by Carl Sagan
[Part of the "Cosmos" series, transcribed by Tara Carreon]
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JOHANNES KEPLER, 1571-1630Ma Kepler [Katherine] was released, after fourteen months of imprisonment. She could not return to Leonberg, though, because the populace threatened to lynch her. Six months later she died.
It was against this background that Kepler wrote the Harmony of the World.
-- ARTHUR KOESTLER, The Watershed
She was carried out of her house in an oak linen chest, and taken to the prison in Leonberg. She was then seventy-three years of age. (He writes that God himself "was too kind to remain idle and began to play the game of signatures, signing his likeness into the world.") There were forty-nine accusations against her, and numerous supplementary charges. She was said to have failed to weep when the Holy Scriptures were read to her. (He resolves the harmonies into regular polygons.) Katherine Kepler replied that she had shed so many tears in her life, she had none left. (The irregular polygons, and all figures that cannot be constructed by compass and ruler, he says, are unclean because they defy the intellect. Inscibilis. Ineffabilis. Non-entia. Unspeakable. Nonexistences. And this is the reason, he writes, "why God did not employ the septagon and the other figures of this species to embellish the world.") Her son Johannes Kepler answered the Act of Accusation by an Act of Contestation, which was refuted by an Act of Acceptation to which was submitted an Act of Exception and Defense which was answered by an Act of Deduction and Confutation. Finally, in her defense her son submitted an Act of Conclusion, one hundred and twenty-eight pages long. (He then discovers regular polygons inscribed in the movements of heavenly bodies. And of these he writes: ''The heavenly motions are nothing but a continuous song for several voices ... a music which ... sets landmarks in the immeasurable flow of time.")
After that, her case, by order of the duke, was sent to her son's university, where the faculty found that Katherine should be questioned under torture, but suggested that proceedings stop at the territio -- questioning under threat of torture. (As part of the harmony of the world, Kepler reveals that the ratio which exists between the periodic times of any two planets is precisely one and one half of the power of their mean distances.) She was led to the place of torture; the executioner was presented to her; all his instruments shown her and their effect on the body described. Great pain and dolor awaited her if she did not confess, she was told. The terror of the place had wrought confessions from many before her, but she said that even if they tore her veins from her body one by one, she had nothing to confess. (On discovering that the heavenly bodies move in ellipses rather than perfect circles, Kepler apologizes for having to bring a small cartload of dung into the universe in order to rid it of a far vaster quantity of dung.) She fell on her knees then and asked God to give a sign if she was a witch or a monster, and then said she was willing to die, that God would reveal the truth after her death. (He writes: "Yes, I give myself up to holy ravings. I mockingly defy all mortals with this open confession; I have robbed the golden vessel of the Egyptians to make out of them a tabernacle for my God....") In this way, and due to the efforts of her son, and the respect he commanded in the world, Katherine Kepler was released.
-- Woman and Nature: The Roaring Inside Her, by Susan Griffin
There are two ways to view the stars: as they really are and as we might wish them to be. These are the Pleides, a group of young stars astronomers recognize as leaving their stellar nurseries of gas and dust, and this is the Crab Nebula, a stellar graveyard where gas and dust are being dispersed back into the interstellar medium. Inside it is a dying pulsar. Both the Pleides and the Crab Nebula are in a constellation that astrologers long ago named Taurus the Bull. They imagined it to influence our daily lives.
Astronomers say that the planet Saturn is an immense globe of hydrogen and helium encircled by a ring of snowballs 50,000 km. wide, and that Jupiter's great red spot is a giant storm raging for perhaps a million years. But the astrologers see the planets as affecting human character and fate. Jupiter represents a regal bearing and a gentle disposition, and Saturn, the gravedigger, fosters, they say, mistrust, suspicion and evil. To astronomers Mars is a place as real as the Earth, a world awaiting exploration. But the astrologers see Mars as a warrior, the instigator of quarrels, violence and destruction. Astronomers and astrologers were not always so distinct. For most of human history the one encompassed the other. But there came a time when astronomy escaped from the confines of astrology. The two traditions began to diverge in the life and mind of Johannes Kepler. It was he who demystified the heavens by discovering that a physical force lay behind the motions of the planets. He was the first astrophysicist and the last scientific astrologer.
The intellectual foundations of astrology were swept away 300 years ago, and yet astrology is still taken seriously by a great many people. Have you ever noticed how easy it is to find a magazine on astrology? Virtually every newspaper in America has a daily column on astrology. Almost none of them have even a weekly column on astronomy. People wear astrological pendants, check their horoscopes before leaving the house, even our language preserves an astrological consciousness. For example, take the word "disaster." It comes from the Greek for "bad star." The Italians once believed that disease was caused by the influence of the stars. It's the origin of our word "influenza." The zodiacal signs used by the astrologers even ornament this statue of Prometheus in New York City. Prometheus who stole fire from the gods.
What is all this astrology business? Fundamentally, it's the contention that which constellations the planets are in at the moment of your birth profoundly influence your future. A few thousand years ago the idea developed that the motions of the planets determine the fates of kings, dynasties, empires. Astrologers studied the motion of the planets and asked themselves what had happened last time, let's say, that Venus was rising in the constellation of the goat? Maybe something similar would happen this time as well. It was a subtle and risky business. Astrologers became employed only by the state. In many countries, it became a capital offense for anyone but the official astrologer to read the portents in the skies. Why? Because a good way to overthrow a regime was to predict its downfall. Chinese court astrologers who made inaccurate predictions were executed. Others simply doctored the record so that afterwards they were in perfect conformity with events. Astrology developed into a strange discipline, a mixture of careful observations, mathematics and record keeping with fuzzy thinking and pious fraud.
Nevertheless, astrology survived and flourished. Why? Because it seems to lend a cosmic significance to the routine of our daily lives. It pretends to satisfy our longing to feel personally connected to the universe. Astrology suggests a dangerous fatalism. If our lives are controlled by a set of traffic signals in the sky, why try to change anything?
Look at this. Here's two different newspapers published in the same city on the same day. Let's see what they do about astrology. Suppose you were a Libra, that is born between September 23 and October 22. According to the astrologer for the New York Post, compromise will help ease tension. Well, maybe, it's sort of vague. According to the New York Daily News' astrologer, demand more of yourself. Well, also vague, but also pretty different. It's interesting that these predictions are not predictions. They tell you what to do, they don't say what's going to happen. They are consciously designed to be so vague that they could apply to anybody, and they disagree with each other.
Astrology can be tested by the lives of twins. There are many real cases like this. One twin is killed in childhood, in say a riding accident, or is struck by lightning, but the other lives to a prosperous old age. Suppose that happened to me. My twin and I would be born precisely in the same place and within minutes of each other. Exactly the same planets would be rising at our births. If astrology were valid, how could we have such profoundly different fates? It turns out that astrologers can't even agree among themselves what a given horoscope means. In careful tests, they are unable to predict the character and future of people they know nothing else about except the time and place of birth. Also, how could it possibly work? How could the rising of Mars at the moment of my birth affect me, then or now? I was born in a closed room. Light from Mars couldn't get in. The only influence of Mars which could affect me is its gravity, but the gravitational influence of the obstetrician was much larger than the gravitational influence of Mars. Mars is a lot more massive but the obstetrician was a lot closer.
The desire to be connected with the cosmos reflects a profound reality. We are connected. Not in the trivial ways that pseudo-science of astrology promises, but in the deepest ways. Our little planet is under the influence of a star. The sun warms us, it drives the weather, it sustains all living things. Four billion years ago it brought forth life on Earth. But our sun is only one of a billion trillion stars within the observable universe. And those countless suns all obey natural laws, some of which are already known to us.
How did we discover that there are such laws? If we lived on a planet where nothing ever changed, there wouldn't be much to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world where things changed in random or very complex ways, we wouldn't be able to figure things out, and again there would be no such thing as science. But we live in an inbetween universe where things change alright, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it's possible to figure things out. We can do science and with it we can improve our lives.
Human beings are good at understanding the world. We always have been. We were able to hunt game or build fires only because we had figured something out. There once was a time before television, before motion pictures, before radio, before books. The greatest part of human existence was spent in such a time. And then, over the dying embers of the campfire, on a moonless night, we watched the stars.
The night sky is interesting. There are patterns there. If you look closely, you can see pictures. One of the easiest constellations to recognize lies in the northern skies. In North America it's called "The Big Dipper." The French have a similar idea. They call it "La Casserole." The Casserole. In Medieval England, this same pattern of stars reminded people of a simple wooden plow. The ancient Chinese had a more sophisticated notion. To them, these stars carried the celestial bureaucrat on his rounds about the pole of the sky, seated on the clouds and accompanied by his eternally hopeful petitioners. The people of northern Europe imagined yet another pattern. To them it was Charles' wane, or wagon, a medieval cart. But other cultures saw these seven stars as part of a larger picture. It was the tail of a great bear which the ancient Greeks and Native Americans saw instead of the handle of a dipper. But surely the most imaginative interpretation of this larger group of stars was that of the ancient Egyptians. They made out a curious procession of a bull and a reclining man followed by a strolling hippopotamus with a crocodile on its back. What a marvelous diversity in the images various cultures saw in this particular constellation. But the same is true for all the other constellations.
Some people think these things are really in the night sky. But we put these pictures there ourselves. We were hunter folk so we put hunters and dogs, lions and young women up in the skies, all manner of things of interest to us. When 17th Century European sailors first saw the southern skies they put all sorts of things of 17th Century interest up there: microscopes and telescopes, compasses, and the sterns of ships. If the constellations had been named in the 20th Century, I suppose we'd put there refrigerators and bicycles, rock stars, maybe even mushroom clouds. A new set of human hopes and fears placed among the stars.
But there is more to the stars than just pictures. For example, stars always rise in the east and always set in the west, taking the whole night to cross the sky if they pass overhead. There are different constellations in different seasons. The same constellations always rise at say at the beginning of autumn. It never happens that a new constellation suddenly appears out of the east, one that you never saw before. There's a regularity, a permanence, a predictability about the stars. In a way, they are almost comforting.
The return of the sun after a total eclipse. Its rising in the morning after its troublesome absence at night and the reappearance of the crescent moon after the new moon, all spoke to our ancestors of the possibility of surviving death. Up there in the skies was a metaphor of immortality.
Almost a thousand years ago in the American southwest, the Anasazi people built a stone temple, an astronomical observatory to mark the longest day of the year. Dawn on that day must have been a joyous occasion, a celebration of the generosity of the sun. They built this ceremonial calendar so that the sun's rays would penetrate a window and enter a particular niche on this day alone. That kind of precision is a triumph of human intelligence. It outlives its creators. Today, this is a lonely place. The Anasazi people are no more. They had learned to predict the changing of the seasons; they could not predict the changing of the climate and the failure of the rains. But their temple continues to catch the sun's first rays on the Summer Solstice.
I imagine the Anasazi people gathered in these pews every June 21st, dressed with feathers and turquoise to celebrate the power of the sun. These upper niches -- there are 28 of them -- may represent the number of days for the moon to reappear in the same constellation. These people paid a lot of attention to the sun and the moon and the stars. And other devices based on somewhat similar designs can be found in Angkor Wat in Cambodia, Stonehenge in England, Abu Simbel in Egypt, Chichenetza in Mexico, and in the great plains of North America.
Now why did people all over the world go to such great trouble to teach themselves astronomy? It was literally a matter of life and death to be able to predict the seasons. We hunted antelope or buffalo whose migrations ebbed and flowed with the seasons. Fruits and nuts were ready to be picked at some times and not at others. When we invented agriculture, we had to take care and sow our seeds and harvest our crops at just the right season. Annual meetings of far flung nomadic peoples were set for prescribed times.
Now some alleged calendrical devices might be due to chance; for example, the accidental alignment of a window and a niche. But there are other devices that are wonderfully different. Today, only the dry ruins of the great Anasazi cities have survived the ravages of time. Not far from these ancient cities, in an almost inaccessible location, there is another solstice marker, this one of singular and unmistakable purpose. The deliberate arrangement of three great stone slabs allows a sliver of sunlight to pierce the heart of a carved spiral, only at noon on the longest day of the year.
The wind whips through the canyons here in the American southwest and there's no one to hear it but us, a reminder of the 40,000 generations of thinking men and women who preceded us, about whom we know next to nothing, upon whom our society is based.
When our prehistoric ancestors studied the sky after sunset, they observed that some of the stars were not fixed with respect to the constant pattern of the constellations. Instead, five of them moved, slowly forward across the sky, then backward for a few months, then forward again, as if they couldn't quite make up their minds. We call them planets, the Greek word for "wanderers." These planets presented a profound mystery. The earliest explanation was that they were living beings. How else to explain their strange looping behavior. Later they were thought to be gods, and then disembodied astrological influences. But the real solution to this mystery is that the planets are worlds, that the Earth is one of them, and that they all go around the sun according to precise mathematical laws. This discovery has led directly to our modern global civilization. The merging of imagination with observation produced an exact description of the solar system. Only then could you answer the fundamental question that is at the root of modern science, "What makes it all go?" Two thousand years ago, no such question would even have been asked. The prevailing view had then been formulated by Claudius Ptolemy, an Alexandrian astronomer and also the preeminent astrologer of his time.
Ptolemy believed that the Earth was at the center of the universe, that the sun and the moon and the planets, like Mars, went around the Earth. It's the most natural idea in the world. The Earth seems steady, solid, immobile, while we can see the heavenly bodies rising and setting every day. But then, how to explain the loop de loop motion of the planets in the sky? Mars, for example? This little machine shows Ptolemy's model. The planets were imagined to go around the Earth attached to perfect crystal spheres, but not attached directly to the spheres, but indirectly through a kind of off-center wheel. The sphere turns and the little wheel rotates and as seen from the Earth, Mars does its loop de loop. This model permitted reasonably accurate predictions of planetary motion, where a planet would be on a given day. Certainly good enough predictions for the precision of measurement in Ptolemy's time and much later.
Supported by the church through the Dark Ages, Ptolemy's model effectively prevented the advance of astronomy for 1,500 years. Finally, in 1543, a quite different explanation of the apparent motion of the planets was published by a Polish cleric named Nicholas Copernicus. Its most daring feature was the proposition that the sun, not the Earth, was at the center of the universe. The Earth was demoted to just one of the planets. The retrograde, or loop de loop motion happens as the Earth overtakes Mars in its orbit, and see that from the standpoint of the Earth, Mars is now going slightly backwards, and now it is going in its original direction. This Copernican model worked at least as well as Ptolemy's crystal spheres, but it annoyed an awful lot of people. The Catholic Church later put Copernicus' work on its list of forbidden books, and Martin Luther described Copernicus in these words. He said, "People give ear to an upstart astrologer. This fool wishes to reverse the entire science of astronomy." The confrontation between the two views of the cosmos, earth-centered and sun-centered, reached its climax with a man who like Ptolemy was both an astronomer and an astrologer.
He lived in a time when the human spirit was fettered and the mind chained, when angels and demons and crystal spheres were imagined up there in the skies. Science still lacked the slightest notion of physical laws underlying nature. But the brave and lonely struggle of this man was to provide the spark that ignited the modern scientific revolution. Johannes Kepler was born in Germany in 1571. He was sent to the Protestant Seminary School in the provincial town of Maulbronn to be educated for the clergy. It was a strict, disciplined life, up before dawn to begin a long day of prayer and study. This was the age of the Reformation. Maulbronn was a kind of education and ideological bootcamp, training young Protestants in the use of theological weaponry against the fortress of Roman Catholicism.
There was little reassurance or comfort here for a sensitive boy like Kepler. He was intelligent and he knew it. That, together with his stubbornness and his fierce independence, served to isolate him from the other boys. Kepler made few friends in his two years at Maulbronn, so he kept to himself, withdrawn into the world of his own thoughts which were often concerned with his imagined unworthiness in the eyes of God. He despaired of ever attaining salvation. But God to him was more than punishment. God was also the creative power of the universe, and the young Kepler's curiosity about God was even greater than his fear. He wanted to know God's plan for the world. He wanted to read the mind of God.
This was his obsession. It was to inspire all of his great achievements. It was to take him and Europe out of the cloister of medieval thought. In places like Maulbronn, the faint echoes of the genius of antiquity still reverberated. Here, in addition to theology, Kepler was exposed to Greek and Latin and music and mathematics. And it was in geometry that he thought he glimpsed the image of perfection. He was later to write, "Geometry existed before the creation. It is co-eternal with the mind of God. Geometry provided God with a model for the creation. Geometry is God himself."
But the real world of Kepler's time was far from perfect. It was haunted by fear, pestilence, famine and war. Superstition's a natural refuge for people who are powerless. Only one thing seemed certain: the stars themselves. It was remembered that in ancient times the astrologer Ptolemy and the sage Pythagoras had taught that the heavens were harmonious and changeless. And Ptolemy had said that the motions of the planets through the stars of the zodiac were portents of events here below. Was it the influence of Mars and Venus that made his father a brutal man, a mercenary who had abandoned him? Did an unfortunate conjunction of planets in an adverse sign make his mother a mischievous and quarrelsome woman? If such things were fated by the stars, then perhaps there were hidden patterns underlying the unpredictable chaos of daily life. Patterns as constant as the stars.
But how could you discover them? Where would you begin? If the world and everything in it was created by God, then shouldn't you begin with a careful study of physical reality? Was not all of creation an expression of the harmonies in the mind of God? The book of nature had waited 1,500 years for a reader.
In 1589, Kepler left Maulbronn to continue his studies at the great university in Tubingen. It was a liberation to find himself amidst the most vital intellectual currents of the time. One of his teachers revealed to him the revolutionary ideas of Copernicus. Kepler relished this urbane, scholarly community. Here, his genius was recognized at last.
Kepler was not to be ordained after Tubingen. Instead, to his great surprise, he found himself summoned to Graz in Austria to become a teacher of high school mathematics. Kepler was not a very good teacher. The first year in Graz's mathematic's class had only a handful of students. The second year, none. He mumbled. He digressed. He was at times utterly incomprehensible. He was distracted by an incessant clamor of speculations and associations that ran through his head. And one pleasant summer afternoon, with his students longing for the end of the lecture, he was visited by a revelation that was to alter radically the future course of astronomy and the world.
There were only six planets known in his time: Mercury, Venus, Earth, Mars, Jupiter and Saturn. For some time, Kepler had been wondering why only six planets? Why not 20 planets or 100? And why this particular spacing between their orbits? No one had ever asked such questions before. In the course of a lecture on astrology, Kepler inscribed within the circle of the zodiac a triangle with three equal sides. He then noticed quite by accident that a smaller circle inscribed within the triangle bore the same relationship to the outer circle as did the orbit of Jupiter to the orbit of Saturn. Could a similar geometry relate the orbits of the other planets? Now Kepler remembered the perfect solids of Pythagoras. Of all the possible three-dimensional shapes, there were five and only five whose sides were regular polygons. He believed that the two numbers were connected, that the reason there were only six planets was that there were only five regular solids, and these perfect solids nested one within the other. He believed he had discovered the invisible supports for the spheres of the six planets. And this connection between geometry and astronomy could, he thought, admit only one explanation: The Hand of God Mathemetician.
"The intense pleasure I received from this discovery can never be told in words," he said. "Now I no longer became weary at work. Days and nights I passed in mathematical labors until I could see whether my hypothesis would agree with the orbits of Copernicus or if my joy should vanish into thin air." But no matter how hard he tried, the perfect solids and the planetary orbits did not agree with each other very well. Why didn't it work? Because unfortunately, it was wrong. The true orbital size of the planets, we now know, have absolutely nothing to do with the five perfect solids, as the later discovery of Uranus, Neptune and Pluto shows. But Kepler spent the rest of his life pursuing this geometrical phantasm. He couldn't abandon it, and he couldn't make it work. His frustration must have been enormous. Finally, he decided it must be the long accepted planetary observations that were inaccurate, and not his model of the nested solids. There was only one man in the world who had access to more precise observations. That man was Tycho Brahe who, as chance would have it, had recently written Kepler to come and join him. Kepler was reluctant at first, but he had no choice.
In 1598, a wave of oppression enveloped Graz. It was spearheaded by the local archduke who vowed to restore the Catholic faith to the province, and in his own words, "would rather make a desert of the country than rule over heretics." Kepler's school was closed, people were forbidden to worship or to sing hymns, or to own books of a heretical nature. Those who refused to embrace Catholicism were fined 10% of their assets and exiled from the country on pain of death. Kepler chose exile.
"Hypocrisy I have never learned. I am in earnest about faith. I do not play with it!" For Kepler, it was only the first in a series of religious exiles forced upon him by religious fanatics.
Now he decided to accept Tycho Brahe's open invitation. Brahi, a wealthy Danish nobleman, lived in great splendor, and had recently been appointed Imperial Mathemetician at Prague. Kepler left Graz with his wife and step-daughter and set out on the difficult journey. Kepler's wife was not a happy woman. She was chronically ill and had recently lost two young children. The marriage itself was no comfort. She had no understanding of her husband's work, and regarded his profession with contempt.
Kepler was married to his work, and every tedious mile was bringing him closer to the great Tycho Brahe, whose observations he devoutly hoped would confirm his theory. Kepler envisioned Tycho's domain as a sanctuary from the evils of the time. He aspired to be a worthy colleague to the illustrious Tycho who, for 35 years, had been immersed in exact measurements of a clockwork universe, ordered and precise.
But Tycho's court was not at all what Kepler had expected. Tycho himself was a flamboyant figure, adorned with a gold nose. The original had been lost in a student duel fought over who was the superior mathematician, and he maintained a circus-like entourage of assistants, distant relatives and assorted hangers-on.
Kepler had no use for the endless revelry. He was impatient to see Tycho's data, but Tycho would give him only a few scraps at a time. "Tycho," he said, "gave me no opportunity to share his studies. He would only, in the course of a meal and in-between other matters, mention, as if in passing, today the figure of the apogee of one planet, tomorrow the nodes of another." Kepler was ill-suited for such games, and the general climate of intrigue offended his sense of propriety. Their cruel mockery of the pious and scholarly Kepler depressed and saddened him. "My opinion of Tycho is this: He's superlatively rich, but knows not how to make proper use of it. Tycho possesses the best observations. He also has collaborators. He lacks only the architect who would put all of this to use."
Tycho was unable to turn his observations into a coherent theory of the solar system. He knew he needed the brilliant Kepler's help. But simply to hand over his life's work to a potential rival? That was unthinkable. Tycho was the greatest observational genius of the age, and Kepler the greatest theoretician. Either man alone could not achieve the synthesis which both felt was now possible. The birth of modern science, which is the fusion of observation and theory, teetered on the precipice of their mutual distrust.
The two repeatedly quarreled and were reconciled, until a few months later, Tycho died of his habitual overindulgence in food and wine. Kepler wrote to a friend on the last night of Tycho's gentle delirium: "He repeated over and over again these words, like someone composing a poem: 'Let me not seem to have lived in vain; let me not seem to have lived in vain.'" And he did not. Eventually, after Tycho's death, Kepler contrived to extract the observations from Tycho's reluctant family, observations of the apparent motion of Mars through the constellations obtained over a period of many years. The data from the last few decades before the invention of the telescope were by far the most precise ever obtained up to that time. Kepler worked with a kind of passionate intensity to understand Tycho's observations. What real motions of the Earth and Mars about the sun could explain to the precision of measurement the apparent motion as seen from the Earth of Mars in the sky? And why Mars? Because Tycho had told Kepler that the apparent motion of Mars was the most difficult to reconcile with a circular orbit. After years of calculation, he believed that he had found the correct values for a Martian circular orbit which matched ten of Tycho Brahe's observations within two minutes of arc.
Now there are 60 minutes of arc in an angular degree, and of course 90 degrees from horizon to zenith. So a few minutes of arc is a very small quantity to measure, especially without a telescope. But Kepler's ecstasy of discovery soon crumbled into gloom because two further observations of Tycho were inconsistent with his orbit by as much as eight minutes of arc. Kepler wrote, "If I had believed that we could ignore these eight minutes, I would have patched up my hypothesis accordingly. But since it was not permissible to ignore them, those eight minutes pointed the road to a complete reformation of astronomy.
The difference between a circular orbit and the true orbit of Mars could be distinguished only by precise measurement and by a courageous acceptance of the facts. Kepler was profoundly annoyed at having to abandon a circular orbit. It shook his faith in God as the maker of a perfect celestial geometry. "Having cleaned the stable of astronomy of circles and spirals," he said, 'I was left with only a single cartful of dung." He tried various oval-like curves, calculated away, made some arithmetical mistakes which caused him, in fact, to reject the correct answer, and months later, in some desperation, tried the formula for the first time for an ellipse. The ellipse matched the observations of Tycho beautifully. In such an orbit, the sun is not at the center, but is offset. It's at one focus of the ellipse. When a given planet is at the far point in its orbit from the sun, it goes more slowly. As it approaches the near point, it speeds up. Such motion is why we describe the planets as forever falling toward the sun, but never reaching it. Kepler's First Law of Planetary Motion is simply this: A planet moves in an ellipse, with the sun at one focus.
As the planet moves along its orbit, it sweeps out, in a given period of time, an imaginary wedge-shaped area. When the planet is far from the sun, the area is long and thin. When the planet is far from the sun, the area is short and squat. Although the shapes of these wedges are different, Kepler found that their areas are exactly the same. This provided a precise mathematical description of how a planet changes its speed in relation to its distance from the sun. Now, for the first time, astronomers could predict exactly where a planet would be in accordance with a simple and invariable law. Kepler's Second Law is this: A planet sweeps out equal areas in equal times.
Kepler's first two laws of planetary motion may seem a little remote and abstract. Alright, planets move in ellipses and they sweep out equal areas in equal times. So what? It's not as easy to grasp as circular motion. We might have a tendency to dismiss it, to say it's a mere mathematical tinkering, something removed from everyday life. But these are the laws our planet itself obeys as we, glued by gravity to the surface of the Earth, hurtle through space. We move in accordance with laws of nature which Kepler first discovered. When we send spacecraft to the planets, when we observe double stars, when we examine the motion of distant galaxies, we find that all over the universe, Kepler's laws are obeyed.
Many years later Kepler came upon his third, and last law of planetary motion, a law which relates the motion of the various planets with each other, which lays out correctly the clockwork of the solar system. He discovered a simple mathematical relationship between the size of a planet's orbit and the average speed with which it travels around the sun. This confirmed his long-held belief that there must be a force in the sun that drives the planets, a force stronger for the inner, fast-moving planets, and weaker for the outer, slow-moving planets. Isaac Newton later identified that force as gravity, answering at last the fundamental question, "What makes the planets go?"
Kepler's Third, or Harmonic Law, states that the squares of the periods of the planets, the time for them to make one orbit, are proportional to the cubes, to the third power, of their average distances from the sun. So the further away a planet is from the sun, the slower it moves, but according to a precise mathematical law. Kepler was the first person in the history of the human species to understand correctly and quantitatively how the planets move, how the solar system works.
The man who sought harmony in the cosmos was fated to live at a time of exceptional discord on Earth. Exactly eight days after Kepler's discovery of his Third Law, there occurred in Prague an incident that unleashed the devastating Thirty Years War. The war's convulsions shattered the lives of millions of people. Kepler lost his wife and young son to an epidemic spread by the soldiery. His royal patron was deposed and he was excommunicated from the Lutheran Church for his uncompromising independence on questions of belief. He was a refugee once again.
The conflicts, portrayed on both sides as a holy war, was more an exploitation of religious bigotry by those hungry for land and power. This war introduced organized pillage to keep armies in the field. The brutalized population of Europe stood by helpless as their ploughshares and pruning hooks were literally beaten into swords and spears. Rumor and paranoia swept through the countryside enveloping especially the powerless. Among the many scapegoats chosen were elderly women living alone who were charged with witchcraft. Kepler's mother was taken away in the middle of the night in a laundry chest. It took Kepler six years of unremitting effort to save her life.
In Kepler's little home town, about three women were arrested, tortured and killed as witches every year between 1615 and 1629, and Katarina Kepler was a cantankerous old woman. She engaged in disputes which annoyed the local nobility, and she sold drugs. Poor Kepler thought that he himself had contributed inadvertently to his mother's arrest. It came about because he had written one of the first works of science fiction. It was intended to explain and popularize science, and was called "The Somnium." The Dream. He imagined a journey to the moon, with the space travelers standing on the lunar surface looking up to see, rotating slowly above them, the lovely planet Earth.
Part of the basis for the charge of witchcraft was that in his Dream, Kepler used his mother's spells to leave the Earth. But he really believed that one day human beings would launch celestial ships with sails adapted to the breezes of heaven, filled with explorers who, he said, would not fear the vastness of space. He speculated on the mountains, valleys, craters, climate, and possible inhabitants of the moon. Before Kepler, astronomy had little connection with physical reality, but with Kepler came the idea that a physical force moves the planets in their orbits. He was the first to combine a bold imagination with precise measurements, to step out into the cosmos. It changed everything.
This fusion of facts with dreams opened the way to the stars. As a boy Kepler had been captured by a vision of cosmic splendor, a harmony of the worlds, which he sought so tirelessly all his life. Harmony in this world eluded him. His Three Laws of Planetary Motion represent, we now know, is a real harmony of the worlds, but to Kepler, they were only incidental to his quest for a cosmic system based on the perfect solids, a system which, it turns out, existed only in his mind. Yet, from his work we have found that scientific laws pervade all of nature, that the same rules apply on Earth as in the skies, that we can find a resonance, a harmony between the way we think and the way the world works.
When he found that his long cherished beliefs did not agree with the most precise observations, he accepted the uncomfortable facts. He preferred the hard truth to his dearest illusions. That is the heart of science.