Free Essay

Johannes Kepler|Summary

In: Other Topics

Submitted By aceabrio
Words 13704
Pages 55
Context

Johannes Kepler was born in the midst of an exciting and confusing time for Europe. The continent was entering the Renaissance, a reawakening of thought across the continent. By the time of Kepler's birth, the Renaissance had reinvigorated European culture, politics, philosophy, religion, literature, and science. The authority of the Catholic Church was challenged for the first time in centuries by the reformer Martin Luther, who pointed out the wrongs that he felt the Church had committed. Luther's rebellion spurred the Protestant Reformation, in which Luther and his followers freed themselves from the authority of the Church, creating a new sect of Christianity. Kepler, a Protestant, often found himself caught in the midst of the resulting tension between Catholicism and Protestantism. Catholics frequently persecuted him.
A similar challenge of scientific authority was also in progress, a radical shift in thought that later became known as the Scientific Revolution. Scientists in all fields were beginning to question the wisdom of the ancient philosophers who had molded their disciplines. They gradually began rely on objective facts and observation and to turn away from the mysticism, religion, and unfounded theorizing that had previously dominated the field. This drastic change in scientific practices and beliefs was most apparent in the field of astronomy.
Physics and astronomy had been dominated by the work of Aristotle, a philosopher from the time of ancient Greece, and Ptolemy, an astronomer from the second century A.D. Astronomy was rooted in both philosophy and theology, and it was difficult for scientists to separate their work from that of the mystics or the clergy.
Through the work of the four fathers of the astronomical revolution, Copernicus, Kepler, Galileo, and Newton, both the practice of astronomy and man's view of the universe were transformed. Astronomers rejected the Ptolemaic view of the universe that had held court for centuries. They supplanted Ptolemy's earth-centered universe with a new sun-centered system. These modern thinkers, far ahead of their time, persevered against the mockery, apathy, and anger of their peers. And eventually, through Newton's synthesis of math, physics, and astronomy, they triumphed.
The work of these astronomers shook the world. They denied everything that humans had held certain for centuries. The excitement and confusion that these astronomers left in their wake in is reflected in John Donne's seventeenth century poem "An Anatomy of the World – The First Anniversarie." As he wrote, "And new Philosophy calls all in doubt. 'Tis all in pieces, all coherence gone. "

General Summary

Johannes Kepler was born in Germany in 1571, in the middle of the Scientific Revolution. The weak and sickly child was abandoned by his father Heinrich in early childhood. Because his family moved around so much, it took Kepler twice as long as usual to get through elementary school. He eventually graduated, moving on to a theological seminary and then to the University of Tuebingen.
At the university, Kepler decided to pursue a graduate degree in theology, but he was soon distracted from that goal. A Protestant school in the Austrian town of Gratz offered him a job as a professor of math and astronomy. Although Kepler believed he had no special skills in those subjects, he took the job. Once there, he turned his attention toward deciphering the mysteries of the universe. Kepler was convinced that God had created a universe with some discernable pattern or structure, and he devoted himself to figuring out what it might be.
In 1595 Kepler decided that the planets were spaced as they were because the planetary orbits were arranged around geometric figures: the perfect solids. Perfect solids are three-dimensional figures whose sides are all identical, and Kepler was convinced that God had used these forms to build the universe. He elaborated on this view in his first book, the Mysterium Cosmographicum, or the Cosmic Mystery. Kepler's theory was incorrect, but the book was the first major work in support of the Copernican system since Copernicus's death fifty years before. The book was also significant because Kepler was the first major astronomer in centuries to address physical reality, rather than being content with a mere mathematical description of the universe.
Kepler could not quite get his data to fit his theory; he needed a source of more accurate data. He found this in Tycho de Brahe, a wealthy Danish astronomer. Tycho was the best observational astronomer of his age, and Kepler decided that only Tycho's observations would do. So Kepler traveled to Prague to work in Tycho's lab. Tycho, an arrogant, demanding, and unpleasant employer, died after only a year. But Kepler worked for seven more years on the problem he had started on while there: constructing the orbit of Mars.
Kepler's work on Mars led him to discover his first two planetary laws: that the planets travel in elliptical orbits and that they sweep out equal areas of their orbits in equal times. He published his results in 1609 in the Astronomia Nova, or the New Astronomy, revolutionizing astronomy and greatly simplifying the Copernican system.
Kepler was considered one of the top astronomers in Europe–although not because of his published work. Few of his peers recognized the importance of his planetary laws, and few even accepted that they were true. It was difficult for his colleagues to recognize him as a scientist of the modern age, when his work remained mired in the mysticism of the past.
The years just before and after the Astronomia Nova were a professional triumph for Kepler – he was well known and well respected. He spent these years researching lenses, as well as astronomy, adding several major contributions to the field of optics. At the same time, his personal life was taking a turn for the worse. In quick succession, Kepler's wife and favorite son died, and his patron went insane and abdicated the throne. His new home, Prague, was torn apart by civil war, and his mother was accused of being a witch.
Through it all, Kepler continued to work toward his greatest goal: finding a way to explain the structure of the universe. He had been forced to abandon most of his theory of the perfect solids, and needed something new to replace it. After years of thought, he came up with a new idea: the theory of universal harmonies. Kepler decided that the planets were spaced around the harmonic ration of another set of geometrical figures. Once again, he believed he had looked directly into the mind of God. Once again, his theory was completely wrong. Butthe pursuit of an incorrect theory led him to a stroke of scientific genius.
In 1618, Kepler published the Harmonice Mundi, or the Harmony of the World, in which he explained his new harmonic theory. Kepler's third law offered a specific mathematical relationship between the distance of a planet's orbit from the sun and the time it took a planet to circle the sun. Kepler thought little of this law, as did his peers, because it made little sense to him at the time. It was only later, when Sir Isaac Newton created the theory of universal gravitation, that the fundamental importance of this law became clear.
Kepler continued to publish important works. In 1619, he published Epitome Astronomiae Copernicanae, a summary of the Copernican system, adjusted to accommodate Kepler's laws. The Copernican system as we now know it is basically the one offered in the Epitome. Then, in 1627, Kepler published the Tabulae Rudolphine, or the Rudolphine Tables, a comprehensive list of astronomical observations, predictions, and explanations, all based on Tycho's data and Kepler's discoveries.
Kepler's final publication came a few years after his death. Though filled with scientific explanations, it is not actually a scientific work – instead, it is a science fiction story. Somnium, or Dream, tells the story of a young boy's trip to the moon. Much of the story seems to be a thinly veiled autobiography. However, the Somnium was also packed with notes on the scientific ramifications of Kepler's discoveries. The accuracy of his prediction of what a lunar journey would be like reveals what remarkable physical intuition he had.
Kepler is perhaps the least known of the major figures of the Scientific Revolution. His lack of fame may be due to the fact that he is difficult to classify – he seems less modern than the other scientists of the time, and he relies on mysticism and religion. His scientific contributions are themselves harder to simplify than those of Copernicus or Newton. But while he may be less known than his peers, Kepler is no less important. Physics and astronomy had been separated for two thousand years before Kepler's birth. It was an incredible leap for him to put the two together – and in doing so, he paved the way for the Newtonian revolution that was to come.

Important People, Terms, and Events

People

Copernicus - Copernicus was a Polish astronomer and clergyman who, in 1543, introduced a new heliocentric system of the universe. In Copernicus's system, the planets revolved on a complex system of epicycles, but they all revolve around the sun. This was a revolutionary idea in the sixteenth century. Everyone was firmly convinced that the earth was motionless at the center of the universe. To imagine that it moved around the sun seemed ridiculous. It took several decades for the Copernican system to become fully accepted by astronomers and the public. Kepler was the first major astronomer to publicly acknowledge his support of it.
Tycho de Brahe - Tycho de Brahe was a Danish nobleman who made a name for himself in the late sixteenth century as Europe's best observational astronomer. He kept a closely guarded collection of astronomical observations, the most accurate astronomical data available at the time. Eager to use Tycho's figures to develop his own system, Kepler traveled to Prague to work in Tycho's lab. In addition to being a brilliant astronomer, Tycho was also an arrogant and temperamental man. Tycho and Kepler had a love-hate relationship; they respected one another, but each was also jealous of the other's achievements and potential. Several times, Kepler fled the lab, only to return full of apologies. When Tycho died, he expressed a hope that Kepler would use his data to develop the Tychonic system of the universe, in which the planets orbited the sun, which orbited the earth. Instead, Kepler applied Tycho's observations to the Copernican system, which led him to discover his first two laws. Galileo Galilei - Galileo was an Italian astronomer who discovered the moons of Jupiter. Galileo was the first major astronomer to use a telescope to observe the heavens. When these observations yielded findings that the scientific community was reluctant to believe, Kepler lent him public support Galileo later became a symbol of science's break from religion during the scientific revolution. He was put on trial by the Catholic Church and convicted of heresy for his support of the Copernican system Heinrich Kepler - Kepler's father, Heinrich, was an itinerant criminal who repeatedly abandoned his family. At one point he owned a tavern, at another, he was nearly hanged for an alleged crime. One of Kepler's younger brothers was forced to run away from home when Heinrich threatened to sell him. Heinrich left for good in 1588 – he was not missed. Katherine Kepler - Katherine Kepler, Kepler's mother, was born Katherine Guldenmann. She was the daughter of an innkeeper and the niece of a woman who had been burned at the stake as a witch. Kepler later described her as a petty, angry, quarrelsome woman. She came back into Kepler's life in 1615, when her fellow villagers accused her of being a witch. Kepler was quick to come to her defense. After five years of argument and negotiation, Katherine was interrogated under threat of torture. When she continued to deny being a witch, she was finally released. She was driven from her town and died six months later. Michael Maestlin - Michael Maestlin was Kepler's most influential teacher at the University of Tuebingen. Maestlin was the first to teach Kepler about the Copernican system. In the classroom, Maestlin was a strong supporter of the Copernican system, but on paper, he continued to propound the Ptolemaic system. Kepler turned to Maestlin for help and advice throughout his life, but Maestlin seems to have grown tired of his troublesome student. He often ignored Kepler's letters for years at a time.
Barbara Muehleck - Kepler married Barbara Muehleck in 1597. It was a marriage of convenience, not love. Kepler's friends had decided it was time for him to marry and had chosen Barbara as a good mate; Kepler acquiesced. They were married for fourteen years and had four children. Barbara died in 1611 of the Hungarian fever.
Susanna Pettinger - Two years after his first wife died, Kepler married the 24-year-old Susanna Pettinger. They had eleven children together and Kepler had nothing negative to say about her in later life – a ringing endorsement considering the way he described most of his family members.
Ptolemy - Ptolemy, an astronomer from the second century A.D., formulated a system of the universe that lasted for over one thousand years after his death. His system placed the earth at the center of the universe, with the planets and the stars revolving around it. Ptolemy insisted that the planets in his system moved with uniform circular motion. Because this is not actually how the planets move, he was forced to introduce the following mathematical devices. The deferent is the main circle around which each planet orbits the earth. An epicycle is a smaller circle around which the planet orbits the deferent. Finally, the equant is an imaginary point in the exact center of the planetary orbits. Ptolemy's system was so complex that, by the time of Copernicus, it contained somewhere between forty and eighty epicycles.

Terms

Astronomia Nova - · The Astronomia Nova, or the New Astronomy was Kepler's masterpiece. Published in 1609, it was the result of over eight years of work. Kepler spent those years trying to work out the shape of the orbit of Mars. Using Tycho's data about the motion of the planets, Kepler was finally able to determine the shape of the orbit more accurately than anyone who had come before him. This resulted in the formation of his first two laws, which were published in the Astronomia Nova.
Geocentric - · A geocentric system is one in which the earth is at the center of the universe. For thousands of years, scientists, philosophers, and theologians believed that the universe was geocentric. They were unwilling to believe Copernicus when he challenged that assumption.
Harmonice Mundi - · The Harmonice Mundi, or Harmony of the World was the culmination of Kepler's life-long study of the structure of the universe. Published in 1618, it described a system in which the spacing between the planets was determined by universal harmonies. The theory was wrong, but the book is nonetheless important, as it marks the first appearance of Kepler's third law.
Heliocentric - · A heliocentric system is one in which the sun is at the center of the universe. The system that Copernicus introduced was a heliocentric system. This was not a completely original idea – some of the philosophers of ancient Greece had imagined that the universe might be constructed in this way. However, the dominant view had always been that the universe was geocentric, so Copernicus's claims were a shock to the European system.
Kepler's Three Laws - · Kepler is best known today for his contribution of the three planetary laws, which were instrumental in Newton's later development of his theory of universal gravitation. They are as follows: 1. The planets travel around the sun in elliptical orbits with the sun located at one focus. 2. As the planets travel around their orbits, they sweep out the same amount of area per unit of time, no matter where they are on the orbit. 3. The distance a planet's orbit is from the sun, cubed, is directly proportional to the time it takes the planet to travel around the orbit, squared. Mathematically, this can be stated as a 3/p 2 = K where "a" is the distance a planet's orbit is from the sun, "p" is the period, the time it takes for a planet to revolve around the sun once, and "K" is a constant.
Mysterium Cosmographicum - · Published in 1597, the Mysterium Cosmographicum, or Mysteries of the Cosmos, was Kepler's first major work. It described his theory of the perfect solids, which, although he never fully admitted it, was completely wrong. More importantly, the Mysterium was Kepler's first step to rejoining physics and astronomy, as he grasped for physical explanation for the structure of the universe. He was the first astronomer in centuries to do so. It is in the Mysterium that Kepler first proposes that the sun be moved to the exact, physical center of the universe, and that a force from the sun is responsible for moving the planets around their orbits. The Mysterium was also the major work in fifty years to support the Copernican system.
Perfect solid - · A perfect solid a three dimensional figure, such as a cube, whose sides are all identical. There are only five perfect solids: the tetrahedron (which has four triangular sides), cube (six square sides), octahedron (eight triangular sides), dodecahedron (twelve pentagonal sides), and icosahedron (twenty triangular sides). Each perfect solid can be inscribed in and circumscribed around a sphere. In the beginning of his career, Kepler believed that the planetary orbits could all be inscribed in one of the perfect solids.

Growing Up

Johannes Kepler was born on December 27, 1571, in the small German town of Weil- der-Stadt. He was born at the tail end of the European Renaissance, an age of intellectual, religious, cultural, and scientific transformation. But Kepler's own early childhood showed no such signs of enlightenment. The young Kepler was trapped in his own period of personal depression and darkness. The Kepler family tree had distinguished roots – his arrogant grandfather Sebaldus Kepler had even served as town mayor. But by the time Kepler came on the scene, the family had fallen into a state of disrepair, filled with tormented personalities, hot tempers, invalids, and criminals.
Sebaldus and his wife, Katherine Mueller, had twelve children. Heinrich, Kepler's father, was the oldest surviving child; three others had died in infancy. When he was twenty-four years old, Heinrich married Katherine Guldenmann – Johannes was their first child. Katherine had a slightly less auspicious pedigree than Heinrich. She was an innkeeper's daughter whose aunt had been accused of being a witch and had been burned at the stake.
Heinrich was a restless husband who abandoned his family often. When Kepler was only three, Heinrich left to fight the Protestant armies in the Netherlands. This was a public embarrassment for the Keplers – one of many that Heinrich would cause – since the Kepler family itself was solidly Protestant. Heinrich came and left frequently through Kepler's youth. At one point, he was accused of a crime and almost hanged. After briefly running a tavern, the itinerant Heinrich abandoned the family for good in 1588.
Johannes Kepler had six brothers and sisters, three of whom died in childhood. Of the remaining three, two grew up to be normal, law-abiding citizens. The last one, Heinrich, was an epileptic who was always either sick or in trouble. He eventually ran away from home after Heinrich Sr. threatened to sell him.
Historians have an incredibly detailed sketch of Kepler's childhood, thanks, in large part, to the scientist himself. At the age of twenty-six, Kepler drafted a horoscope of his entire family. He also spent a fair amount of time analyzing his own personality. Kepler recorded everything, including the time of his conception (May 16, 1571), the length of his mother's pregnancy (224 days, nine hours, and fifty-three minutes), and his own opinions of each member of his family.
The image we are left with is not a pretty one. Grandfather Sebaldus was "remarkably arrogantshort tempered and obstinate" and Grandmother Katherine was "restless, clever, and lyingan inveterate troublemaker, extreme in her hatred, a bearer of grudges" Mother Katherine is described as "small, thin, swarthy, gossiping, and quarrelsome." But it is Kepler's father who bears the brunt of Kepler's familial criticisms. In Kepler's autobiographical study, Heinrich appears as a man "vicious, inflexible, quarrelsome, and doomed to a bad end."
Kepler spares no one in his autobiography, least of all himself. He portrays himself as a sickly child, weak in health and personality, always picked on by other children. He describes a miserable childhood filled with illness, injury, and skin disorders. His chronological listing of events from his early days reveals that Kepler was not one to look on the bright side – the list is a recital of moments of suffering and weakness. In 1575, Kepler almost died of smallpox; in 1585, he suffered from a series of sores, wounds, and skin problems. The litany of complaints breaks for only a few events, including the sighting of a comet in 1577 and, a few years later, a sighting of a lunar eclipse. As these astronomical events marked a few bright moments in a childhood of darkness, astronomy itself would soon illuminate Kepler's troubled adult life.

Becoming an Astronomer

Neither of Kepler's parents were interested enough in their oldest son or his future to invest much effort into his education. Fortunately, the region of Germany in which Kepler lived was known for its strong educational system. The schools encouraged students from all economic classes and offered scholarships to those who could not afford tuition. Kepler was launched into academics at an early age.
In elementary school, Kepler learned Latin, which was then considered to be the only language fit for scholarly writing. Due to his frequent illnesses and his family's wanderings, Kepler was unable to attend school consistently – it took him twice as long to finish elementary school as it took the other children. When he was thirteen years old, he entered a theological seminary. There he studied Greek, Latin, theology, rhetoric, music, and math.
According to his own reminiscences, Kepler was a weak, odd, unlikable student who often got bullied and beat up by his peers. But Kepler's enemies were no harsher on him than he was on himself. In his later self-analysis, written in third person, Kepler noted the "dog-like nature" of both his appearance and personality, and added that "morally he was the worst among his contemporaries."
From the theological seminary, Kepler went on to the renowned University of Tuebingen, where he decided to continue his religious studies. He got perfect grades – as did almost every other student at the school. He was successful in his math and physics classes, but decided to devote his life to God.
Before he could earn his graduate degree in divinity, Kepler recieved an unexpected job offer. A Protestant school in the Austrian city of Gratz was in need of a new math professor – and the University of Tuebingen recommended Kepler. Kepler was at first reluctant to accept the job, primarily because he didn't think he was cut out to be an astronomer. He eventually accepted, on the condition that he would be allowed to return to Tuebingen to complete his divinity studies when he wanted to. Tuebingen agreed, but Kepler never returned. He was an astronomer for life.
Kepler arrived in Gratz in April 1594, where he was officially appointed the Mathematicus of the Province. He didn't expect to be a particularly good teacher. From the start, few wanted to take his class, by his second year of teaching, he had no students.
Kepler was initially miserable in Gratz. The town was much smaller and more provincial than he was used to, he was often sick, and as a Protestant, he was constantly on the defense against an oppressive Catholic regime. He was also convinced that the school authorities hated him, and often begged his old associates at Tuebingen to find him a job closer to home. When they were unable to do so, Kepler was forced to remain in Gratz and, contrary to what he believed, the school authorities were happy to keep him there. They expected great things from the young astronomer.
On the rare occasion that Kepler did find himself in front of a class full of students, he distinguished himself from other astronomers of the time. Kepler was one of the only astronomers of the time willing – and in this case – eager to teach the heliocentric system of the universe, which put the sun rather than the earth at its center.
For almost two thousand years, all of Europe had relied upon an intricate vision of the universe created in the second century A.D by the astronomer Ptolemy. Ptolemy's geocentric system places Earth at the center of the universe. This seemed a reasonable enough assumption, since from humanity's point of view, the sun, stars, and planets do seem to revolve around the Earth. Ptolemy argued that the planets and the sun circled the earth in perfectly circular orbits, traveling at constant speeds over time. These two assertions had been the central tenets of astronomical philosophy since the time of Ancient Greece.
However, as it turns out, neither of these two facts are actually true. So in order to make his observations fit his theories, Ptolemy was forced to incorporate a number of imaginary mathematical devices into his system. Each planet's circular orbit around the earth was known as the deferent. But, according to Ptolemy, the planets did not actually travel on the deferent. Instead, they traveled in small orbits around the deferent called epicycles. The system is so intricate that it is difficult to make an accurate count of these wheels-within-wheels, but by Kepler's era, there were somewhere from forty to eighty of them. The final mathematical device required to make reality fit theory was the equant. This was an imaginary point that rotated around the center of the deferent. This was yet another device used to explain why the planets did not appear to be circling the earth with constant, circular motion – when viewed from the equant, the planetary orbits suddenly became circular.
With this type of reasoning, Ptolemy created a universe with an imaginary point for a center. No one believed that such a thing as the equant existed in space – any more than they believed that the planets were actually spinning around on an elaborate system of epicycles. But for centuries, the world was willing to make these mathematical compromises in order to preserve the notion of constant circular motion. Astronomy became a mathematical field divorced from any sense of physical reality. Ptolemy created a geometrically possible system on paper, but steered clear of explaining how the universe actually worked. No one successfully challenged this view for almost two thousand years.

The Sun-Centered Universe

In 1543, twenty-eight years before Kepler's birth, Copernicus published the landmark astronomical text De Revolutionibus, or On the Revolutions of the Heavenly Spheres. The standard story about Copernicus's achievement is that by the sixteenth century, the Ptolemaic system had gotten too complicated and inaccurate to bear. In a stroke of genius, Copernicus moved the sun to the center of the universe creating a new system of brilliant simplicity and inarguable accuracy. Despite the attempts of the Catholic Church to drown out Copernican arguments, Ptolemy's system was soon overthrown. The Copernican system is thus heralded as a prime example of the triumph of a new, modern scientific era.
The story is true only in part. Copernicus did revolutionize astronomy by introducing a heliocentric system. But the concept of a sun-centered universe was not brand new and, in fact, had occurred to many of the ancient philosophers. Despite popular belief, Copernicus did not drastically simplify the Ptolemaic system. What we now think of as the Copernican system – six planets traveling around in the sun in simple, circular orbits and no epicycles – was only made possible by Kepler's later refinements. In fact, Copernicus's new heliocentric universe contained almost as many epicycles as the old system. Copernicus was just as devoted as his colleagues to the concept of uniform circular motion, and was willing to introduce as many mathematical devices as was necessary to simulate it. The Copernican system was no less complicated than the Ptolemaic system, nor was it any more accurate. Each of the systems yielded predictions that were accurate enough for the astronomers and navigators of the time. Copernicus's achievement was undeniably remarkable. But almost as remarkable was the ability of a few astronomers to grasp the truth of the heliocentric system, even though there was little evidence to recommend it.
Kepler was one of those insightful few. At a time when the Ptolemaic system still ruled in the European universities and the public mind, when other astronomers refused to publicly support Copernicus for fear of ridicule, Kepler was an unabashed Copernican. Although he had no technical evidence supporting one system over the other, he remained certain that the sun was at the center of the universe. While historians can never be sure exactly Kepler latched on to the heliocentric view so quickly and so firmly, most believe that he was attracted to it by the same combination of physical intuition and mystical theorizing that guided him throughout his professional career.
Kepler learned of the Copernican system at the University of Tueringen, from his first mentor, the professor Michael Maestlin. Maestlin publicly supported the Ptolemaic system – he had even written an astronomy textbook based on Ptolemy. However, in the safety of his own classroom, Maestlin was a full- fledged Copernican, and Kepler soon followed suit. Kepler would soon become the first well-known astronomer to support the Copernican system. At the same time, he would recreate that system in a much more physically and mathematically accurate form. What we now think of as the Copernican conception of the universe is actually Kepler's system.
Once at Gratz, Kepler focused on studying and refining Copernican astronomy. He accepted the Copernican construction of the universe, but one all-encompassing question remained: why were the planets arranged the way they were? More specifically, he wondered why there were only six planets (as was thought at the time), why they moved at the speed they did, and why they were spaced as they were. These were revolutionary questions. Before Kepler, no one had thought to wonder about why the universe was constructed in a certain way. For millennia, astronomers had devoted themselves to describing the way the planets moved, rather than questioning why that movement occurred. In the centuries before Kepler, astronomy had been purely mathematical. Kepler was the first major astronomer of the modern age to introduce questions of physics into the study of the stars.
A deeply devout man, Kepler was convinced that God had created an orderly universe, and his first major pursuit was figuring out what God's intentions might have been. Kepler played with the numbers for months, searching fruitlessly for a pattern. Finally on July 9, 1595, he found one.
On that day, while standing at the blackboard drawing a geometrical figure for his class, Kepler had an epiphany. He believed it was a divine inspiration. Kepler had drawn a triangle with a circle circumscribed around it, which meant that each of the triangle's corners touched the rim of the circle. Then he inscribed another circle inside the triangle, which meant that the center of each side of the triangle touched the inner circle.
When Kepler stepped back and looked at what he had drawn, he realized with a shock that the ratios of the two circles were the same as the ratios of the orbits of Saturn and Jupiter. And with that realization, inspiration struck. Jupiter and Saturn were the outermost planets of the solar system, and the triangle was the simplest polygon. Kepler wondered whether you could fit the orbits of the other planets around other geometric figures, and tried his best inscribing circles in squares and pentagons. But the planetary orbits refused to fit.
Then Kepler had a second epiphany. The solar system was three dimensional – so why would he think that its governing pattern would be found in two dimensional figures? Kepler turned to three dimensional objects, and found his answer in the five perfect solids. A perfect solid is a three dimensional figure, such as a cube, whose sides are all identical. Conveniently for Kepler, there are only five perfect solids: the tetrahedron (which has four triangular sides), cube (six square sides), octahedron (eight triangular sides), dodecahedron (twelve pentagonal sides), and icosahedron (twenty triangular sides). Each perfect solid can be inscribed in and circumscribed around a sphere.
Kepler believed that the orbits of the six known planets – Mercury, Venus, Earth, Mars, Jupiter, and Saturn – could be fit around the five regular solids. He had finally found his answer to his question of "why." The reason there were only six planets was because there were only five perfect solids; the spacing of the planets was determined by the spacing between the solids.
Kepler's new system was wrong. Kepler had made the incredible leap of asking the question "why" – but had come up with a completely wrong answer. However, Kepler would continue to cling to this system in some form for the rest of his life – he valued it far above all his other achievements. And perhaps he was right to do so. Though incorrect, his idea would launch him on a lifelong path of investigation and discovery. It would lead him to revolutionize astronomy and take his place as one of the fathers of the scientific revolution.

Mysteries of the Cosmos

In 1597, Kepler published his first major work, Mysterium Cosmographicum, or the Cosmic Mystery. In this long and rambling book, Kepler lays out his entire philosophy of the structure of the universe. As his ideas relied on a heliocentric system, Kepler began by trying to convince the reader that Copernicus had been correct. The heliocentric theory was still a new, untested, and unpopular idea – in fact, Kepler's book was the first major work to support the Copernican system since Copernicus's death, fifty years before.
Although the Copernican system was not yet accepted by the scholarly authorities of the time, Kepler took few risks in propounding it. Copernican advocates were not persecuted – the worst they could expect was a bit of ridicule from their colleagues, which in itself was enough to scare off most potential supporters. Many people's attitude at the time was that the Copernican system was mathematically sound but physically implausible.
This attitude offered a convenient out for scholars who wanted to use the Copernican system but feared the wrath of the Church should they try claim that the earth was actually revolving around the sun. Such rationalizing may stem from the publication of Copernicus's own treatise, whose preface included the following caution not to blame the author for his suggestions: "For these hypotheses need not be true nor even probable; if they provide a calculus consistent with the observations, that alone is sufficient." It continues to assert that astronomy will never be able to offer physical truths about the universe – nor should this be expected of it. For decades after the publication of De Revolutionibus, this was the attitude most scholars took toward the heliocentric theory.
Kepler refused to go along with the crowd. As he set out to write the Mysterium, the head of the theological faculty at Tuebingen warned him to steer clear of discussing "whether these theories correspond to existing things or not." Kepler ignored the advice. For him, the whole point of astronomy was to fit theories to "existing things." Throughout his career, he insisted on finding physical explanations, and it was this determination that propelled him toward his greatest discoveries.
By the time he published the Mysterium, Kepler had refined his grand ideas about the layout of the universe, but they continue to rely on one fundamental assertion: that the orbits of the six planets could be fit around the five perfect solids. In Kepler's system, the orbit of Saturn circumscribes a cube. Inscribed in the cube is the orbit of Jupiter, which circumscribes a tetrahedron. Inscribed in the tetrahedron is the orbit of Mars, which circumscribes a dodecahedron. Inscribed in the dodecahedron is the orbit of Earth, which circumscribes an icosahedron. Inscribed in the icosahedron is the orbit of Venus, which circumscribes an octahedron. Finally, the orbit of Mercury is inscribed in the octahedron.
It was an intricately beautiful creation, and it worked.
Almost.
Kepler's construction looked nice, and it fit the approximate orbits of the planets, but this wasn't good enough for the mathematical perfectionist in Kepler. He spent a large portion of the book comparing actual astronomical observations to his predictions and trying to work out the differences.
Kepler was convinced that his idea was correct, and believed that if the facts didn't fit his theory, then there must be something wrong with the facts. So he played around with the numbers, trying to find ways the observations could be reinterpreted. One of his ideas for manipulating the data was to take a closer look at the center of the planetary orbits. In Copernicus's system, as in Ptolemy's, the planets orbited an imaginary point in space. Kepler wondered: What would happen if he put the sun in the physical center of the universe? So he did.
Unfortunately for Kepler, the shift didn't help fit his perfect solids system to the observations. But Kepler had accomplished something far more important. He had moved the sun to the center of the universe, replacing an imaginary point with a physical object, and making a gigantic leap toward achieving an accurate physical depiction of the universe. For all the wrong reasons, Kepler had done exactly the right thing, and it was something no one had thought to do for thousands of years.
Once it had occurred to Kepler to place the sun in the center, he realized that this was the only position that made sense. The sun was the most powerful and important object in the universe, he argued, so it followed that the sun should be physically responsible for the motion of the planets. Astronomers had long known that the farther away the planets were from the center of the universe, the slower they moved around their orbits – but no one had ever stopped to wonder why. Once again, Kepler asked the question that no one else thought to ask, and concluded that a solar force must be responsible for the movement. He imagined a force emanating from the sun that pushed the planets around in their orbits, and grew weaker with increased distance.
Kepler got it wrong. The force he imagined at this point is nothing like the gravity that actually guides the planets around in their orbits. But his theorizing is revolutionary nonetheless, because he was for the first time offering a physical explanation for celestial motion. With one small shift of the sun, Kepler made physical sense of the universe. He rejoined astronomy and physics, fields that had been separate since the fall of ancient Greece.

God in the Numbers

The Mysterium Cosmographicum was a landmark in Kepler's scientific career and, thanks to his revolutionary insights about the sun, in the history of astronomy itself. But the text was not purely "scientific," as the word is meant in the twenty-first century. Chapters of it are filled with astrology, numerology, and mysticism. Even those passages discussing astronomy itself are peppered by references to God and the divine plan.
In the centuries before Kepler, astronomy had been inextricably linked with other studies of the heavens, such as astrology and theology. In the centuries after him, astronomers broke away completely from such things. But in Kepler's era, astronomy was only beginning to turn away from its interdisciplinary nature. More than any astronomer of the time, Kepler and his work represent the contradictions and confusions of this transitional period. Kepler saw no battle between astronomy, religion, and mysticism. For him, each was necessary and had its place. He incorporated each into his work, his theorizing guided alternately by scientific and divine forces.
The discussions of astrology in the Mysterium Cosmographicum reflect Kepler's fascination with the field. Astrology, the study of the stars' effect on human destiny, was popular in the seventeenth century, among both scholars and the public. It usually went hand in hand with astronomy. An astronomer's job often involved interpreting the stars, in addition to observing them.
While at Gratz, it was part of Kepler's job to compile an annual calendar of astrological forecasts. He resented the tedium of the work, as well as the unscientific, superstitious nature of astrology itself. But despite his disdain, Kepler always believed that astrology had scientific potential. He argued that the sky affected man's behavior in some unknown way, and he spent much of his time trying to figure out what that influence might be. The self-analysis he wrote of himself and his family at age twenty-six contained numerous references to astrology. Each person's personality characteristics and major life events were attributed to the stars.
Kepler was not just a reluctant mystic – he was a devout Protestant. His deeply held beliefs assured him that God was ultimately responsible for the structure of the universe, and this idea certainty guided him on his lifelong quest for answers. Tensions over the Copernican system did exist between scientific and religious authorities. But in the age of Kepler, there was still a close bond between the two. Many members of the clergy were also highly acclaimed scientists; similarly, most of the leaders of the Scientific Revolution (such as Copernicus and Newton) were deeply devout. "Science" was rarely referred to by that name – instead it was known as "Natural Philosophy," due to the interrelationship between science, philosophy, theology, and the humanities. The practice of natural philosophy was an all-encompassing pursuit that incorporated both the technical and the divine. Kepler exemplifies this unity.
Kepler was a Protestant, a fact that got him into trouble all his life, as he was continually forced to flee from Catholic persecution. However, it caused him no trouble in terms of his scientific work. Many astronomers and theologians had difficulty reconciling the heliocentric universe to the Bible – which at several points clearly refers to the motion of the sun. If one is to take the Bible as the word of God, then the Copernican theory cannot be physically true. But Kepler glossed over such difficulties – as he argued throughout his career, the Bible is not an astronomical text, and should not be taken as such. Any astronomical comments in the Bible are merely figures of speech, according to Kepler, and should be taken as such.
Though he carefully attempted to separate astronomical teachings from holy writings, Kepler firmly believed that the study of the stars was the study of God's plan. He was driven to develop his theory of the perfect solids because he believed that God must have imposed some discernable pattern on the universe. This is a constant refrain throughout his life's work. Kepler remained convinced that through astronomical study, he could come to understand the mind of God. For Kepler, while science and theology may have been two distinct disciplines, astronomy and God were one and the same. As he wrote in the introduction of the Mysterium Cosmographicum, "The ideas of quantities have been and are in God from eternity, they are God himself" For Kepler, God was in the numbers.

Biding His Time

Kepler published the Mysterium Cosmographicum in the spring of 1597. Although the idea behind the book was entirely wrong, Kepler always looked back on it as his most important work, as it was the cause of everything that followed. The rest of his career would be spent on trying to revise and improve this theory. All of Kepler's important contributions stemmed from this one incorrect idea – an idea that Kepler valued far above anything else he'd done.
When it came on the scene, however, the Mysterium failed to make much of a splash. Kepler was an unknown astronomer, and his wildly enthusiastic ramblings failed to capture the interest of the scholarly elite. The book was read, but rarely understood. Scientists who considered themselves a part of the modern scientific era disdained it, because they were determined to leave such mysticism behind. They overlooked its revolutionary scientific potential. On the other hand, scientists of the old era thought Kepler's book was wonderful, mainly because they had latched onto the religious and mystical portions. They failed to see the book's scientific potential. Few people were able to see the work for what it really was, a radically modern scientific work covered by the trappings of the old era. Fortunately for Kepler, at least one astronomer did read and understand the promise of the Mysterium: Tycho de Brahe.
Born in 1546, Tycho de Brahe was one of the seventeenth century's top astronomers. Wealthy and arrogant, he had once entered into a duel over who was the best mathematician and had a piece of his nose sliced off. Undaunted, Brahe had a new nose made from gold and silver and wore it proudly. For much of his professional life, he lived in Denmark, on the island of Hveen. The ruler of Denmark so valued Tycho that he had given Tycho the entire island, where Tycho ruled like a feudal master. He built a grand observatory called Uraniburg, in which he kept a collection of the era's best observational equipment.
Tycho was obsessed with making observations, an unpopular pursuit at the time. Observing the stars wasn't considered a necessary element of astronomy. The telescope had yet to be invented, and many astronomers were content to use data that had been collected over the preceding centuries. Even Copernicus, in his revolutionary work, included fewer than thirty new observations. Tycho was ahead of his time in recognizing the importance of accurate and current data.
Kepler was also unusually concerned with accuracy, and needed more data to revise his system of the universe – he knew that only Tycho could provide it. But unfortunately, Tycho lived in Denmark. Even if Tycho had invited Kepler to join him, the younger astronomer had no funds to make the long and arduous journey.
Kepler knew that someday he would need to find a way to get to Tycho, and get his hands on Tycho's observations, but for the moment, he bided his time. From 1597 to 1599, Kepler stayed in Gratz, studying mathematics and busying himself with a number of minor astronomical investigations.
Kepler also turned his attention toward his personal life, as his friends had decided it was time for him to take a wife. After a complicated yearlong courtship, Kepler married Barbara Muehleck, a 23-year-old widow. Kepler and Muehleck were set up by a mutual friend. Kepler seems to have had little early affection for his new wife, noting that she was "simple of mind and fat of body." None of his later writings contradicted this early view – Kepler believed her to be stupid, cranky, temperamental, and greedy. Nevertheless, they stayed together for fourteen years, having four children.
In 1598, life in Gratz got distinctly less pleasant for Kepler, when the Catholic Archduke Ferdinand of Hapsburg decided to rid Austria of as many Protestants as possible. In the summer of 1598, the Protestant school where Kepler taught was closed down. Then, in September, the town of Gratz exiled all the Protestant preachers and teachers – including Kepler. Thanks to the help of a friend in the Jesuit order, a very pro-science Catholic sect, Kepler was allowed to return home in only a month. But Kepler was now unhappier than ever. He wrote again to his old teacher Maestlin, begging the older man to help Kepler find a job in his native land. Maestlin was either unable or unwilling to help, and Kepler was forced to remain where he was.
In 1599, Tycho got into a fight with the new King of Denmark, and fled the country for Prague. The Emperor Rudolph II appointed Tycho to be the Imperial Mathematicus – head mathematician and astronomer, and gave him a castle in the town of Benatek. Prague was much closer to Gratz than Denmark had been, and the journey seemed much more bearable to Kepler now that he was so desperate to leave. On January one, 1600, Kepler began the new century by setting off for Prague.

Life with Tycho

Kepler arrived at the Benatek observatory on February 4, 1600, and Tycho was pleased to see him – for Tycho needed Kepler as much as Kepler needed Tycho. Kepler had come to Tycho hoping that Tycho would share his observations of the stars and planets, as Kepler needed the data to perfect his universe of perfect solids. But Tycho was secretly hoping that Kepler would reconsider this plan. Tycho had his own theory of how the universe was constructed. He imagined that the sun revolved around the earth and the other planets revolved around the sun. Tycho hoped that Kepler would help him develop the system so Tycho could take his place among the great names in astronomy.
If Kepler had been hoping for a new mentor, he must have been sorely disappointed. Tycho treated Kepler like a family dog, and not a particularly well-loved one. Tycho refused to pay Kepler the salary he had been promised, refused to share any more observations with him than were absolutely necessary, and forced Kepler to waste his time writing attacks on Tycho's enemies. Their short relationship was filled with bitterness and fighting. Several times Kepler left the lab in anger, only to return days or weeks later begging Tycho's forgiveness.
Kepler was trapped. In July of 1600, he was permanently expelled from Gratz, along with the rest of the town's Protestants. Kepler once again turned to Maestlin for help and, once again, Maestlin declined. He did not respond to Kepler's letters for another five years. It was a miserable moment for Kepler, but a fortunate one for Tycho, as it meant that Kepler had nowhere else to turn.
Frustrated as he was about his relationship with Tycho, once Kepler went to work in the lab, nothing could have distracted him from the problem at hand. As the most junior member of the staff, Kepler had been assigned to work on the orbit of Mars: the trickiest and thus least desirable of the planetary orbits. Kepler was undaunted, and even bet one of his colleagues that the task would take him only a week. It eventually took him seven years – it would be the most frustrating and most fruitful years of his life.
Kepler and Tycho's relationship was short-lived. On October 13, 1601, Tycho went to a fancy dinner with the Baron Rosenberg and a number of other members of upper crust society. As Kepler recorded, Tycho was too polite to leave the table to use the bathroom, instead putting an unhealthy amount of pressure on his bladder. According to Kepler, this caused the infection that killed him less than two weeks later.
Tycho's last words seemed directed at Kepler: "Let me not seem to have lived in vain," he pleaded. But Tycho's pleas fell on deaf ears; Kepler would not raise the Tychonic planetary system to the glory that Tycho had hoped. Instead, Kepler finally got a hold of Tycho's observations and used them to create a new vision of the Copernican universe.
After Tycho's death, Kepler was appointed to his position as Rudolph II's Imperial Mathematicus. This title carried prestige and a salary, meaning that Kepler could finally afford to immerse himself in his studies. He worked on the orbit of Mars for five more years and then, when he was finally ready to publish, was almost prevented from doing so by a petty family feud.
Kepler had based all his research on Tycho's observations – the same observations that Tycho had so jealously guarded during his lifetime. After Tycho's death, Kepler took advantage of his access to the lab. Without asking anyone's permission, took the observations for himself, reasoning that he was the only one who could make good use of them. When Tycho's family realized this, they went on the offensive. Led by the Junker Tengnagel, Tycho's son-in-law and former assistant, the Brahe family tried every legal strategy they could think of to gain control of the observational data. As the Brahes had powerful connections at court, Kepler was left at their mercy. The feud took four years to resolve, until, in 1608, Tengnagel finally gave permission for the book to be published. The Astronomia Nova was finally published in 1609; it would be Kepler's most important work.

The New Astronomy

Today, Kepler is perhaps best known for his three laws of planetary motion. Two of those laws were first introduced in his seminal work of 1609, Astronomia Nova, or the New Astronomy. Kepler's first law states that the planets travel around the sun in elliptical orbits, with the sun positioned at one of the ellipse's foci.
This was an almost heretical idea, even more so that Copernicus's new system. For over two thousand years, astronomers, philosophers, and theologians had believed that the planets traveled with uniform motion around circular orbits. In fact, part of Copernicus's intention in the creation of his system was to preserve circular motion. Who was Kepler to go against the wisdom of millennia?
Kepler's new law finally made sense of the astronomical data. His second law, which he actually discovered first, contributed to the demolition of the ancient assumptions. It stated that the planets swept out equal areas of their orbits in equal times. He was forced to dispose of the idea of circular planetary orbits, and had to reject the ancient belief that the planets traveled their orbits with a consistent speed. Instead, he tweaked the notion of uniform motion. Kepler discovered that the planets' speeds varied as they circled the sun – they went faster when they were at a point on their orbit closer to the sun than they did when they were farther away from it. But the area of the elliptical orbit that was covered in a certain amount of time always remained the same.
Kepler's first two laws were important for a number of reasons. They made sense of the universe's structure – astronomers could finally throw out the epicycles and the equant, and construct a simplified version of the Copernican universe. The epicycles had never been intended to model the actual motion of the planets; they were only there to preserve the appearance of uniform circular motion. Now that there was no need for such preservation, astronomy could for the first time describe the physical reality of the universe. Kepler also reiterated his belief that a force emanating from the sun causes the motion of the six planets. He was the first astronomer to fully address the cause of celestial motion, rather than the mere mathematical description of it.
The book itself offers an interesting insight into Kepler's mind, as he records the path he took to get to the two laws – mistakes and all. And Kepler made quite a few mistakes.
Kepler often commented later that had he not been assigned to work on the shape of Mars's orbit, he would never have figured out the planetary orbits. Only Mars's orbit was irregular enough to offer the necessary data. Kepler called it an act of "Divine Providence" that the problem had fallen into his lap. The Mars orbit represented Kepler's greatest challenge yet. In the dedication of the Astronomia Nova, he refers to it as "the mighty victor over human inquisitiveness, who made a mockery of all the stratagems of astronomers."
Luck was finally on Kepler's side. While he made a number of mistakes in calculation and reasoning as he went along, they always seemed to cancel each other out. At one point, he seemed to have stumbled upon the right answer. His results almost matched his predictions. They differed by only a very small error, eight minutes of arc. No astronomer before Kepler would have paused at such a figure – they would have blithely gone on and declared their theory to be true. Kepler himself, at the time of his Mysterium Cosmographicum had clung to his theory in the face of conflicting data, deciding that the data must be wrong.
But Kepler had changed. Accuracy was now his watchword, and eight minutes of arc error was unacceptable. So he threw out his theory and went back to the drawing board.
In the end, it was the formulation of the first law that gave him the most difficulty. Once Kepler was finally convinced that the planetary orbits were oval-shaped, rather than circular, he strove to find a mathematical formula that would describe the shape of the ovals. But try as he might, he was unable to find one. He worked on this problem for over a year, at one point complaining to a friend that things would be so much easier if the ovals were just ellipses. In fact they were, but Kepler was unable to see it.
He worked and worked at the problem, finally coming up with an equation that seemed to exactly describe the orbit. In fact, it was the equation for an ellipse, but Kepler didn't recognize it as such. While testing out his theory, he made a minor mistake in the calculations and concluded that the equation must be incorrect. Throwing up his hands in disgust, Kepler threw out the formula and finally deciding to see what would happen if he treated the orbit as if it was an ellipse. It wasn't until these calculations finally led him to the same place he'd started that he realized he had had the answer all along.

Fame and Misfortune

In terms of the public reaction it received, the Astronomia Nova didn't fare much better than the Mysterium Cosmographicum. Once again, Kepler's peers didn't understand the profound importance of his work. The full significance of the two planetary laws did not become apparent until years later, when Newton used them to formulate his theory of universal gravitation. Until then, Kepler's system was little more than an aesthetic monstrosity. Even Kepler was dismayed by the loss of uniform circular motion – he disliked the idea of elliptical orbits as much as everyone else.
Although no one fully understood the ramifications of his work, it was accorded respect by the scientific community. Kepler was in a far different position than he'd been in ten years before. By the time the Astronomia Nova was published, Kepler was one of the most famous astronomers in Europe, primarily due to his title as the Imperial Mathematicus. He was also well respected for the other scientific research he'd done while working on the orbit of Mars, including the impressive work he'd done in the field of optics. In 1604, a new star had appeared in the sky and Kepler had proved that it was indeed a new star, not merely an atmospheric phenomena. As an indication of his newfound fame, the star became known as Kepler's Nova. While few recognized the Astronomia Nova for the landmark work that it was, the book only added to his prestige. Kepler's star was on the rise.
As one of Europe's top astronomical experts, Kepler was expected to have an opinion on any news in the field. The scientific community was eager to hear he had to say in 1610, when an Italian scientist named Galileo Galilei announced he had made a startling discovery. Galileo, who was a few years older than Kepler, was the first major astronomer to make use of a brand new tool for observing the stars: the telescope. In 1610, Galileo published his short book Sidereus Nuncius, or A Message From the Stars. He announced that he had discovered four new celestial bodies: the moons of Jupiter.
Kepler and Galileo had corresponded briefly in earlier years; in 1597, Galileo had complemented Kepler on his support of the Copernican system. In a later, Galileo admitted that he too supported it, but was hesitant to make that fact public. Kepler responded with a letter urging Galileo to get over his fears – a letter which Galileo may have taken as a personal affront, as he never responded.
Kepler and Galileo had not spoken for twelve years, but when the report of Galileo's observations came out, Kepler supported them. Kepler was the only one; the rest of the scientific community was quick to decry Galileo's discoveries. When Kepler requested that Galileo send him a telescope so that he could make an independent confirmation of Galileo's discoveries, Galileo ignored him. Frustrated and a bit embarrassed that he had staked his scientific reputation on a discovery of which he had no evidence, Kepler persevered. Finally, he was able to borrow the telescope of a nearby nobleman and publish Observation – Report on Jupiter's Four Wandering Satellites. It was the first independent confirmation of the existence of the moons of Jupiter.
But if Kepler's professional life was finally soaring, his personal life was falling apart. In 1611, Kepler's wife and favorite child died of the Hungarian Fever. Adding to this misery, the situation in Prague was becoming increasingly unstable. In 1611, Kepler's patron, Rudolph II, went insane and was forced to give up the throne; he died in January of 1612. While Kepler continued to serve as the Imperial Mathematicus, his new patron was not nearly as interested in astronomy as Rudolph II had been. The new emperor didn't care whether his imperial astronomer was by his side or across the country, so Kepler was free to leave Prague. The city was being torn apart by civil war, and Kepler decided to leave immediately.
He moved to Linz, a small town in Upper Austria, where he served as Provincial Mathematicus for fourteen years. The position was less glamorous than Kepler was used to, but it afforded him more freedom, as he was no longer at the beck and call of the emperor. The next year, Kepler married his second wife, the 24-year- old Susanna Pettinger. Kepler had had a difficult time convincing his first wife that he was worthy of marriage; this time, he had eleven different women to choose from, all eager to have his hand. Kepler and Susanna had eleven children and, since he rarely mentioned her or her shortcomings in later life, seem to have lived happily.
Kepler had only a short time to enjoy his marital bliss. It wasn't long before yet another crisis interceded in his life. In 1615, he was forced to rush to his mother's side in the town of Leonberg, to save her from being burned at the stake. The townspeople were convinced that Katherine Kepler was a witch.
Although the seventeenth century was a time of modernization and scientific progress for Europe, it was also the peak of the European witch-hunts. Weil-der- Stadt, Kepler's hometown, had burned thirty-eight supposed witches in the years between 1615 and 1629. Katherine's new home Leonberg was no more tolerant. It took Kepler five years of arguments and trials to save his mother's life. In 1620, it was decreed that Katherine be interrogated under threat of torture. When the old woman refused to confess anything, even in that precarious situation, the powers that be finally decided that she must be innocent. She was released, but was unable to go home, as the townspeople threatened to lynch her. She died six months later.
Incredible as it seems, Kepler had remained hard at work throughout this period of political crises and personal torment. In 1618, he published his newest discoveries in his last major work, Harmonice Mundi, or Harmony of the World. In a footnote to the Harmonice Mundi, Kepler implied that he could block out, but not ignore, the troubles around him: "The Earth sings Mi-Fa-Mi, so we can gather even from this that Misery and Famine reign on our habitat."

The Third Law

Like the Mysterium Cosmographicum, the Harmonice Mundi relied on a theory that was absolutely wrong. But hidden within Kepler's lyrical ravings about having finally deciphered God's plan is the final piece of his planetary puzzle: Kepler's third law.
Kepler had fixated on trying to find a pattern or structure for the spacing of the planets. By this point, he had realized that his perfect solids universe was mathematically unfeasible. But Kepler had a new vision, one that encompassed math, astronomy, music, and God. Kepler argued that the same harmonies we find in music were embedded in the geometrical proportions of the universe.
Kepler searched for any consistency that he might interpret as a harmonic pattern. He finally found a relationship that worked: the speed of the planets around their orbits versus their distance from the sun. Kepler's third law states that the distance a planet is from the sun, cubed, is directly proportional to the time it takes to complete the orbit, squared. More simply, Kepler found that the distance a planet was located from the sun directly determined the time it took that planet to revolve around the sun. This was the first time anyone had discovered the exact relationship between these two quantities – in fact, this was the first time anyone had even thought to wonder about the relationship.
Kepler was pleased to have discovered such a relationship – but he was ecstatic to have found the final piece in his harmonic puzzle. The harmonic universe, he believed, would truly be the greatest achievement of his life. In 1618, he published his vision in the Harmonice Mundi. Much like his earlier Mysterium Cosmographicum Kepler went on and on, joyfully extolling the divine basis of his theory. In the preface to his fifth book, he admitted this himself: "Yes, I give myself up to holy raving." To Kepler, the relationships he had discovered seemed so beautiful that they must have come directly from God. He congratulated himself for having the wisdom to finally understand God's plan: "I have robbed the golden vessels of the Egyptians to make out of them a tabernacle for my God, far from the frontiers of Egypt[my book] may wait a hundred years for a reader, since God has also waited six thousand years for a witness." This passage appears in the same book as one of the most important scientific discoveries of the seventeenth century.
Kepler still considered himself to be a modern scientist. Even with his mysticism and his religious devotion, Kepler was at the forefront of modern science. Yes, he was still rooted in the past. But his work in the Harmonice Mundi confirms that he was looking toward the future, asking the questions that none of his colleagues had thought to ask, and forging mathematical relationships where none had existed before.
Of course, Kepler realized none of this. He was proud of the achievement of his harmonic universe – but he spared no pride for his formation of the third law. Neither Kepler nor his peers understood the importance of the equation, which would prove integral to Newton's later discovery of universal gravitation. Until Newton's work made sense of it, the third law was nothing more than an interesting relationship between numbers, with no physical basis. Only from a distance is it easily recognizable as one of the most crucial pieces for solving the mysteries of universal motion.
Kepler was unable to make sense of the relationship between the planets' speeds and their distances from the sun because he did not know about gravity. But he did come painfully close to discovering it. In the preface Astronomia Nova, he had written of gravity as the tendency of two bodies to come together, with a force proportionate to their mass. Indeed, this is an accurate description of gravity. But later in the book, when Kepler was groping for a force to explain the motion of the planets around the sun, the attractive gravitational force had not occurred to him. Instead, he imagined that a force emanating from the sun pushed the planets around.
Kepler comes even closer to a full understanding of gravity in his last published work, Somnium, or Dream, published in 1634 after his death. Somnium, one of the first modern stories of science fiction, tells of a young boy's journey to the moon. Much of the story is a thinly veiled autobiographical tale: the young boy's mother is a sorceress with a hot temper, and the boy is forced to spend five years on an island studying under Tycho de Brahe. Even the description of life on the moon mirrors Kepler's impression of himself. The two moon races, the Prevolvans and the Subvolvans, lead miserable, nomadic lives and are constantly beset by skin ailments – much like Kepler himself.
Embedded in the fantastical and autobiographical fiction is a minutely detailed scientific vision of what a journey to the moon might be like. And it is here that Kepler finally seems to fully, if almost unconsciously, grasp the gravitational force. He describes the force of acceleration on take-off, and then hypothesizes a zone of apparent zero gravity at the point where the ship is equally attracted by the earth and the moon.

End of Days

The Harmonice Mundi was Kepler's last major original contribution, but he continued to publish important works for the rest of his life. In 1619, he published the Epitome Astronomiae Copernicae, a description of the universe. It was basically an updated view of the Copernican system, with all Kepler's planetary laws incorporated. This was the first astronomy textbook to use a heliocentric system, and it is the first complete appearance of the simplified system now associated with Copernicus – the Keplerian universe.
In 1627, Kepler published the Tabulae Rudolphinae, or the Rudolphine Tables. These tables were an extensive list of observations, predictions, and explanations that had been a tedious nightmare for Kepler to compile. For over one hundred years, scientists and navigators used them to calculate the positions of the stars and planets.
The publication of the Tabulae Rudolphinae marked the beginning of the end for Kepler. During the publication process, he left Linz forever. Thanks to increasing religious persecution and a series of peasant revolts, life there had become intolerable. Kepler, who all his life had considered himself a nomad in exile, now began his final wanderings. Left with no home to return to, he traveled aimlessly around the region, leaving a number of rejected job offers in his wake. After months of this wandering, he contracted a fever. He died two weeks later, on November 15, 1630.
Kepler is one of the more complicated figures in the history of science, and he is largely overlooked by historians. Books about the Scientific Revolution often devote only a few pages to Kepler's innovations, and the few biographies on his life hardly compare to the multitude of books about Copernicus, Galileo, and Newton.
Kepler is a mess of contradictions that mirror the confusion of his transitional era. His love of astronomy was combined with a hidden passion for astronomy; his best scientific work was sprinkled with wild ideas about magical solids and heavenly harmonies. Even his most fundamental scientific contributions – his planetary laws – were discovered only because he felt driven to confirm his spiritual inspirations about the structure of the universe. On the other hand, although Kepler believed firmly in a divinely constructed universe, he was one of the first to attempt a fully mechanized system that could operate without the Divine influence.
It is difficult to fully explain the effect he had on his field. Kepler's achievements were not obvious, and his mistakes were many. Even Kepler did not fully appreciate the value of his own work – he always valued his theories of the perfect solids and harmonic ratios far more than his three laws.
But more important than Kepler's many wrong answers is the fact that he asked so many right questions. This ranting mystic was also one of the most modern scientific thinkers of his time. He challenged the common wisdom of the preceding millennia that astronomy's goal was to create geometrical models of planetary motion. Instead, Kepler insisted that astronomy should be a physical science, concerned with the actual motion of planetary bodies. Thus he rejoined astronomy and physics, which had been separated for centuries.
Kepler lived and worked at a turning point in the age of astronomy. His love of philosophy, astrology, mysticism, and religion, and his passion for divine aesthetics of the universe made him one of the last great astronomers of the past. But his devotion to accuracy, his endless questioning, and his unification of astronomy and physics marked him as one of the first great astronomers of the modern era.

Study & Essay

Study Questions

What are Kepler's three laws? Why are they significant?
Answer for Study Question 1 >>
Kepler's first law states that the planets travel around the sun in elliptical orbits with the sun located at one focus. This was significant because, until Kepler, it had been firmly believed that the planets traveled in circular orbits. No one was pleased with the aesthetically distasteful idea of ellipses. The second law, which Kepler discovered first, states that as the planets travel around their orbits, they sweep out the same amount of area per unit of time, no matter where they are on the orbit. Like Kepler's first law, this second law destroyed a long-held belief. Astronomers had always assumed that the planets traveled with a uniform speed – Kepler proved that the speed varied as the planets traveled around the orbits. It was only the area covered that remained uniform. Finally, the third law states that the cube of the distance a planet's orbit is from the sun is directly proportional to the square of the period, or time it takes the planet to travel around the sun. This was the first time anyone had thought to question the relationship between a planet's distance from and speed around the sun. The equation was nothing more than an interesting mathematical relationship to Kepler; it wasn't until Newton created the theory of universal gravitation that the meaning of this relationship became clear.
Close

What was Kepler's theory of the perfect solids?
Answer for Study Question 2 >>
In 1595, Kepler had an epiphany. He was searching for a rationale for the number and spacing of the planets, and he believed he had found it in the perfect solids. A perfect solid is a three dimensional figure, such as a cube, whose sides are all identical. There are only five perfect solids, each of which can be inscribed in and circumscribed around a sphere. Kepler believed that the orbits of the six known planets could be fit around the five regular solids. He felt he had seen into the mind of God and finally understood the structure of the universe. He described this theory in his first book, the Mysterium Cosmographicum. Kepler's theory was incorrect, but developing this idea became his motivation for a lifetime of astronomical study.
Close

What role did Tycho de Brahe play in Kepler's life?
Answer for Study Question 3 >>
Had Kepler not crossed paths with the famous astronomer Tycho, he may never have formulated any of his three laws. Kepler needed Tycho's incredibly accurate and comprehensive astronomical observations in order to fully develop his own system. In 1600, Kepler traveled to Prague to work in Tycho's lab. Although he was there for only a year before Tycho died, that year marked a turning point in Kepler's life. Tycho was a tyrannical boss, but he provided Kepler with the two tools Kepler would need to revolutionize astronomy: detailed observations and the orbit of Mars. Tycho assigned Kepler to figure out the shape of the orbit of Mars. The thorny problem would take him over half a decade to solve, but the struggle was worth it. Only in the irregular orbit of Mars could Kepler have discovered the fundamental properties of the planetary orbits. Once Tycho died, Kepler took his astronomical observations from the laboratory and went to work on the Mars problem. Eight years later, he published his results in the Astronomia Nova. Tycho had hoped that Kepler would apply his theories to the Tychonic system of the universe, but Kepler stayed true to the Copernican system. Kepler used the Copernican system to develop the Astronomia Nova.
Close

Essay Topics

What was the difference between the original Copernican system and Kepler's interpretation of it?
What were some of the events that caused Kepler to feel he'd had a miserable life?
Discuss the contents and importance of Kepler's three major works, the Mysterium Cosmographicum, the Astronomia Nova, and the Harmonice Mundi.
What was Kepler's impression of his own work? Which of his achievements did he most value and which did he overlook?
Kepler is one of the founding fathers of the Scientific Revolution, along with Copernicus, Galileo, and Newton. What is the importance of each of them in Kepler's life and work?
Why can it be said that Kepler rejoined astronomy and physics? Why is this significant?

Johannes Kepler
1571-1630
German Astronomer and Mathematician
Johannes Kepler was a mathematician and astronomer. He used observations of heavenly bodies to destroy the ancient idea that planets move in perfect circles. He also mathematically described the relationship of Sun and planets in our solar system. His three laws of planetary motion, along with the work of Nicolaus Copernicus (1473-1543) and Galileo (1564-1642), helped Isaac Newton (1642-1727) devise his law of universal gravitation.
Kepler was born in 1571 in Weil, Germany, a sickly, myopic child with a brilliant mind and intermittent double vision. He became interested in astronomy after seeing the 1577 comet when he was six years old and an eclipse of theMoon when he was nine. He attended a seminary and the University of Tubingen intending to enter the church. His abilities as a mathematician led him instead to teach math in Graz, Austria, where he was also district mathematician. He cast official horoscopes and was court astrologer. While in Graz he cast many horoscopes for local citizens and published a calendar of astrological forecasts to augment his income. At this time he already believed that Earth moves around the Sun, not vice versa. Kepler was an original thinker and could grasp and manipulate new ideas. He was exceedingly patient and made calculations with scrupulous care.
In 1596 he published his first book corroborating Copernicus and looking for a relation between planetary bodies. In 1600 he moved to Prague, where he became an assistant to Tycho Brahe (1546-1601), Imperial Mathematician. This was a fateful association because Brahe, a Dane, was a tireless recorder of movements of heavenly bodies. When Brahe died, Kepler became Imperial Mathematician and possessor of Brahe's observations. Brahe's family insisted that he had usurped the data, but Kepler was able to keep and use the material.
[pic]

Johannes Kepler. (Library of Congress. Reproduced with permission.)
It is said that Kepler "discovered" his three laws, but it is more accurate to say he constructed them to fit the observations. Kepler explained celestial phenomena to fit these observations and believed that a mathematical relationship existed between celestial bodies. In 1602 he discarded perfect circles, which had been the model of the heavens since the Greeks. Using Brahe's data, he postulated that a planet's distance from the Sun determined its speed and calculated the exact relationship with precise accuracy. This became his second law. In 1605 he came to the conclusion that planets move in elliptical orbits, his first law. These were the first instances of discoveries made to fit observed data. In 1618 he formulated the third of his three laws, which states that the square of the time a planet takes to revolve around the Sun is proportional to the cube of its distance from the Sun.
He occasionally corresponded with Galileo, but they worked on different aspects of astronomy. After he and his family moved to Linz, Austria, Kepler published several books on astronomy and the harmony of the spheres. They were unique but read by few because they were complex and hard to understand. He continued to look for relations between planets and the Sun.Some of his published ideas failed or were deemed absurd. His reputation was not helped by the fact that his mother was put on trial for witchcraft in 1615 and imprisoned for a time.
When he died in November 1630 in Regensburg, Germany, he was famous for his writings and revered as a careful mathematician whose work had aided the advancement of of astronomy. Kepler's work assisted Newton in formulating his 1687 theory of universal gravitation that led to modern ideas about physics and astronomy.
Kepler's Mother's Witch Trial
Johannes Kepler's mother, Katharina, was known in her hometown as a cantankerous old woman. During the upheavals of the Thirty Years' War she became a victim of witch-hunting. A dutiful son, Kepler helped in her defense, which was both long and costly. Katharina's accusers pointed to dozens of occasions where various aliments or actions had occurred due to her magical potions or spells. Kepler's successful defense strategy was to show how all these occurrences could be explained by natural causes. For instance, a young girl claimed Katharina had made her arm temporarily paralyzed. Kepler pointed out that she had been carrying many bricks, and the heavy load had caused her problem. A woman's sickness was revealed to be from an abortion. The schoolmaster had been injured while jumping a ditch. The butcher had lumbago. And so on. Kepler was careful never to dismiss witchcraft out of hand, as many officials believed deeply in such magic. However, he showed that for each specific event attributed to witchcraft there was a more likely natural cause that explained the result at least as well. Yet, while Katharina was acquitted, she died shortly after, a broken woman.

Similar Documents

Free Essay

Lit1

...Task 1 In ancient civilizations it was believed that the Earth was the center of the Universe (Geocentric model). This was the accepted belief at the time. Many philosophers and scientists wrote works based on the Geocentric model. The understanding that the Earth being the center of the universe began to change as scientists (Copernicus, Galileo and Kepler) researched, used mathematics and physics. The findings of there work led to the belief that the Sun was the center of the Universe (Heliocentric model). Copernicus used mathematics (On the Revolutions of the Celestial Spheres) to form the Heliocentric model of the universe. Galileo used physics (Dialogue Concerning the Two Chief World Systems) to support Copernicus’ Heliocentric theory. Kepler mathematics (laws of planetary motion) and his expertise in optics (inventing an improved version of the refracting telescope (Keplerian Telescope) and gave credit to Galileo for his telescopic discoveries) to support the Heliocentric model. The Heliocentric model was accepted as the structure of the Solar System because of the work of these ancient scientists and the work of those that came after them. In the mid-to-late 20th century supremacy in space exploration between the Soviet Union and United States began. This is now known as the “Space Race”. During this tense time known as the “Cold War” both the Soviet Union and the United States felt that being first in space exploration was necessary for national security......

Words: 439 - Pages: 2

Free Essay

Astronomy Then and Now

...Astronomy: Then and Now Have you ever heard the saying you can’t teach an ole dog new tricks? What about the one where three old dogs teach new tricks? I’m sure you have heard that one, anyone who knows about our solar system can thank the three old dogs. Well, they’re not dogs at all, and at their time they weren’t old but in our time their long gone. Of course, I am speaking about Ptolemy, Copernicus, and Kepler. Funny thing is each one of them challenged and changed their predecessor's work, for the better of course, but we will get to that later. We have these three men to thank for a whole lot of new tricks. To name a few would be, our solar system, the way we form our maps, and we can’t forget the numerous mathematical formulas used to make ideas come to life. In this research paper, we will touch base on the lives of three great astronomers and the tricks they have taught us. We will also see how astronomers of today contribute to our everyday lives. Some say that our first astronomer was a great astronomer. Other say, “Ptolemy was the only great astronomer of Roman Alexandria.” (Brown, 2016) It’s all a matter of opinion, but what we cannot deny was Ptolemy was a great astronomer of his time and today. We do not know much about Ptolemy’s personal life. What we do know about him came from his work. He was born around 85ce in Egypt to a Greek family even though he bore a roman name. To say Ptolemy was diverse is an understatement. He was also diverse in his......

Words: 3691 - Pages: 15

Free Essay

Scientific Revolution and Women

...Observation, experiment and invention existed as early as middle ages but in the mid-15th century the belief about the physical universe was questioned. Curiosity among talented people around the world intensified. This ultimately led to development of science. In 1543, Nicolaus Copernicus published the Revolution of the Heavenly Spheres. His model of the Universe was alternative to Claudius Ptolemy’s geocentric system which was widely accepted since ancient times. It is believed that Copernicus’s theory of Revolution of the Heavenly Spheres lit the torch in scientific revolution. In 1576, Tycho Brahe set up Uranilborgh observatory. It was a huge step in astronomy. The mystery of the physical universe had begun to reveal. Soon after, Johannes Kepler in 1609 followed up with the Astronomia Nova which included his decade long research of the motion of mars. Galileo Galilei published Starry Messenger in 1610 which was a method of observing our galaxy with a telescope. In 1610, Francis Bacon published introduced the new instruments of science. Finally, Sir Isaac Newton, a...

Words: 896 - Pages: 4

Free Essay

Miss

...Reflection by Thitichaya Rattanasrithong ID: 1356704 Studying abroad must be difficult, but at the same time, it is a great opportunity for a girl like me who has never experienced any sorts of this challenging journey at home before. An opportunity to get to know more about people, an opportunity to speak out loud in other languages, an opportunity to learn and understand how people from other countries think of and lastly, a gigantic opportunity to be adaptable in a whole new world. I was personally born in Thailand and had never ever left my country this far away. Literally, I was asked many times why I decided to come to Austria and study at Johannes Kepler University Linz(JKU). At that time, I honestly didnʼt know WHY. It was 50:50 percent chances mixed of coincident and intention. But now, it has been 1 month passed by, I have got an answer for them. Coming this far away is one of the best thing in my life. My heart was beating fast and my hand was shaking. That was the first feeling I could remember after entering the room full of crowd. That was the first day of the training session, I remembered that I was so nervous, because I was all by myself. The other 2 Thai friends of mine decided not to participate, that was one of the reasons why I was more frustrated. But, that was going to be fine, I was thinking inside my head. I could not believe that there were so many people coming from around 30-40 different countries, which was incredible. Maybe, it was even more than......

Words: 907 - Pages: 4

Free Essay

Scientific Revolution and Discoveries

...Society. Galileo supported Copernicus and developed the science of motion. In the twentieth century, Alexandre Koyré introduced the term scientific revolution, centering his study on Galileo, and the term became widely popular in his Origins of Modern Science by Butterfield. The Scientific Revolution was known all over Europe as an international phenomenon; scholars from all over took part in it. The most-important leading figures were Nicolaus Copernicus (Father of Modern Astronomy), Tycho Braye, Johannes Kepler, Galileo Galilei, and Isaac Newton. Some of the important discoveries of this time period and their effects were; Copernicus discovered that earth and all the planets revolve around the sun. Before Copernicus discovery astronomers believed, the earth was the center of the universe, and the sun and planets revolved around it. Tycho Braye discovered new stars that are known as supernovae in 1573. He was well-known throughout his life as an alchemist and astronomer. Kepler contributed the three laws of planetary motion, which helped Isaac Newton later on. These...

Words: 967 - Pages: 4

Premium Essay

Who Are the Scientists

...Who are those scientists? Write briefly on their achievements in sciences. * Aristotle (384-322 BC) Aristotle was born in North Greece to a physician of Royal family of Macedonia; He studied philosophy in in Plato’s Academy in Athens. After leaving Athens, Aristotle travelled and had some study on biology. As he returned to his home town he opened a school there name Lyceum. During the Athens dominance on Macedonia, he left his land to save his life and soon after his departure from Macedonia he died. There are 150 philosophical materials written by Aristotle. His writings includes lectures also on philosophy, biology, physics and politics. He had contribution in Zoology as well, his observations about sea organisms like Octopus, cuttlefish were accurate and fact on those early times. Arsitotle first segregated the genera of living organisms, categorized the animals into two categories. He also had contribution in Metrology. * Aristarchus (310-230 BC) He was one of the great astronomer and mathematician of the Greece history. He was the first one to give the concept of sun as center of the universe. He claimed that sun is the main source of flame. He contributed towards calculating the distance between sun and moon. He was strong in geometry in give resources and knowledge of that time, but his research and work on astronomy made the base for today’s advancements in this field. * Nicolas Copernicus (1473 – 1543) Nicola Copernicus was also one of the......

Words: 645 - Pages: 3

Free Essay

Masa de Los Planetas Y Las Leyes de Kepler

...Santa María de Montesclaros Adriana Marisol Ligorría Duque Física Fundamental Mariela Juárez Los planetas y las leyes de Kepler LOS PLANETAS DEL SISTEMA SOLAR Planeta | Masa (kg) | Diámetro (km) | Gravedad (m/s) | Mercurio | 3.3x10 23| 4870| 3.72 | Venus | 4.87x1024 | 12100 | 8.82 | Tierra | 5.98x1024 | 12756 | 9.8 | Marte | 6.4x1023 | 6670 | 3.72 | Júpiter | 1.9x1027 | 143760| 23.13 | Saturno | 5.68x1026 | 120420| 9.01 | Urano | 8.7x1025 | 51300 | 8.72 | Neptuno| 1x1022 | 40500 | 10.97 | LAS LEYES DE KEPLER Las leyes de Kepler fueron enunciadas por Johannes Kepler para describir matemáticamente el movimiento de los planetas en sus órbitas alrededor del Sol. Aunque él no las describió así, en la actualidad se enuncian como sigue: Primera ley (1609): Todos los planetas se desplazan alrededor del Sol describiendo órbitas elípticas. El Sol se encuentra en uno de los focos de la elipse. Segunda ley (1609): el radio vector que une un planeta y el Sol barre áreas iguales en tiempos iguales. La ley de las áreas es equivalente a la constancia del momento angular, es decir, cuando el planeta está más alejado del Sol (afelio) su velocidad es menor que cuando está más cercano al Sol (perihelio). En el afelio y en el perihelio, el momento angular  es el producto de la masa del planeta, su velocidad y su distancia al centro del Sol. Tercera ley (1618): para cualquier planeta, el cuadrado de su período orbital es directamente proporcional al cubo de...

Words: 311 - Pages: 2

Free Essay

History

...13.5. The Scientific Revolution   Until the mid-1500s,Europeans' view of the universe was shaped by the theories of the ancient writers Ptolemy and Aristotle. In1543, Polish scholar Nicolaus Copernics published the Revolutions of the Heavenly Spheres. In it, he proposed a heliocentric, or sun-centered, model of the universe. In the late 1500s, the Danish astronomer Tycho Brahe provided evidence that supported Copernicus's theory. After Brahe's death, his assistant, the brilliant German astronmer and mathematician Johannes Kepler, used Brahe's data to calculate the orbits of the planets revolving around the Sun.   Scientests from many different lands built on the foudations laid by Copernicus and Kepler. In Italy, Galileo Galilei assembled an astronomical telescope. Galileo's discoveries caused an uproar. Despite the opposition of the Church, by the early 1600s a new approach to science had emerged, based upon observation and experimentation. Two gaints of this revolution were the Englishman Francis Bacon and the Frenchman Rene Descartes   Bacon and Descartes differed in their methods, however. Over time, a step-by-step process of discovery evolved that became known as the scientific method.to explain the data, scientists used reasoning to propose a logical hypothesis,  or possible explanation.  The 1500s and 1600s saw drmatic changes in many branches of science, especially medicine and chemistry. Medieval physicians relied on the works of the ancient......

Words: 337 - Pages: 2

Premium Essay

Dooda

...The Age of Enlightenment Directions Please save this document before you begin working on the assignment. Type your answers directly in the document. _________________________________________________________________________ Part 1 Write your answers to the following questions in two or three sentences. (Each question is worth three points) 1. Why did religious and political authorities find the idea of a heliocentric model of the universe to be so objectionable? Type your response here: 2. Which thinker does not belong in the following list, and why not? Galileo, Aristotle, Kepler, Copernicus Type your response here: 3. What are the five steps in the scientific method? Type your response here: 4. Why did most Medieval philosophers and scientists feel that experimentation was unnecessary? Type your response here: 5. Why did the Enlightenment writer Voltaire get into so much trouble in France and elsewhere? Type your response here: Part 2 Write a well-developed essay of two to three paragraphs on one of the topics below. Make sure you use specific information from this lesson and, if need be, from previous lessons. Proofread your essay to eliminate errors in grammar and spelling. (Each question is worth 15 points) 1. Choice #1: Compare and contrast the careers of Galileo Galilei and Isaac Newton. What discoveries did each make? How were their methods similar or different?......

Words: 295 - Pages: 2

Premium Essay

Essay

...The Age of Enlightenment Directions Please save this document before you begin working on the assignment. Type your answers directly in the document. _________________________________________________________________________ Part 1 Write your answers to the following questions in two or three sentences. (Each question is worth three points) 1. Why did religious and political authorities find the idea of a heliocentric model of the universe to be so objectionable? Type your response here: 2. Which thinker does not belong in the following list, and why not? Galileo, Aristotle, Kepler, Copernicus Type your response here: 3. What are the five steps in the scientific method? Type your response here: 4. Why did most Medieval philosophers and scientists feel that experimentation was unnecessary? Type your response here: 5. Why did the Enlightenment writer Voltaire get into so much trouble in France and elsewhere? Type your response here: Part 2 Write a well-developed essay of two to three paragraphs on one of the topics below. Make sure you use specific information from this lesson and, if need be, from previous lessons. Proofread your essay to eliminate errors in grammar and spelling. (Each question is worth 15 points) 1. Choice #1: Compare and contrast the careers of Galileo Galilei and Isaac Newton. What discoveries did each make? How were their methods similar or different?......

Words: 295 - Pages: 2

Free Essay

Ethics

...Business Ethics and Crisis Management: Circumstances for a Second Chance Dr. Stefan MAYR Researcher at the Institut für Controlling und Consulting, Johannes Kepler Universität Linz, Austria Johannes Kepler Universität Linz Institut für Controlling und Consulting Altenberger Straße 69 4040 Linz Austria Stefan.mayr@jku.at Keywords: Corporate responsibility, corporate restructuring, enterprise crisis, bankruptcy 1238 Abstract Discourse regarding ethics and corporate responsibility arose in the last years linked with an increasing number of accounting fraud scandals. The recent financial crisis has had a lasting negative influence on corporate profits. Companies have had to satisfy the interests of several stakeholders, such as its employees, banks, customers and the community, and at the same time successfully manage the consequences of the crisis. An empirical qualitative study which was conducted in Austria in 2008 is presented in this paper aimed at investigating business ethics and crisis management. The stakeholder theory will be used as a reference framework. This paper concludes with lessons that can be learned and political recommendations and policies put forth to grant failed businesses a second chance. 1. Introduction In the past few years, an increasing number of fraud cases and accounting scandals is linked to fierce discourse with respect to ethics and corporate accountability. Business ethics has likewise become a current research subject in...

Words: 5533 - Pages: 23

Free Essay

World History

...|Objectives | | |By the end of this lesson, students will be able to: | | |describe the scientific method and its effect on Western Europe | | |distinguish between the scientists Copernicus, Kepler, Galileo, Newton, and Harvey and their works | | |compare the political theories of Hobbes and Locke | | |explain how science and philosophy influenced one another during the Enlightenment | | |explain the term enlightened despot, using the model of Frederick II of Prussia | | |Click here for the course glossary | | |Click here for a Timeline of The Enlightenment and Scientific Revolution | | |This lesson discusses European society between 1600 and 1800--an era marked by the power of ideas and rational | | |thinking. The term Scientific Revolution is used to describe the growing acceptance and influence of the scientific| | |method and the belief......

Words: 7624 - Pages: 31

Free Essay

Hellenistic Medicine

...Alexander the Great, king of Macedonia, ruled an empire that stretched from the Balkans to the Himalayas and from Egypt to the Caspian Sea during the mid-4th century BC. But his empire soon fell apart after his sudden and unexpected death in Babylon. His goal of further conquest was thus cut short, and his empire was left without a successor. What Alexander left behind was not a huge empire, but the spread and intermingling of ideas among the areas he conquered. Some important advancement in medicine and science were thus made, owing to the collaborative work of many Hellenistic intellectuals from Alexander’s former empire. The source of Greek knowledge about medicine came from Egypt, which was fairly well-developed by the Greece was entering its Golden Age. Greek figures such as Pythagoras traveled widely, and picked up discoveries from places and brought them back to Greece. Thales gained first-hand experience of medicine when he was training in Egypt. Similar to Greek medicine, Egyptian medicine also lied in religion and spirituality. The Egyptian god of medicine was Imhotep, whose role was analogous to that of Asclepius. People would pray to him and other gods for healing, and it was believed that gods played a role in matters of health and disease. Despite these religious origins and beginnings, Egyptian medicine was rather rational and scientific. Blood was thought to be an important nutritive and regulatory substance, and the heart was considered to be the center of......

Words: 2680 - Pages: 11

Free Essay

Student

...topicmodels: An R Package for Fitting Topic Models Bettina Grun ¨ Johannes Kepler Universit¨t Linz a Kurt Hornik WU Wirtschaftsuniversit¨t Wien a Abstract This article is a (slightly) modified and shortened version of Gr¨n and Hornik (2011), u published in the Journal of Statistical Software. Topic models allow the probabilistic modeling of term frequency occurrences in documents. The fitted model can be used to estimate the similarity between documents as well as between a set of specified keywords using an additional layer of latent variables which are referred to as topics. The R package topicmodels provides basic infrastructure for fitting topic models based on data structures from the text mining package tm. The package includes interfaces to two algorithms for fitting topic models: the variational expectation-maximization algorithm provided by David M. Blei and co-authors and an algorithm using Gibbs sampling by Xuan-Hieu Phan and co-authors. Keywords: Gibbs sampling, R, text analysis, topic model, variational EM. 1. Introduction In machine learning and natural language processing topic models are generative models which provide a probabilistic framework for the term frequency occurrences in documents in a given corpus. Using only the term frequencies assumes that the information in which order the words occur in a document is negligible. This assumption is also referred to as the exchangeability assumption for the words in a document and this assumption......

Words: 6498 - Pages: 26

Premium Essay

Reearch

...HIST Y AN PHILO PHY TORY ND P OSOP Y OF S ENCE SCIE E COMM MON CO OURSE IN ENG E GLISH BBA (I Seme A ester) BA/BS (IV Se Sc emester)     2011 A dmission onwards o UNIV VERSI ITY OF CAL F LICUT SC CHOOL OF DI L ISTANC EDU CE UCATIO ON Calicut Universi P.O. M ity Malappur ram, Kera India 673 635 ala, a 106 School of Distance Education   UNIVERSITY OF CALICUT  SCHOOL OF DISTANCE EDUCATION  BBA (I Semester)  BA/BSc (IV Semester) Common Course in English 2011 Admission onwards HISTORY AND PHILOSOPHY OF SCIENCE MODULE  I & II    Prepared by :  House No. 21   “Pranaam”  Keltron Nagar, Kolazhi,  Thrissur  Ms. GAYATHRI MENON .K  MODULE III  & IV Prepared  by: Ms. SWAPNA M.S.  Department of English  K. K. T. M. Govt. College  Pullut, Thrissur  Dr. Anitha Ramesh K  Associate Professor  Department of English  ZG College, Calicut  © Reserved  2  Scrutinised by :     Layout:   Computer Section, SDE  History and Philosophy of Science  School of Distance Education   Contents MODULE I ANCIENT HISTORY OF SCIENCE 1. Introduction 2. Origins of Scientific Enquiry 3. European Origins of Science 4. Contributions of Early India 5. Science in China 6. The role of Arabs in the History of Science MODULE 2 7. Science in the Middle Ages MODULE 3 MODERN SCIENCE 8. Newton and After 9. The Advancing Frontiers: Modern Medicine to Nanotechnology MODULE 4 PHILOSOPHY OF SCIENCE 10. Basic concepts in the Philosophy of Science 11. Some Issues in the......

Words: 34637 - Pages: 139