foreign [Music] [Applause] [Music] thank you thank you Kepler's Three Laws describe the Motions of the planet but they don't explain them Isaac Newton's explanation of those laws was the culmination of the Scientific Revolution it's known as the solution to the Kepler problem let me remind you again briefly of the story we've heard so many times in 1543 Copernicus wrote his little book a generation later Kepler discovered his three laws and then 150 years after Copernicus Isaac Newton came along and explained for us why the universe works the way it does today we're going to begin the job of seeing exactly how Newton's Laws explain everything that Kepler found in the heavens and that sounds hard and it is but it's one of the crowning achievements of Western thought it's a part of your cultural heritage in the same sense as Shakespeare's plays or Beethoven symphonies or the ceiling of the Sistine Chapel and so I'd like you to learn this not merely as a part of your vocational training for those of you who are going to be scientists but as a part of your education as human beings now what we're going to learn today differs from a play or a symphony or a painting in a fundamental way a painting for example is the creation of a single person if anyone else had painted the ceiling of the Sistine Chapel it would have come out completely differently but what we're going to learn today is a fact about the physical universe if it had not been discovered by Newton it would have been discovered by somebody else and so there's no need for us to do it in exactly the same way that Newton did we can use tricks that came along later like vectors and energy things that will make the words simpler and that's what we'll do but once it's done then unlike a painting it's something that will belong to you every bit as much as it originally belonged to Newton it will be your very own to take with you forever this is the job we've been preparing for ever since we started and now it's time to get going Isaac Newton guest that the force of gravity gives rise to Elliptical orbits and he found the proof of that guess in worldly mathematics [Music] into Newton's mathematics when his inverse Square law of gravity as well as his second law of motion and out came a differential equation for the orbit whose solution is the algebraic equation not only of an ellipse [Music] but of any conic section [Music] and that Vision Isaac Newton's enormous leap of insight Rose to stand among the greatest achievements of Western culture [Music] it was in its own right the mathematical equivalent of Michelangelo's ceiling in the Sistine Chapel the crowning glory of the Renaissance Michelangelo's subjects seem to be in constant movement never at rest and by virtue of this perspective Michelangelo like Copernicus seems to glorify the never-ending motions of the earth and all its creatures [Music] with such a brilliant perception both the scientist and the artist shared The Uncommon world view of the greatest playwright in history in creating his extraordinary world where did William Shakespeare place the Sun what light through yonder window breaks it is the East and Juliet is the Sun arise Fair sun and kill the envious Moon Shakespeare lived in the days of Galileo and Kepler and just as surely as they did he worked under the influence of the heavens and often used Celestial references her eye discourses I will answer it I am too bold it is not to me she speaks two of the fairest stars in all the heaven having some business doing treat her eyes to twinkle in their spheres to lay return what if her eyes were there they in her head the brightness of her cheek would shame those Stars as daylight that the lamb her eye in heaven of course Shakespeare wasn't the only creative genius to make a powerful connection between the Arts and the Sciences finding his inspiration to compose Ode to Joy in the Stars Ludwig van Beethoven sang the Praises of the Heavenly firmament [Music] fine art drama music mathematics and physics each is a brilliant Gem of Western culture [Music] and collectively they are the crown jewels of Western achievement [Music] even as a Young Man Newton realized that gravity was the common force of Heaven and Earth he saw it as a fundamental force that consistently pulls rather than pushes or twists through the universe [Music] years later with that in mind Isaac Newton fully appreciated the meaning of Kepler's laws of planetary motion [Music] twist or Torque cannot be applied by gravity [Music] foreign torque together with Newton's Second Law leads to a differential equation ready to be integrated when there is no tour a certain quantity Mr Cross B is constant that quantity is called the angular momentum foreign [Music] orbiting with constant angular momentum stays in a single plane its orbital speed varies in a precisely determined way [Music] the area swept out by its radius Vector changes at a constant rate oh [Music] [Applause] [Music] that's Kepler's second law [Music] [Applause] when Johannes Kepler rolled toward his second law the art of astrology and the science of astronomy were one and the same and whichever it was called the terms were interchangeable then Kepler liked the typical mathematician of his day used it as a means of producing income but unlike the others Kepler used astronomy as a vehicle to reach a mathematical truth that had been hidden within the heavens since the day of creation [Music] at the same time with his poetic interpretation of astronomy Shakespeare searched for a universal equation that could explain the complex actions and complicated emotions of women and men [Music] and like Isaac Newton his observations influence the way humans perceive reality their methods differ Newton was hardly known for his sense of humor like Shakespeare Newton asked questions that deeply affected perception of how the world works Newton's discovery that the orbits of all objects in the heavens obeyed the equation of the conic sections started out as a question why are the planetary orbits ellipses sweeping out equal areas in equal times [Music] [Music] [Music] the answer is most easily found in polar coordinates where the rate of change of area is equal to one-half r squared D Theta DT in terms of angular momentum the result is a differential equation obeyed by all objects moving under any Central Force including planets moving in elliptical orbits under force of Newton's universal law of gravity the heavens themselves the planets and this Center observed degree priority and place insist your course proportions in Shakespeare's time the Earth influenced by disordered and wandering planets was at the core of the solar system [Music] yet in troilus and Cressida did he not Place Saul of the Sun at the center of his drama is the Glorious Planet Saul in Noble Eminence enthroned and spared amidst the other whose medsinnable eye corrects the ill aspects of planet's evil and posts like the Commandment of a king was William Shakespeare in fact a copernican did he share the same worldview as Johannes Kepler [Music] like a tragic character of Elizabethan drama Kepler traveled a path of cruel and ironic twists seeing Perfect Harmony in the heavens while experiencing total Discord on Earth [Music] as a young boy Kepler was abandoned by his father a brutal mercenary who drifted from war to war young Kepler was shipped off to a Protestant seminary in the German provinces it was a strict and Spartan life with endless hours of study and prayer Kepler was a frail and sickly land who had virtually no friends and was stubbornly independent Kepler's mother was an eccentric in the extreme obsessed with astrology and the occult his aunt was burned at the stake as his religious training progressed he despaired about ever being saved and became increasingly guilty about his mother's fascination with the occult [Music] later as for his own family he lost his first wife and seven of his 11 children [Music] a Wandering victim of the 30 Years War ried his pain from City to City seeking a port in the violent storm that followed him the last 12 years of his life of course things could have been worse and they soon were [Music] in 1615 Kepler's mother was put on trial for the Fairly common but forbidden practice of witchcraft devastated by the news of his mother's arrest and trial Kepler wrote it caused my heart to almost burst though he was finally making real progress in his life's work he stood by his mother in one way or another for six long years because Kepler himself described her as a stubborn and quarrelsome gossip Kepler's heartfelt concern for his mother seems a curious footnote other than a dutiful son's strength of character was there another reason to owe the old woman so very much [Music] in the story of his childhood which is a dark Chronicle of misery Kepler wrote of only one bright moment when he was five years old Curious and very impressionable his mother took his hand and they strolled out into the night they climbed to the top of a nearby Hill and together they saw a comet while the reason behind his accomplishments must Trail off in speculation the accomplishments themselves remain indelible [Music] while William Shakespeare probably would have overlooked the mathematics that reflect Kepler's Third Law surely he would have found irony in the title of Kepler's work the harmony of the world despite his mother's ordeal his loss of one child after another his ongoing conflict between scientific fact and religious Dogma nothing could keep Johannes Kepler from completing the harmony of the world [Music] and yet even though his mind was able to cross the most advanced frontiers of the world of mathematics Kepler himself never fully realized the extent of its reach [Music] on the final leg of his wandering he almost came across the calculus but that would be reached by leibniz and Newton by the same token Kepler came close to the universal law of gravity but that would be the destiny of Isaac Newton alone [Music] not only did it fall upon him to discover the universal law of gravitation the law itself fell into Newton's hands as the key to the Kepler problem with his law of gravity Isaac Newton unlocked the door Kepler head approached for a lifetime stepped Across the Threshold into the secret of the Skies the universal law of gravitation the second law of motion [Music] the conservation of angular momentum vectors cross together by Shakespeare's star-crossed lovers in a combination as potent as Michelangelo's hand of God [Music] setting off a ballet of vectors as spirited as a Beethoven symphony [Music] the equations of the heavens find their simplest expression in the elegant language of differential calculus integral to The Grand Design and constant in addition [Music] the ellipses of the heavens are revealed as an expression of the perfect circle of underlying geometry [Music] the product of these events once order is exchanged and Mad Max allowed its play [Music] thank you comes to resemble an old friend a curve a familiar aspect [Music] ellipse Parabola and hyperbola thank you all find their arcs described on the celestial tapestry so as Isaac Newton was the first to discover the force of gravity moves all Heavenly Bodies along conic sections and since planets move in closed curves their orbits are ellipses Newton casually shared this discovery with Edmund Halley [Music] but Howdy's reaction may have soon changed from pure joy to Absolute horror not only had Newton lost his calculations for solving the Kepler problem but he'd even forgotten how he had derived the mathematical proof however urged on by Halle Newton calmly started once again to solve perhaps the most complex problem in the scientific world and this time he went on to reveal the mathematical secret of the universe considering such beautiful lines Shakespeare's dialogue Beethoven's phrasing Michelangelo's brush strokes and The Strokes of Genius in Newton and Kepler becomes increasingly clear that the greatest art in science endure not only for their Elegance but for their truth [Music] Johannes Kepler lived at the same time as William Shakespeare Queen Elizabeth the first Mary Queen of Scots and of course Galileo so far as I know no two of those people ever met each other but Kepler and Galileo certainly knew about each other and in fact they even exchanged a few letters I'd like to read to you a little bit from those letters the first one is written in 1597. Kepler had a copy of a book he had written sent to Galileo and Galileo sent back his reply he wrote your book my learning doctor I received merely a few hours ago I congratulate myself on having an associate in the study of Truth and Truth spelled with a capital T meant to Galileo the copernican system of the world he had not yet admitted openly that he believed in it in fact later on in the letter he writes so far I have been frightened by the fate of Copernicus himself our teacher who though he acquired Immortal thing with some is yet to an infinite multitude of others for such as the number of fools an object of ridicule and derision you remember that 40 years later Galileo himself was put on trial for adopting the copernican system the second letter was written in 1610. Galileo had made His Brilliant discoveries with the new telescope written a book called The Starry Messenger but the book was received with either indifference or hostility by the rest of the world he had a copy sent to the great Kepler and waited with anxiety for his reply Kepler replied with his characteristic generosity and Galileo then wrote back to him I thank you because you are the first and nearly the only one who has shown complete faith in my assertions not at all surprising such as your nobility in the height of your Genius Kepler ask Galileo how he could get to see the heavens through a telescope of the quality of the one that Galileo had made Galileo wrote back saying there was none available to him either he wrote indeed mine is truly excellent and it multiplies images more than a thousand times it is no longer mine the most Serene Grand Duke of Tuscany sought it from me so that he might store it in his tribunal and there among more distinguished and costly things preserve it in lasting memory every scientist today is familiar with the risks and Hazards of working on the government patronage Kepler did personally meet Tico Bry in that meeting changed the history of the world these were bad times in 1597 Tico's Patron King Frederick died and he was succeeded by Christian IV who couldn't stand the Arrogant astronomer and soon Tico had to leave Denmark he wound up in Prague as Imperial mathematician to Rudolph II where his job of course was to cast horoscopes meanwhile back in Austria Kepler who was born a Protestant was hounded out of the Catholic town of Graz and so on a date that's very easy to remember the first of January 1600 he set out to join the great tico in Prague and that's how the two of them met immediately they both realized that they couldn't stand each other but neither one could get along without the other Tico needed Kepler's mathematical genius to organize his observations and Kepler had to have Tico's data to do the cosmology which was his life's mission and so for 18 stormy months the two of them stayed tied together unable to escape from each other until Tico died in 1601. and even then Kepler was not able to turn all of his attention to the cosmology that he so badly wanted to do because first he had the responsibility to produce this book this book is called the rudolphin tables after the emperor Rudolph who paid the bill it's written by Johannes Kepler published in 1627 and it is Kepler's publication of Tico's data even if Kepler had never discovered his three laws we would remember him today for this book because this book made astronomy a hundred times more precise than it ever been before we'll go on with our story next time thank you again foreign media [Music] for information about this and other Annenberg media programs call 1-800 learner and visit us at www.learner.org [Music]