses and double-concave diverging lenses—and how they are combined to produce a Galilean telescope—as well as the concepts of real
Real image
In optics, a real image is a representation of an object in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen...

 vs. virtual
Virtual image
In optics, a virtual image is an image in which the outgoing rays from a point on the object always diverge. It will appear to converge in or behind the optical device . A simple example is a flat mirror where the image of oneself is perceived at twice the distance from oneself to the mirror...

 images, upright vs. inverted images, and the effects of focal length on magnification and reduction. He also described an improved telescope—now known as the astronomical or Keplerian telescope—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.
Around 1611, Kepler circulated a manuscript of what would eventually be published (posthumously) as Somnium
Somnium (Kepler)
Somnium is a fantasy written between 1620 and 1630, in Latin, by Johannes Kepler. In the narrative, a student of Tycho Brahe is transported to the Moon by occult forces. It presents a detailed imaginative description of how the earth might look when viewed from the moon, and is considered the...

(The Dream). Part of the purpose of Somnium was to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a non-geocentric system. The manuscript, which disappeared after changing hands several times, described a fantastic trip to the moon; it was part allegory, part autobiography, and part treatise on interplanetary travel (and is sometimes described as the first work of science fiction). Years later, a distorted version of the story may have instigated the witchcraft trial against his mother, as the mother of the narrator consults a demon to learn the means of space travel. Following her eventual acquittal, Kepler composed 223 footnotes to the story—several times longer than the actual text—which explained the allegorical aspects as well as the considerable scientific content (particularly regarding lunar geography) hidden within the text.

Work in mathematics and physics


As a New Year's gift that year, he also composed for his friend and some-time patron Baron Wackher von Wackhenfels a short pamphlet entitled Strena Seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow). In this treatise, he published the first description of the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical atomistic
Atomism
Atomism is a natural philosophy that developed in several ancient traditions. The atomists theorized that the natural world consists of two fundamental parts: indivisible atoms and empty void.According to Aristotle, atoms are indestructible and immutable and there are an infinite variety of shapes...

 physical basis for the symmetry and posed what later became known as the Kepler conjecture
Kepler conjecture
The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...

, a statement about the most efficient arrangement for packing spheres. Kepler was one of the pioneers of the mathematical applications of infinitesimal
Infinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

s, see Law of Continuity
Law of Continuity
The Law of Continuity is a heuristic principle introduced by Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite"...

.

Personal and political troubles


In 1611, the growing political-religious tension in Prague came to a head. Emperor Rudolph
Rudolf II, Holy Roman Emperor
Rudolf II was Holy Roman Emperor , King of Hungary and Croatia , King of Bohemia and Archduke of Austria...

—whose health was failing—was forced to abdicate as King of Bohemia  by his brother Matthias
Matthias, Holy Roman Emperor
Matthias of Austria was Holy Roman Emperor from 1612, King of Hungary and Croatia from 1608 and King of Bohemia from 1611...

. Both sides sought Kepler's astrological advice, an opportunity he used to deliver conciliatory political advice (with little reference to the stars, except in general statements to discourage drastic action). However, it was clear that Kepler's future prospects in the court of Matthias were dim.

Also in that year, Barbara Kepler contracted Hungarian spotted fever, then began having seizure
Seizure
An epileptic seizure, occasionally referred to as a fit, is defined as a transient symptom of "abnormal excessive or synchronous neuronal activity in the brain". The outward effect can be as dramatic as a wild thrashing movement or as mild as a brief loss of awareness...

s. As Barbara was recovering, Kepler's three children all fell sick with smallpox
Smallpox
Smallpox was an infectious disease unique to humans, caused by either of two virus variants, Variola major and Variola minor. The disease is also known by the Latin names Variola or Variola vera, which is a derivative of the Latin varius, meaning "spotted", or varus, meaning "pimple"...

; Friedrich, 6, died. Following his son's death, Kepler sent letters to potential patrons in Württemberg and Padua
Padua
Padua is a city and comune in the Veneto, northern Italy. It is the capital of the province of Padua and the economic and communications hub of the area. Padua's population is 212,500 . The city is sometimes included, with Venice and Treviso, in the Padua-Treviso-Venice Metropolitan Area, having...

. At the University of Tübingen
Eberhard Karls University of Tübingen
Eberhard Karls University, Tübingen is a public university located in the city of Tübingen, Baden-Württemberg, Germany. It is one of Germany's oldest universities, internationally noted in medicine, natural sciences and the humanities. In the area of German Studies it has been ranked first among...

 in Württemberg, concerns over Kepler's perceived Calvinist
Calvinism
Calvinism is a Protestant theological system and an approach to the Christian life...

 heresies in violation of the Augsburg Confession
Augsburg Confession
The Augsburg Confession, also known as the "Augustana" from its Latin name, Confessio Augustana, is the primary confession of faith of the Lutheran Church and one of the most important documents of the Lutheran reformation...

 and the Formula of Concord
Formula of Concord
Formula of Concord is an authoritative Lutheran statement of faith that, in its two parts , makes up the final section of the Lutheran Corpus Doctrinae or Body of Doctrine, known as...

 prevented his return. The University of Padua
University of Padua
The University of Padua is a premier Italian university located in the city of Padua, Italy. The University of Padua was founded in 1222 as a school of law and was one of the most prominent universities in early modern Europe. It is among the earliest universities of the world and the second...

—on the recommendation of the departing Galileo—sought Kepler to fill the mathematics professorship, but Kepler, preferring to keep his family in German territory, instead travelled to Austria to arrange a position as teacher and district mathematician in Linz
Linz
Linz is the third-largest city of Austria and capital of the state of Upper Austria . It is located in the north centre of Austria, approximately south of the Czech border, on both sides of the river Danube. The population of the city is , and that of the Greater Linz conurbation is about...

. However, Barbara relapsed into illness and died shortly after Kepler's return.

Kepler postponed the move to Linz and remained in Prague until Rudolph's death in early 1612, though between political upheaval, religious tension, and family tragedy (along with the legal dispute over his wife's estate), Kepler could do no research. Instead, he pieced together a chronology manuscript, Eclogae Chronicae, from correspondence and earlier work. Upon succession as Holy Roman Emperor, Matthias re-affirmed Kepler's position (and salary) as imperial mathematician but allowed him to move to Linz.

Linz and elsewhere (1612–1630)


In Linz, Kepler's primary responsibilities (beyond completing the Rudolphine Tables) were teaching at the district school and providing astrological and astronomical services. In his first years there, he enjoyed financial security and religious freedom relative to his life in Prague—though he was excluded from Eucharist
Eucharist
The Eucharist , also called Holy Communion, the Sacrament of the Altar, the Blessed Sacrament, the Lord's Supper, and other names, is a Christian sacrament or ordinance...

 by his Lutheran church over his theological scruples. His first publication in Linz was De vero Anno (1613), an expanded treatise on the year of Christ's birth; he also participated in deliberations on whether to introduce Pope Gregory
Pope Gregory XIII
Pope Gregory XIII , born Ugo Boncompagni, was Pope from 1572 to 1585. He is best known for commissioning and being the namesake for the Gregorian calendar, which remains the internationally-accepted civil calendar to this date.-Youth:He was born the son of Cristoforo Boncompagni and wife Angela...

's reformed calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...

 to Protestant German lands; that year he also wrote the influential mathematical treatise Nova stereometria doliorum vinariorum, on measuring the volume of containers such as wine barrels (though it would not be published until 1615).

Second marriage


On October 30, 1613, Kepler married the 24-year-old Susanna Reuttinger. Following the death of his first wife Barbara, Kepler had considered 11 different matches. He eventually returned to Reuttinger (the fifth match) who, he wrote, "won me over with love, humble loyalty, economy of household, diligence, and the love she gave the stepchildren." The first three children of this marriage (Margareta Regina, Katharina, and Sebald) died in childhood. Three more survived into adulthood: Cordula (b. 1621); Fridmar (b. 1623); and Hildebert (b. 1625). According to Kepler's biographers, this was a much happier marriage than his first.

Epitome of Copernican Astronomy, calendars and the witch trial of his mother


Since completing the Astronomia nova, Kepler had intended to compose an astronomy textbook. In 1615, he completed the first of three volumes of Epitome astronomia Copernicanae (Epitome of Copernican Astronomy); the first volume (books I-III) was printed in 1617, the second (book IV) in 1620, and the third (books V-VII) in 1621. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipse-based system. The Epitome became Kepler's most influential work. It contained all three laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

 and attempted to explain heavenly motions through physical causes. Though it explicitly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all the planets as well as the Moon and the Medicean satellites of Jupiter
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...

, it did not explain how elliptical orbits could be derived from observational data.

As a spin-off from the Rudolphine Tables and the related Ephemerides, Kepler published astrological calendars, which were very popular and helped offset the costs of producing his other work—especially when support from the Imperial treasury was withheld. In his calendars—six between 1617 and 1624—Kepler forecast planetary positions and weather as well as political events; the latter were often cannily accurate, thanks to his keen grasp of contemporary political and theological tensions. By 1624, however, the escalation of those tensions and the ambiguity of the prophecies meant political trouble for Kepler himself; his final calendar was publicly burned in Graz.
In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Christoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft
European witchcraft
European Witchcraft is witchcraft and magic that is practised primarily in the locality of Europe.-Antiquity:Instances of persecution of witchcraft are documented from Classical Antiquity, paralleling evidence from the Ancient Near East and the Old Testament.In Ancient Greece, for example, Theoris,...

; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler. The accusers had no stronger evidence than rumors, along with a distorted, second-hand version of Kepler's Somnium, in which a woman mixes potions and enlists the aid of a demon
Demon
call - 1347 531 7769 for more infoIn Ancient Near Eastern religions as well as in the Abrahamic traditions, including ancient and medieval Christian demonology, a demon is considered an "unclean spirit" which may cause demonic possession, to be addressed with an act of exorcism...

. Katharina was subjected to territio verbalis, a graphic description of the torture
Torture
Torture is the act of inflicting severe pain as a means of punishment, revenge, forcing information or a confession, or simply as an act of cruelty. Throughout history, torture has often been used as a method of political re-education, interrogation, punishment, and coercion...

 awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work to focus on his "harmonic theory". The result, published in 1619, was Harmonices Mundi ("Harmony of the World").

Harmonices Mundi


Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world." In Harmony, he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music. The central set of "harmonies" was the musica universalis
Musica universalis
Musica universalis is an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica . This 'music' is not usually thought to be literally audible, but a harmonic and/or mathematical and/or religious concept...

or "music of the spheres," which had been studied by Pythagoras
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

, Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

 and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd
Robert Fludd
Robert Fludd, also known as Robertus de Fluctibus was a prominent English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, Rosicrucian apologist...

, who had recently published his own harmonic theory.

Kepler began by exploring regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...

s and regular solids, including the figures that would come to be known as Kepler's solids. From there, he extended his harmonic analysis to music, meteorology and astrology; harmony resulted from the tones made by the souls of heavenly bodies—and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity
Orbital velocity
Orbital velocity can refer to the following:* The orbital speed of a body in a gravitational field.* The velocity of particles due to wave motion, in particular in wind waves....

 and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler—with Tycho's data and his own astronomical theories—treated them much more precisely and attached new physical significance to them.

Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

. He then tried many combinations until he discovered that (approximately) "The square of the periodic times are to each other as the cubes of the mean distances." Although he gives the date of this epiphany (March 8, 1618), he does not give any details about how he arrived at this conclusion. However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. For when conjoined with Christian Huygens' newly discovered law of centrifugal force it enabled Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

, Edmund Halley and perhaps Christopher Wren
Christopher Wren
Sir Christopher Wren FRS is one of the most highly acclaimed English architects in history.He used to be accorded responsibility for rebuilding 51 churches in the City of London after the Great Fire in 1666, including his masterpiece, St. Paul's Cathedral, on Ludgate Hill, completed in 1710...

 and Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

 to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them. This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.

Rudolphine Tables and his last years


In 1623, Kepler at last completed the Rudolphine Tables
Rudolphine Tables
The Rudolphine Tables consist of a star catalogue and planetary tables published by Johannes Kepler in 1627 using data from Tycho Brahe's observations.-Previous tables:...

, which at the time was considered his major work. However, due to the publishing requirements of the emperor and negotiations with Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

's heir, it would not be printed until 1627. In the meantime religious tension—the root of the ongoing Thirty Years' War
Thirty Years' War
The Thirty Years' War was fought primarily in what is now Germany, and at various points involved most countries in Europe. It was one of the most destructive conflicts in European history....

—once again put Kepler and his family in jeopardy. In 1625, agents of the Catholic Counter-Reformation
Counter-Reformation
The Counter-Reformation was the period of Catholic revival beginning with the Council of Trent and ending at the close of the Thirty Years' War, 1648 as a response to the Protestant Reformation.The Counter-Reformation was a comprehensive effort, composed of four major elements:#Ecclesiastical or...

 placed most of Kepler's library under seal, and in 1626 the city of Linz was besieged. Kepler moved to Ulm
Ulm
Ulm is a city in the federal German state of Baden-Württemberg, situated on the River Danube. The city, whose population is estimated at 120,000 , forms an urban district of its own and is the administrative seat of the Alb-Donau district. Ulm, founded around 850, is rich in history and...

, where he arranged for the printing of the Tables at his own expense.

In 1628, following the military successes of the Emperor Ferdinand
Ferdinand II, Holy Roman Emperor
Ferdinand II , a member of the House of Habsburg, was Holy Roman Emperor , King of Bohemia , and King of Hungary . His rule coincided with the Thirty Years' War.- Life :...

's armies under General Wallenstein
Albrecht von Wallenstein
Albrecht Wenzel Eusebius von Wallenstein , actually von Waldstein, was a Bohemian soldier and politician, who offered his services, and an army of 30,000 to 100,000 men during the Danish period of the Thirty Years' War , to the Holy Roman Emperor Ferdinand II...

, Kepler became an official advisor to Wallenstein. Though not the general's court astrologer per se, Kepler provided astronomical calculations for Wallenstein's astrologers and occasionally wrote horoscopes himself. In his final years, Kepler spent much of his time traveling, from the imperial court in Prague to Linz and Ulm to a temporary home in Sagan
Zagan
Zagan may refer to:*Zagan - a demon in the Ars Goetia*Żagań - a town in west Poland...

, and finally to Regensburg
Regensburg
Regensburg is a city in Bavaria, Germany, located at the confluence of the Danube and Regen rivers, at the northernmost bend in the Danube. To the east lies the Bavarian Forest. Regensburg is the capital of the Bavarian administrative region Upper Palatinate...

. Soon after arriving in Regensburg, Kepler fell ill. He died on November 15, 1630, and was buried there; his burial site was lost after the Swedish army destroyed the churchyard. Only Kepler's self-authored poetic epitaph survived the times:
Mensus eram coelos, nunc terrae metior umbras
Mens coelestis erat, corporis umbra iacet.

I measured the skies, now the shadows I measure
Skybound was the mind, earthbound the body rests.

Reception of his astronomy


Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

 completely ignored Kepler's Astronomia nova. Many astronomers, including Kepler's teacher, Michael Maestlin
Michael Maestlin
Michael Maestlin was a German astronomer and mathematician, known for being the mentor of Johannes Kepler.-Career:...

, objected to Kepler's introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced Kepler's area law with uniform motion in respect to the empty focus of the ellipse while Seth Ward
Seth Ward (bishop)
Seth Ward was an English mathematician, astronomer, and bishop.-Early life:He was born in Hertfordshire, and educated at Sidney Sussex College, Cambridge, where he graduated B.A. in 1636 and M.A. in 1640, becoming a Fellow in that year...

 used an elliptical orbit with motions defined by an equant
Equant
Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of heavenly bodies....

.

Several astronomers tested Kepler's theory, and its various modifications, against astronomical observations. Two transits of Venus and Mercury across the face of the sun provided sensitive tests of the theory, under circumstances when these planets could not normally be observed. In the case of the transit of Mercury in 1631, Kepler had been extremely uncertain of the parameters for Mercury, and advised observers to look for the transit the day before and after the predicted date. Pierre Gassendi
Pierre Gassendi
Pierre Gassendi was a French philosopher, priest, scientist, astronomer, and mathematician. With a church position in south-east France, he also spent much time in Paris, where he was a leader of a group of free-thinking intellectuals. He was also an active observational scientist, publishing the...

 observed the transit on the date predicted, a confirmation of Kepler's prediction. This was the first observation of a transit of Mercury. However, his attempt to observe the transit of Venus
Transit of Venus
A transit of Venus across the Sun takes place when the planet Venus passes directly between the Sun and Earth, becoming visible against the solar disk. During a transit, Venus can be seen from Earth as a small black disk moving across the face of the Sun...

 just one month later, was unsuccessful due to inaccuracies in the Rudolphine Tables. Gassendi did not realize that it was not visible from most of Europe, including Paris. Jeremiah Horrocks
Jeremiah Horrocks
Jeremiah Horrocks , sometimes given as Jeremiah Horrox , was an English astronomer who was the only person to predict, and one of only two people to observe and record, the transit of Venus of 1639.- Life and work :Horrocks was born in Lower Lodge, in...

, who observed the 1639 Venus transit, had used his own observations to adjust the parameters of the Keplerian model, predicted the transit, and then built apparatus to observe the transit. He remained a firm advocate of the Keplerian model.

Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler's death it was the main vehicle for spreading Kepler's ideas. Between 1630 and 1650, it was the most widely used astronomy textbook, winning many converts to ellipse-based astronomy. However, few adopted his ideas on the physical basis for celestial motions. In the late 17th century, a number of physical astronomy theories drawing from Kepler's work—notably those of Giovanni Alfonso Borelli
Giovanni Alfonso Borelli
Giovanni Alfonso Borelli was a Renaissance Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo's custom of testing hypotheses against observation...

 and Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

—began to incorporate attractive forces (though not the quasi-spiritual motive species postulated by Kepler) and the Cartesian
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

 concept of inertia. This culminated in Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's Principia Mathematica
Philosophiae Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726...

(1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

.

Historical and cultural legacy




Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the philosophy
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...

 and historiography of science
Historiography of science
Historiography is the study of the history and methodology of the discipline of history. The historiography of science is thus the study of the history and methodology of the sub-discipline of history, known as the history of science, including its disciplinary aspects and practices and to the...

. Kepler and his laws of motion were central to early histories of astronomy such as Jean Etienne Montucla’s 1758 Histoire des mathématiques and Jean-Baptiste Delambre's 1821 Histoire de l’astronomie moderne. These and other histories written from an Enlightenment
Age of Enlightenment
The Age of Enlightenment was an elite cultural movement of intellectuals in 18th century Europe that sought to mobilize the power of reason in order to reform society and advance knowledge. It promoted intellectual interchange and opposed intolerance and abuses in church and state...

 perspective treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later Romantic
Romanticism in science
Romanticism, also known as the “Age of Reflection,” describes the intellectual movement from 1800-1840 that originated in Western Europe as a counter-movement to the Enlightenment of the late 18th century...

-era natural philosophers viewed these elements as central to his success. William Whewell
William Whewell
William Whewell was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge.-Life and career:Whewell was born in Lancaster...

, in his influential History of the Inductive Sciences of 1837, found Kepler to be the archetype of the inductive scientific genius; in his Philosophy of the Inductive Sciences of 1840, Whewell held Kepler up as the embodiment of the most advanced forms of scientific method
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

. Similarly, Ernst Friedrich Apelt
Ernst Friedrich Apelt
Ernst Friedrich Apelt was a German philosopher and entrepreneur. He was a student of Jakob Friedrich Fries, succeeding him at the University of Jena...

—the first to extensively study Kepler's manuscripts, after their purchase by Catherine the Great—identified Kepler as a key to the "Revolution of the sciences
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

". Apelt, who saw Kepler's mathematics, aesthetic sensibility, physical ideas, and theology as part of a unified system of thought, produced the first extended analysis of Kepler's life and work.

Modern translations of a number of Kepler's books appeared in the late-nineteenth and early-twentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early 21st century), and Max Caspar's Kepler biography was published in 1948. However, Alexandre Koyré
Alexandre Koyré
Alexandre Koyré , sometimes anglicised as Alexander Koiré, was a French philosopher of Russian origin who wrote on the history and philosophy of science.-Life:...

's work on Kepler was, after Apelt, the first major milestone in historical interpretations of Kepler's cosmology and its influence. In the 1930s and 1940s Koyré, and a number of others in the first generation of professional historians of science, described the "Scientific Revolution
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

" as the central event in the history of science, and Kepler as a (perhaps the) central figure in the revolution. Koyré placed Kepler's theorization, rather than his empirical work, at the center of the intellectual transformation from ancient to modern world-views. Since the 1960s, the volume of historical Kepler scholarship has expanded greatly, including studies of his astrology and meteorology, his geometrical methods, the role of his religious views in his work, his literary and rhetorical methods, his interaction with the broader cultural and philosophical currents of his time, and even his role as an historian of science.

The debate over Kepler's place in the Scientific Revolution has also produced a wide variety of philosophical and popular treatments. One of the most influential is Arthur Koestler
Arthur Koestler
Arthur Koestler CBE was a Hungarian author and journalist. Koestler was born in Budapest and, apart from his early school years, was educated in Austria...

's 1959 The Sleepwalkers
The Sleepwalkers
The Sleepwalkers: A History of Man's Changing Vision of the Universe is a 1959 book by Arthur Koestler, and one of the main accounts of the history of cosmology and astronomy in the Western World, beginning in ancient Mesopotamia and ending with Isaac Newton. The book challenges the habitual idea...

, in which Kepler is unambiguously the hero (morally and theologically as well as intellectually) of the revolution. Influential philosophers of science—such as Charles Sanders Peirce, Norwood Russell Hanson
Norwood Russell Hanson
Norwood Russell Hanson was a philosopher of science. Hanson was a pioneer in advancing the argument that observation is theory-laden – that observation language and theory language are deeply interwoven – and that historical and contemporary comprehension are similarly deeply interwoven...

, Stephen Toulmin
Stephen Toulmin
Stephen Edelston Toulmin was a British philosopher, author, and educator. Influenced by Ludwig Wittgenstein, Toulmin devoted his works to the analysis of moral reasoning. Throughout his writings, he sought to develop practical arguments which can be used effectively in evaluating the ethics behind...

, and Karl Popper
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...

—have repeatedly turned to Kepler: examples of incommensurability
Commensurability (philosophy of science)
Commensurability is a concept in the philosophy of science. Scientific theories are described as commensurable if one can compare them to determine which is more accurate; if theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is...

, analogical reasoning, falsification
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

, and many other philosophical concepts have been found in Kepler's work. Physicist Wolfgang Pauli
Wolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

 even used Kepler's priority dispute with Robert Fludd
Robert Fludd
Robert Fludd, also known as Robertus de Fluctibus was a prominent English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, Rosicrucian apologist...

 to explore the implications of analytical psychology
Analytical psychology
Analytical psychology is the school of psychology originating from the ideas of Swiss psychiatrist Carl Jung. His theoretical orientation has been advanced by his students and other thinkers who followed in his tradition. Though they share similarities, analytical psychology is distinct from...

 on scientific investigation. A well-received, if fanciful, historical novel by John Banville
John Banville
John Banville is an Irish novelist and screenwriter.Banville's breakthrough novel The Book of Evidence was shortlisted for the Man Booker Prize, and won the Guinness Peat Aviation award. His eighteenth novel, The Sea, won the Man Booker Prize in 2005. He was awarded the Franz Kafka Prize in 2011...

, Kepler (1981), explored many of the themes developed in Koestler's non-fiction narrative and in the philosophy of science. Somewhat more fanciful is a recent work of nonfiction, Heavenly Intrigue (2004), suggesting that Kepler murdered Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

 to gain access to his data. Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer Carl Sagan
Carl Sagan
Carl Edward Sagan was an American astronomer, astrophysicist, cosmologist, author, science popularizer and science communicator in astronomy and natural sciences. He published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books...

 described him as "the first astrophysicist
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

 and the last scientific astrologer."

In Austria, Johannes Kepler left behind such a historical legacy that he was one of the motifs of a silver collector's coin: the 10-euro Johannes Kepler silver coin, minted on September 10, 2002. The reverse side of the coin has a portrait of Kepler, who spent some time teaching in Graz and the surrounding areas. Kepler was acquainted with Prince Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg
Hans Ulrich von Eggenberg was an Austrian statesman, a son of Seyfried von Eggenberg and great-grandson of Balthasar Eggenberger of the House of Eggenberg.- Biography :...

 personally, and he probably influenced the construction of Eggenberg Castle (the motif of the obverse of the coin). In front of him on the coin is the model of nested spheres and polyhedra from Mysterium Cosmographicum.

In 2009, NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

 named the Kepler Mission
Kepler Mission
The Kepler spacecraft is an American space observatory, the space-based portion of NASA's Kepler Mission to discover Earth-like planets orbiting other stars. The spacecraft is named in honor of the 17th-century German astronomer Johannes Kepler...

 for Kepler's contributions to the field of astronomy.

In New Zealand
New Zealand
New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...

's Fiordland National Park there is also a range of Mountains Named after Kepler, called the Kepler Mountains and a Three Day Walking Trail known as the Kepler Track
Kepler Track
The Kepler Track is a circular tramping track which travels through some of the spectacular scenery on the South Island of New Zealand. The track passes through many landscapes of the Fiordland National Park ranging from rocky mountain ridges to tall mossy forests, from lake shores to deep gorges....

 through the Mountains of the same name.

Veneration


Kepler is honored together with Nicolaus Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....

 with a feast day on the liturgical calendar of the Episcopal Church (USA)
Calendar of saints (Episcopal Church in the United States of America)
The veneration of saints in the Episcopal Church is a continuation of an ancient tradition from the early Church which honors important people of the Christian faith. The usage of the term "saint" is similar to Roman Catholic and Orthodox traditions. Those in the Anglo-Catholic tradition may...

 on May 23.

Works

  • Mysterium cosmographicum
    Mysterium Cosmographicum
    Mysterium Cosmographicum, is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621...

    (The Sacred Mystery of the Cosmos) (1596)
  • De Fundamentis Astrologiae Certioribus (Concerning the More Certain Fundamentals of Astrology) (1601)
  • Astronomiae Pars Optica (The Optical Part of Astronomy) (1604)
  • De Stella nova in pede Serpentarii (On the New Star in Ophiuchus's Foot) (1604)
  • Astronomia nova
    Astronomia nova
    The Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year long investigation of the motion of Mars...

    (New Astronomy) (1609)
  • Tertius Interveniens (Third-party Interventions) (1610)
  • Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610)
  • Dioptrice (1611)



  • De nive sexangula (On the Six-Cornered Snowflake) (1611)
  • De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit (1613)
  • Eclogae Chronicae (1615, published with Dissertatio cum Nuncio Sidereo)
  • Nova stereometria doliorum vinariorum (New Stereometry of Wine Barrels) (1615)
  • Epitome astronomiae Copernicanae (Epitome of Copernican Astronomy) (published in three parts from 1618–1621)
  • Harmonice Mundi
    Harmonice Mundi
    Harmonices Mundi is a book by Johannes Kepler. In the work Kepler discusses harmony and congruence in geometrical forms and physical phenomena...

    (Harmony of the Worlds) (1619)
  • Mysterium cosmographicum
    Mysterium Cosmographicum
    Mysterium Cosmographicum, is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621...

    (The Sacred Mystery of the Cosmos) 2nd Edition (1621)
  • Tabulae Rudolphinae
    Rudolphine Tables
    The Rudolphine Tables consist of a star catalogue and planetary tables published by Johannes Kepler in 1627 using data from Tycho Brahe's observations.-Previous tables:...

    (Rudolphine Tables) (1627)
  • Somnium
    Somnium (Kepler)
    Somnium is a fantasy written between 1620 and 1630, in Latin, by Johannes Kepler. In the narrative, a student of Tycho Brahe is transported to the Moon by occult forces. It presents a detailed imaginative description of how the earth might look when viewed from the moon, and is considered the...

    (The Dream) (1634)

Named in his honor


  • Kepler's laws of planetary motion
    Kepler's laws of planetary motion
    In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

     for astronomical calculations
  • The Kepler Mission
    Kepler Mission
    The Kepler spacecraft is an American space observatory, the space-based portion of NASA's Kepler Mission to discover Earth-like planets orbiting other stars. The spacecraft is named in honor of the 17th-century German astronomer Johannes Kepler...

    , a space photometer
    Photometer
    In its widest sense, a photometer is an instrument for measuring light intensity or optical properties of solutions or surfaces. Photometers are used to measure:*Illuminance*Irradiance*Light absorption*Scattering of light*Reflection of light*Fluorescence...

     designed to search for Earth-like planets launched by NASA
    NASA
    The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

     on March 6, 2009
  • The Johannes Kepler ATV
    Johannes Kepler ATV
    The Johannes Kepler ATV, or Automated Transfer Vehicle 002 , was an unmanned cargo resupply spacecraft launched by the European Space Agency . It was named after the German astronomer Johannes Kepler. The spacecraft was launched on 17 February 2011, on a mission to supply the International Space...

    , the second Automatic Transfer Vehicle (ATV) launched by ESA to resupply the ISS
    International Space Station
    The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...

    . The ATV launched in February 2011 and deorbited in June 2011.
  • The Kepler Solids, a set of geometrical constructions, two of which were described by him
  • The Kepler Mountains and the Kepler Track
    Kepler Track
    The Kepler Track is a circular tramping track which travels through some of the spectacular scenery on the South Island of New Zealand. The track passes through many landscapes of the Fiordland National Park ranging from rocky mountain ridges to tall mossy forests, from lake shores to deep gorges....

     on the South Island of New Zealand
    New Zealand
    New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...

  • Kepler's Star, Supernova 1604, which he observed and described
  • Kepler
    Kepler (lunar crater)
    Kepler is a lunar impact crater that lies between the Oceanus Procellarum to the west and Mare Insularum in the east. To the southeast is the crater Encke....

    , a crater on the moon
  • Kepler, a crater on Mars
  • 1134 Kepler
    1134 Kepler
    1134 Kepler is an asteroid. It was discovered by Max Wolf on September 25, 1929. Its provisional designation was 1929 SA. It was named after Johannes Kepler....

    , an asteroid
    Asteroid
    Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

  • Kepler
    Kepler (opera)
    Kepler is an opera by Philip Glass set to a libretto in German and Latin by Martina Winkel. It premiered on 20 September 2009 at the Landestheater in the Austrian city of Linz with Dennis Russell Davies conducting the Bruckner Orchestra. Its libretto is based on the life and work of Johannes...

    , an opera by Philip Glass
    Philip Glass
    Philip Glass is an American composer. He is considered to be one of the most influential composers of the late 20th century and is widely acknowledged as a composer who has brought art music to the public .His music is often described as minimalist, along with...

  • Die Harmonie der Welt
    Die Harmonie der Welt
    Die Harmonie der Welt is an opera in five acts by Paul Hindemith. The German libretto was by the composer....

    , an opera by Paul Hindemith
    Paul Hindemith
    Paul Hindemith was a German composer, violist, violinist, teacher, music theorist and conductor.- Biography :Born in Hanau, near Frankfurt, Hindemith was taught the violin as a child...

  • Johannes Kepler University Linz
    Johannes Kepler University of Linz
    The Johannes Kepler University of Linz is a public institution of higher education in Linz, the capital of Upper Austria...

    : In 1975, nine years after its founding, the College for Social and Economic Sciences Linz (Austria) was renamed Johannes Kepler University Linz in honor of Johannes Kepler, since he wrote his magnum opus
    Masterpiece
    Masterpiece in modern usage refers to a creation that has been given much critical praise, especially one that is considered the greatest work of a person's career or to a work of outstanding creativity, skill or workmanship....

     Harmonice Mundi in Linz.
  • Kepler College
    Kepler College
    Kepler College is an institution of higher learning which was permitted by the state of Washington to grant degrees between March 9, 2000 and March 9, 2010. It focused on interdisciplinary liberal arts with an emphasis on the history of astrology...

    , Seattle, Washington
  • Numerous schools, streets, observatories and others named after him, e.g.:
    • Kepler Gymnasium (high school), Tübingen
      Tübingen
      Tübingen is a traditional university town in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, on a ridge between the Neckar and Ammer rivers.-Geography:...

    • Keplerstraße in Hanau near Frankfurt am Main
    • Keplerstraße in Munich, Germany
    • Keplerstraße and Keplerbrücke in Graz, Austria
    • Keplerplatz, a station on the U1 line of the Vienna U-Bahn
      Vienna U-Bahn
      The Vienna U-Bahn is a rapid transit system consisting of five lines. It is the backbone of one of the best performing public transport systems worldwide according to UITP in June 2009. More than 1.3 million passengers use the Vienna U-Bahn every day...

       rapid transit
      Rapid transit
      A rapid transit, underground, subway, elevated railway, metro or metropolitan railway system is an electric passenger railway in an urban area with a high capacity and frequency, and grade separation from other traffic. Rapid transit systems are typically located either in underground tunnels or on...

       (Metro) system
    • Johannes Kepler Grammar School, at the site where Kepler lived in Prague
  • Kepler Launch Site
    Kepler Launch Site
    Kepler Launch Site is a site for the launch of low and medium power model rockets south of Weil der Stadt in Germany at . Kepler Launch Site, which is named in honor of the astronomer Johannes Kepler born in 1571 in Weil der Stadt, was founded in 2001 on the area of a former site of midsummer fire...


Sources

  • Andersen, Hanne; Peter Barker; and Xiang Chen. The Cognitive Structure of Scientific Revolutions, chapter 6: "The Copernican Revolution." New York: Cambridge University Press
    Cambridge University Press
    Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...

    , 2006. ISBN 0-521-85575-6
  • Armitage, Angus. John Kepler, Faber, 1966.
  • Banville, John. Kepler, Martin, Secker and Warburg, London, 1981 (fictionalised biography)
  • Barker, Peter and Bernard R. Goldstein: "Theological Foundations of Kepler's Astronomy". Osiris, Volume 16. Science in Theistic Contexts. University of Chicago Press
    University of Chicago Press
    The University of Chicago Press is the largest university press in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including The Chicago Manual of Style, dozens of academic journals, including Critical Inquiry, and a wide array of...

    , 2001, pp. 88–113
  • Caspar, Max. Kepler; transl. and ed. by C. Doris Hellman; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover, 1993. ISBN 0-486-67605-6
  • Connor, James A. Kepler's Witch: An Astronomer's Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. HarperSanFrancisco, 2004. ISBN 0-06-052255-0
  • De Gandt, Francois. Force and Geometry in Newton's Principia, Translated by Curtis Wilson, Princeton University Press
    Princeton University Press
    -Further reading:* "". Artforum International, 2005.-External links:* * * * *...

     1995. ISBN 0-691-03367-6
  • Dreyer, J. L. E. A History of Astronomy from Thales to Kepler. Dover Publications Inc, 1967. ISBN 0-486-60079-3
  • Ferguson, Kitty. The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionized science. London: Review, 2002. ISBN 0-7472-7022-8 – published in the US as: Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens. New York: Walker, 2002. ISBN 0-8027-1390-4
  • Field, J. V.. Kepler's geometrical cosmology. Chicago University Press, 1988. ISBN 0-226-24823-2
  • Gilder, Joshua and Anne-Lee Gilder: Heavenly Intrigue: Johannes Kepler, Tycho Brahe, and the Murder Behind One of History's Greatest Scientific Discoveries, Doubleday (May 18, 2004). ISBN 0-385-50844-1 Reviews bookpage.com, crisismagazine.com
  • Gingerich, Owen
    Owen Gingerich
    Dr. Owen Jay Gingerich is a former Research Professor of Astronomy and of the History of Science at Harvard University, and a senior astronomer emeritus at the Smithsonian Astrophysical Observatory...

    . The Eye of Heaven: Ptolemy, Copernicus, Kepler. American Institute of Physics, 1993. ISBN 0-88318-863-5 (Masters of modern physics; v. 7)
  • Gingerich, Owen: "Kepler, Johannes" in Dictionary of Scientific Biography, Volume VII. Charles Coulston Gillispie, editor. New York: Charles Scribner's Sons, 1973
  • Jardine, Nick: "Koyré’s Kepler/Kepler's Koyré," History of Science, Vol. 38 (2000), pp. 363–376
  • Kepler, Johannes. Johannes Kepler New Astronomy trans. W. Donahue, forward by O. Gingerich, Cambridge University Press
    Cambridge University Press
    Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...

     1993. ISBN 0-521-30131-9
  • Kepler, Johannes and Christian Frisch. Joannis Kepleri Astronomi Opera Omnia (John Kepler, Astronomer; Complete Works), 8 vols.(1858–1871). vol. 1, 1858, vol. 2, 1859, vol. 3,1860, vol. 6, 1866, vol. 7, 1868, Francofurti a.M.
    Frankfurt
    Frankfurt am Main , commonly known simply as Frankfurt, is the largest city in the German state of Hesse and the fifth-largest city in Germany, with a 2010 population of 688,249. The urban area had an estimated population of 2,300,000 in 2010...

     et Erlangae
    Erlangen
    Erlangen is a Middle Franconian city in Bavaria, Germany. It is located at the confluence of the river Regnitz and its large tributary, the Untere Schwabach.Erlangen has more than 100,000 inhabitants....

    , Heyder & Zimmer, – Google Books
  • Kepler, Johannes, et al. Great Books of the Western World. Volume 16: Ptolemy, Copernicus, Kepler, Chicago: Encyclopædia Britannica, Inc., 1952. (contains English translations by of Kepler's Epitome, Books IV & V and Harmonices Book 5)
  • Koestler, Arthur
    Arthur Koestler
    Arthur Koestler CBE was a Hungarian author and journalist. Koestler was born in Budapest and, apart from his early school years, was educated in Austria...

    . The Sleepwalkers
    The Sleepwalkers
    The Sleepwalkers: A History of Man's Changing Vision of the Universe is a 1959 book by Arthur Koestler, and one of the main accounts of the history of cosmology and astronomy in the Western World, beginning in ancient Mesopotamia and ending with Isaac Newton. The book challenges the habitual idea...

    : A History of Man's Changing Vision of the Universe.
    (1959). ISBN 0-14-019246-8
  • Koyré, Alexandre
    Alexandre Koyré
    Alexandre Koyré , sometimes anglicised as Alexander Koiré, was a French philosopher of Russian origin who wrote on the history and philosophy of science.-Life:...

    : Galilean Studies Harvester Press 1977. ISBN 0-85527-354-2
  • Koyré, Alexandre: The Astronomical Revolution: Copernicus-Kepler-Borelli Ithaca, NY: Cornell University Press
    Cornell University Press
    The Cornell University Press, established in 1869 but inactive from 1884 to 1930, was the first university publishing enterprise in the United States.A division of Cornell University, it is housed in Sage House, the former residence of Henry William Sage....

    , 1973. ISBN 0-8014-0504-1; Methuen, 1973. ISBN 0-416-76980-2; Hermann, 1973. ISBN 2-7056-5648-0
  • Kuhn, Thomas S. The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, MA: Harvard University Press, 1957. ISBN 0-674-17103-9
  • Lindberg, David C.: "The Genesis of Kepler's Theory of Light: Light Metaphysics from Plotinus to Kepler." Osiris, N.S. 2. University of Chicago Press, 1986, pp. 5–42.
  • Lear, John. Kepler's Dream. Berkeley: University of California Press, 1965
  • North, John. The Fontana History of Astronomy and Cosmology, Fontana Press, 1994. ISBN 0-00-686177-6
  • Pannekoek, Anton: A History of Astronomy, Dover Publications Inc 1989. ISBN 0-486-65994-1
  • Pauli, Wolfgang
    Wolfgang Pauli
    Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

    . Wolfgang Pauli — Writings on physics and philosophy, translated by Robert Schlapp and edited by P. Enz and Karl von Meyenn (Springer Verlag, Berlin, 1994). See section 21, The influence of archetypical ideas on the scientific theories of Kepler, concerning Johannes Kepler and Robert Fludd
    Robert Fludd
    Robert Fludd, also known as Robertus de Fluctibus was a prominent English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, Rosicrucian apologist...

     (1574–1637). ISBN 3-540-56859-X
  • Schneer, Cecil: "Kepler's New Year's Gift of a Snowflake." Isis
    Isis (journal)
    Isis is an academic journal published by University of Chicago Press. It focuses on the history of science, history of medicine, and the history of technology, as well as their cultural influences, featuring both original research articles as well as extensive book reviews and review essays.It was...

    , Volume 51, No. 4. University of Chicago Press, 1960, pp. 531–545.
  • Shapin, Steven. The Scientific Revolution. Chicago: University of Chicago Press, 1996. ISBN 0-226-75020-5
  • Stephenson, Bruce. Kepler's physical astronomy. New York: Springer, 1987. ISBN 0-387-96541-6 (Studies in the history of mathematics and physical sciences; 13); reprinted Princeton:Princeton Univ. Pr., 1994. ISBN 0-691-03652-7
  • Stephenson, Bruce. The Music of the Heavens: Kepler's Harmonic Astronomy, Princeton University Press
    Princeton University Press
    -Further reading:* "". Artforum International, 2005.-External links:* * * * *...

    , 1994. ISBN 0-691-03439-7
  • Toulmin, Stephen and June Goodfield. The Fabric of the Heavens: The Development of Astronomy and Dynamics. Pelican, 1963.
  • Voelkel, James R. The Composition of Kepler's Astronomia nova, Princeton University Press, 2001. ISBN 0-691-00738-1
  • Westfall, Richard S.
    Richard S. Westfall
    Richard S. Westfall was an American academic, biographer and historian of science. He is best known for his biography of Isaac Newton and his work on the scientific revolution of the 17th century.-Life:...

    . The Construction of Modern Science: Mechanism and Mechanics. John Wiley and Sons, 1971. ISBN 0-471-93531-X; reprinted Cambridge University Press, 1978. ISBN 0-521-29295-6
  • Westfall, Richard S. Never at Rest: A Biography of Isaac Newton. Cambridge University Press, 1981. ISBN 0-521-23143-4
  • Wolf, A. A History of Science, Technology and Philosophy in the 16th and 17th centuries. George Allen & Unwin, 1950.

External links