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00:00All right, Gregory.
00:04Gregory, do you want to watch?
00:16Gregory, you're going to stay right here.
00:20Oh, there's a potato phone right here.
00:30density.
00:50There's a...
00:54No, I'm kidding.
00:56I'm kidding.
00:58Eeeee!
01:00Ha ha ha!
01:06Kepler's three laws describe
01:08the motions of the planet.
01:10But they don't explain them.
01:12Flying Gregory!
01:14Isaac Newton's explanation of those laws
01:16was the culmination of the
01:18scientific revolution.
01:20It's known as the solution
01:22to the Kepler problem.
01:24Let me remind you again briefly
01:28of the story we've heard so many times.
01:30In 1543,
01:32Copernicus wrote his little book.
01:34A generation later,
01:36Kepler discovered his three laws.
01:38And then,
01:40150 years after Copernicus,
01:42Isaac Newton came along
01:44and explained for us why the universe
01:46works the way it does.
01:48Today, we're going to
01:50begin the job of seeing
01:52exactly how Newton's laws
01:54explain everything
01:56that Kepler found in the heavens.
02:00Now that sounds hard.
02:01And it is.
02:02But it's one of the
02:04crowning achievements of Western thought.
02:06It's a part of your cultural heritage
02:08in the same sense
02:10as Shakespeare's plays
02:12or Beethoven's symphonies
02:14or the ceiling of the Sistine Chapel.
02:16And so I'd like you to learn this.
02:18Not merely as a part of your vocational training
02:22for those of you who are going to be scientists.
02:24But as a part of your education as human beings.
02:30Now what we're going to learn today
02:32differs from a play or a symphony
02:34or a painting in a fundamental way.
02:36A painting, for example,
02:38is the creation of a single person.
02:40If anyone else had painted
02:42the ceiling of the Sistine Chapel
02:44it would have come out
02:46completely differently.
02:48But what we're going to learn today
02:50is a fact about the physical universe.
02:52If it had not been discovered by Newton
02:55it would have been discovered
02:57by somebody else.
02:59And so there's no need for us to do it
03:03in exactly the same way that Newton did.
03:05We can use tricks that came along later
03:08like vectors and energy
03:10things that will make the world simpler.
03:12And that's what we'll do.
03:14But once it's done
03:16then unlike a painting
03:18it's something that will belong to you
03:20every bit as much
03:21as it originally belonged to Newton.
03:23It will be your very own
03:25to take with you forever.
03:27This is the job we've been preparing for
03:30ever since we started.
03:32And now it's time to get going.
03:34Isaac Newton guessed
03:38that the force of gravity
03:40gives rise to elliptical orbits.
03:42And he found the proof of that guess
03:45in worldly mathematics.
03:47Into Newton's mathematics
03:51went his inverse square law of gravity
03:54as well as his second law of motion.
03:57And out came a differential equation
04:07for the orbit
04:08whose solution is the algebraic equation
04:11not only of an ellipse
04:20but of any conic section.
04:22And that vision
04:33Isaac Newton's enormous leap of insight
04:36proves to stand among the greatest achievements
04:39of Western culture.
04:44It was in its own right
04:46the mathematical equivalent
04:48of Michelangelo's ceiling
04:49in the Sistine Chapel
04:51the drowning glory
04:52of the Renaissance.
04:58Michelangelo's subjects
04:59seem to be in constant movement
05:01never at rest.
05:07And by virtue of this perspective
05:08Michelangelo, like Copernicus
05:11seems to glorify the never ending motions
05:13of the earth
05:14and all its creatures.
05:16With such a brilliant perception
05:23both the scientist and the artist
05:25shared the uncommon world view
05:27of the greatest playwright in history.
05:33In creating his extraordinary world
05:35where did William Shakespeare place the sun?
05:39But soft.
05:40What light through yonder window breaks?
05:44It is the east
05:45and Juliet is the sun.
05:48Arise fair sun
05:49and kill the envious moon.
05:51Shakespeare lived in the days
05:52of Galileo and Kepler.
05:58And just as surely as they did
06:00he worked under the influence of the heavens
06:02and often used celestial references.
06:04Her eye discourses.
06:05I will answer it.
06:07I am too bold.
06:09It is not to me she speaks.
06:11Two of the fairest stars in all the heaven
06:13having some business
06:14do entreat her eyes
06:15to twinkle in their spheres
06:17till they return.
06:19What if her eyes were there
06:21they in her head?
06:23The brightness of her cheek
06:24would shame those stars
06:25as daylight doth allow.
06:28Her eye in heaven
06:29Of course, Shakespeare wasn't the only creative genius
06:32to make a powerful connection
06:33between the arts and the sciences.
06:38Finding his inspiration to compose
06:40Ode to Joy in the Stars
06:42Rudolf von Beethoven sang the praises
06:44of the heavenly firmament.
06:53Fine art.
06:55Drama.
06:56Music.
07:00Mathematics and physics.
07:02Each is a brilliant gem of Western culture.
07:11And collectively
07:12they are the crown jewels of Western achievement.
07:17Even as a young man
07:19Newton realized that gravity
07:20was the common force of heaven and earth.
07:22He saw it as a fundamental force
07:26that consistently pulls
07:27rather than pushes or twists
07:29through the universe.
07:39Years later, with that in mind
07:41Isaac Newton fully appreciated the meaning
07:43of Kepler's laws of planetary motion.
07:45Twist or torque cannot be applied by gravity.
07:46Twist or torque cannot be applied by gravity.
07:52Twist or torque.
07:53Twist or torque cannot be applied by gravity.
08:15No torque, together with Newton's second law, leads to a differential equation ready to be integrated.
08:22When there is no torque, a certain quantity, mr cross beam, is constant.
08:30That quantity is called the angular momentum.
08:45A planet orbiting with constant angular momentum stays in a single plane.
08:53Its orbital speed varies in a precisely determined way.
09:02The area swept out by its radius vector changes at a constant rate.
09:15That's Kepler's second law.
09:30When Johannes Kepler ruled toward his second law,
09:44the art of astrology and the science of astronomy were one and the same.
09:51And whichever it was called, the terms were interchangeable then.
09:56Kepler, like the typical mathematician of his day, used it as a means of producing income.
10:04But unlike the others, Kepler used astronomy as a vehicle to reach a mathematical truth
10:10that had been hidden within the heavens since the day of creation.
10:16At the same time, with his poetic interpretation of astronomy,
10:20Shakespeare searched for a universal equation that could explain the complex actions and complicated emotions of women and men.
10:32And like Isaac Newton, his observations influenced the way humans perceive reality.
10:39Their methods differ. Newton was hardly known for his sense of humor.
10:44Yes, Peter, I have spoken to him. I have to see him again.
10:49But like Shakespeare, Newton asked questions that deeply affected perception of how the world works.
11:00Newton's discovery that the orbits of all objects in the heavens obeyed the equation of the conic sections
11:07started out as a question.
11:10Why are the planetary orbits ellipses sweeping out equal areas in equal times?
11:35The 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.
11:48In terms of angular momentum, the result is a differential equation
11:54obeyed by all objects moving under any central force.
11:58including planets moving in elliptical orbits under the force of Newton's universal law of gravity.
12:13The heavens themselves, the planets, and this center observe degree, priority, and place.
12:23In Shakespeare's time, the earth, influenced by disordered and wandering planets, was at the core of the solar system.
12:34Yet in Troilus and Cressida, did he not place Saul, the sun, at the center of his drama?
12:39Is the glorious planet's soul, in noble eminence enthroned and speared amidst the other,
12:46whose medcinable eye corrects the ill aspects of planets' evil, and posts like the commandment of a king.
12:54Was William Shakespeare, in fact, a Copernican?
12:58Did he share the same world view as Johannes Kepler?
13:01Like a tragic character of Elizabethan drama,
13:08Kepler traveled the path of cruel and ironic twists,
13:12seeing perfect harmony in the heavens,
13:15while experiencing total discord on earth.
13:30As a young boy, Kepler was abandoned by his father,
13:33a brutal mercenary who drifted from war to war.
13:37Young Kepler was shipped off to a Protestant seminary in the German provinces.
13:43It was a strict and spartan life, with endless hours of study and prayer.
13:49Kepler was a frail and sickly lad, who had virtually no friends,
13:54and was stubbornly independent.
13:57Kepler's mother was an eccentric in the extreme,
14:01obsessed with astrology and the occult.
14:05His aunt was burned at the stake.
14:09As his religious training progressed,
14:11he despaired about ever being saved,
14:14and became increasingly guilty about his mother's fascination with the occult.
14:23Later, as for his own family,
14:26he lost his first wife and seven of his eleven children.
14:30A wandering victim of the Thirty Years' War,
14:35he carried his pain from city to city,
14:37seeking a port in the violent storm that followed him
14:40the last twelve years of his life.
14:43Of course, things could have been worse.
14:47And they soon were.
14:49In 1615, Kepler's mother was put on trial,
15:02for the fairly common but forbidden practice of witchcraft.
15:07Devastated by the news of his mother's arrest and trial,
15:10Kepler wrote,
15:11it caused my heart to almost burst.
15:15Though he was finally making real progress in his life's work,
15:19he stood by his mother in one way or another for six long years.
15:23Because Kepler himself described her as a stubborn and quarrelsome gossip,
15:29Kepler's heartfelt concern for his mother seems a curious footnote.
15:34Other than a dutiful son's strength of character,
15:39was there another reason to owe the old woman so very much?
15:43In the story of his childhood, which is a dark chronicle of misery,
15:56Kepler wrote of only one bright moment.
15:59When he was five years old, curious and very impressionable,
16:04his mother took his hand and they strolled out into the night.
16:08They climbed to the top of a nearby hill and together they saw a comet.
16:13While the reason behind his accomplishments must trail off in speculation,
16:18the accomplishments themselves remain indelible.
16:23While William Shakespeare probably would have overlooked
16:27the mathematics that reflect Kepler's third law,
16:31surely he would have found irony in the title of Kepler's work,
16:35the harmony of the world.
16:38Despite his mother's ordeal, his loss of one child after another,
16:45his ongoing conflict between scientific fact and religious dogma,
16:50nothing could keep Johannes Kepler from completing the harmony of the world.
16:54And yet, even though his mind was able to cross the most advanced frontiers
17:01of the world of mathematics, Kepler himself never fully realized the extent of its reach.
17:10On the final leg of his wandering, he almost came across the calculus,
17:15but that would be reached by Leibniz and Newton.
17:20By the same token, Kepler came close to the universal law of gravity,
17:25but that would be the destiny of Isaac Newton alone.
17:34Not only did it fall upon him to discover the universal law of gravitation,
17:38the law itself fell into Newton's hands as the key to the Kepler problem.
17:43With his law of gravity, Isaac Newton unlocked the door Kepler had approached for a lifetime,
17:49and stepped across the threshold into the secret of the skies.
17:59The universal law of gravitation.
18:06The second law of motion.
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