Transcript for:
Lesson 25: Gravity, Planetary Motion, Tides, and Einstein's Theories

foreign [Music] thank you thank you the periods of the planets in their orbits the ebb and flow at the tides the acceleration of a falling body all these phenomena are consequences of the force of gravity and they've inspired the labor of scientists from Kepler to Einstein well we've almost come to the end of our story today I have just a few loose ends I'd like to tie up the first one is Kepler's Third Law that will bring us to the end of a Kepler problem then there's the question of the tides you remember Galileo had a theory of the tides which he considered to be the crowning achievement of his career because it proved that Copernicus had to be right but Galileo was completely wrong today I'll explain to you how the tides really work and then finally I'd like to return to the very first thing we did the law of falling bodies gravity applies a different Force to each body in just such a way that they all fall at exactly the same rate it seemed to Albert Einstein that there ought to be a profound reason for that to be true and in searching for that reason he discovered nothing less than a new theory of the universe so those are our loose ends for today I think we better get started Galileo Galilei was a mathematician who wrote a popular book that got him into a lot of trouble 250 years later Charles lutwidge Dodson another mathematician wrote another popular book dodgson's mathematics was as respectable as the Victorian era in which it was published and almost as forgotten yet like Galileo he may be remembered forever but only under his pen name Lewis Carroll and only as long as children appreciate the wisdom of pure nonsense the time has come the walrus said to talk of many things of shoes and ships and ceiling wax of cabbages and kings and why the sea is boiling hot and whether pigs have wings Lewis Carroll wrote through the looking glass for a child named Alice he could have had Galileo's curious situation in mind for one thing since Galileo used logic when the issue was basically religious he might as well have debated the Mad Hatter pure faith and pure science have never been the same thing so naturally when Church Scholars peered into Galileo's telescope they looked through the glass Darkly and in Galileo's persistent defense of Copernicus they began to see what looked like heresy of course this serious charge had nothing to do with the fantasy walrus or whether pigs have wings but it did have something to do with why the boiling sea has tides to Galileo the tides were more than the ebb and flow of the Earth's oceans they were his evidence that the Earth really moves Tides exist because of the Earth's motion around the sun he argued and he worked out a detailed theory of exactly how the tides were caused Galileo considered his theory of the tides to be the high point of his scientific career but if he had been right there would be only one high tide each day and it would occur at High Noon the sad truth is Galileo's tide theory was really all wet the tides do rise and they recede as well but as anyone can see with a bit of patient observation they do so twice every day to understand why the tides behave this way it helps to take the Long View in the Earth Moon system the Earth and the moon rotate around a Common Center of mass that point is actually inside the earth about three quarters of the distance from the Earth's center to its surface [Music] the strange wobbling motion of the earth seen from this perspective is really a keplerian orbit of the center of the Earth around the center of mass of the Earth Moon system but only the center of the earth is in exactly the right orbit [Music] on the side closest to the moon the moon's gravity is too strong and the water there is pulled toward the moon into a bulge on the opposite side the moon's gravity is too weak to hold the water in place and so there too the water bulges outward trying to escape [Music] [Applause] as the Earth wobbles around the earth Moon Center of mass it also rotates on its axis and as the Earth rotates it passes beneath the bulges at those locations where the rotating Earth passes under the rising water high tides occur and at the points between low tides occur two high tides and two low tides every day and every day as well the sun plays a role in the ongoing drama of the tides since the Sun's gravity tugs at the Earth like the moons it contributes to the tides in the same way though the sun's larger its effect on the tides is about half that of the Moon because it's so much farther away from the Earth at Full Moon and at New Moon Earth the Sun and the Moon fall into a straight line then the tidal effects of sun and moon reinforce each other and create the highest high tides and the lowest low tides high and low the tides rise and fall because the Earth moves [Music] in writing his theory Galileo was not wrong in raising his pen in defense of Copernicus it was a lonely battle but at least in principle he was not alone [Music] in 1618 two years after the church warned Galileo to stop teaching such dangerous ideas Johannes Kepler published a book called Harmony of the Worlds more than an argument for the truth of Copernicus this book was Kepler's proof that he himself had not lived a lie Kepler not only attempted to unwrap and expose the secrets of the universe he tried to tie up and explain them all all in one book and with one all-encompassing synthesis of geometry music and astronomy no work since Plato's in the Golden Age could match the ambitious nature of Kepler's Harmony of the Worlds and when Newton dug into Kepler's ideas he found mathematical Treasures of invaluable worth it might have been tedious to sift through music that couldn't be heard fantasies that made little sense and planetary models that made less but how rewarding it must have been to unearth Kepler's Three Laws according to Newton Kepler's first law said that the orbits of the planets are ellipses II stated that the radius Vector of a planet sweeps out equal areas in equal times and finally Kepler's Third Law the square of any planet's period is proportional to the cube of its semi-major axis but why integrating Kepler's second law through one complete period shows that the period of a planet is proportional to the area of its orbit but also goes inversely as the angular momentum divided by the mass this relation is true of many kinds of motion for example it would be true if the solar system rotated like a solid body with all the planets having the same period [Music] it would also be true if the Solar System's world like a Vortex with every planet having the same angular momentum divided by Mass then the period of each planet would be proportional to the square of the size of its orbit and it's also true for the real motion of the planets [Music] this motion produced and directed by Isaac Newton's law of universal gravitation features an elliptical orbit whose size depends on L over m [Music] [Music] m foreign 4 pi squared the gravitational constant and the mass of the sun connect t squared to a cubed for every planet Kepler's Third Law relates the periods of the planets to the size of their orbits and the connection is simple elegant and altogether profound of course the history of science can be seen as a series of such insightful connections the risky connection between a revolutionary copernican idea and Galileo's theory of the tides the connection Among The Rising Moon the Rising Sun and the rising tides on Earth the connection of all three linked and locked in Eternal orbit the connection between the orbits of all the planets and Kepler's three laws of planetary motion the connection between Kepler's laws which explain how the planets behave and Newton's Laws which explain why and finally from Galileo's law of falling bodies to Kepler's Third Law to Newton's mechanics and his universal law of gravitation the connection explained the Mechanical Universe but a few rare things in the universe seem to go beyond even Newton's explanation and seem to require a change not only in the nature of gravity but even in the meaning of space and time to Albert Einstein the Enigma of gravity time and space was of no small consequence it was a puzzle that promised enormous Challenge and if solved the answer to perhaps some of the deepest mysteries in the cosmos like Newton before him Einstein began with the law of falling bodies Galileo didn't quite understand gravity no one really would until Newton but he discovered the fact that all bodies fall with the same constant acceleration why should the force of gravity lead to such a strange result when calculating the acceleration of a falling Apple the mass cancels out leaving the same acceleration for any falling body but why should that be the case [Music] equals m a the mass determines how much force is needed to produce a given acceleration in other words the mass determines how strongly a body resists changing its inertia [Music] this property of a body has nothing to do with gravity it's called the inertial mass on the other hand in the law of gravity the mass determines how strongly a body attracts every other body in the universe this property has nothing to do with inertia it's called the gravitational Mass Isaac Newton understood that the law of falling bodies meant these two completely different masses had to be exactly the same for everybody in the universe but why why is gravitational Mass always equal to inertial Mass could that be some Cosmic coincidence scientists as a rule don't Place much stock in phenomena that can be explained by mere coincidence Albert Einstein plays none he believed there must be some more profound law of nature that would make the law of falling bodies not a mystery but instead something so simple it would be perfectly obvious and the principle he chose became the basis for his general theory of relativity it's called the principle of equivalence equivalence that is between constant gravity and constant acceleration imagine an experiment in which different objects with different masses all fall with exactly the same acceleration called G that might happen because the laboratory is on the surface of the Earth but the same thing would also happen if the laboratory were far from Earth and everything else say in Intergalactic space it would happen if the laboratory were accelerating upward with acceleration G all the objects inside obeying the law of inertia would not accelerate but they would all seem to fall with the same constant acceleration [Music] Albert Einstein understood that the law of falling bodies and the Mysterious equality of gravitational mass and inertial mass would be perfectly explained if the following fundamental principle were true no experiment of any kind done entirely inside that laboratory could determine whether the objects fall because of the pool of gravity or because the laboratory is accelerating upwards in outer space the idea seems almost too simple to be true but Albert Einstein didn't take it lightly instead he asked how the experiment would come out if it were performed with a beam of light [Music] with the laboratory out in space the answer was easy to see if the rocket accelerates upward while the beam goes straight across it must seem to bend downwards just a tiny bit but then what would happen on Earth the answer comes from the principle itself since no experiment not even this one can tell whether the laboratory is on Earth or in space the result must be exactly the same in other words Einstein concluded that light doesn't travel in straight lines instead it bends ever so slightly because of the gravitational force of the Earth Einstein predicted light would likewise Bend as it passed the Sun and when he said so in this letter to George Ellery Hale it looked extremely good on paper but not quite good enough for astronomers to risk their precious telescopes much less their precious eyesight looking directly at the Sun and so George Ellery Hale Einstein's correspondent and himself one of the great astronomers of the early 20th century made a gentle suggestion why not observe the Sun during an eclipse and in 1919 that's precisely what Sir Arthur Eddington and his party of solar explorers went out and did the triumphant success of that expedition was the first great proof of Relativity and turned the quiet shy Albert Einstein into an instant World Famous folk hero everyone knew about him even though few could understand relativity and no one really knows why the world took Einstein to its heart probably exhausted by World War One People needed a hero his Discovery was benign and Albert Einstein looked like everyone's favorite uncle he also became the symbol for all scientists and it didn't make any difference that few could understand Einstein's great work the principle of equivalence raises an interesting question if flight travels curved paths what is a straight line Einstein said that it makes no sense to talk of straight lines space itself is curved not only space but space time that means that space and time change as they move through gravitational fields but how does that relate to Newtonian physics in his laws of motion Newton said a body moving in a straight line we'll keep moving in that straight line until it's acted upon by an outside force if there are no straight lines what is the meaning of the law of inertia on a flat mapper chart the shortest path between two points is The Familiar straight line that joins them but not on the surface of a globe here the shortest path between two points is not a straight line but is a great circle to generalize the shortest path between any two points on any surface is called a geodesic Einstein said that Starlight may not really be bent by the gravitational force from the Sun instead it can be said to travel inertially along the shortest path between any two points in the local curved space time that makes it seem to bend to any Observer and for the same reason the Earth's orbit doesn't have to be as Newton said a compromise between inertia which makes the Earth want to fly off in a straight line and the Sun's gravity which keeps the Earth circling the Sun just like the light the Earth can be said to move inertially without any forces along a geodesic and the local space-time created by the sun's presence in other words curved space-time or even just curved space can create the appearance of a force even if there is none imagine two beings starting out on a journey obeying the law of inertia on what they think are two straight lines but since they're on the surface of a sphere they're really great circles after a while they start getting closer together as if drawn by some mysterious Force they might even call that Force gravity Einstein did exactly the opposite he eliminated the force of gravity it can be replaced by the curvature of space-time but Einstein now had created a mammoth dilemma how does mass cause space-time to curve he spent the most difficult seven years of his life from 1909 to 1916 working on the riddle and when he finished he had produced nothing less than a new theory of the cosmos it was a theory that was not designed to extend or expand Isaac Newton's Mechanical Universe instead it was designed to replace it completely but how could that be possible could it be that Newton's theory was wrong after all does the moon not fall one twentieth of an inch every second do planets not still sweep out equal areas in equal times and when a spacecraft leaves the Earth who's driving [Applause] [Music] course Newton's Laws work just as well as they always have in most places and most times Newton's universe and Einstein's Universe are so nearly identical that only the most precise instruments of science stretched to the limits of their abilities can detect the tiny differences [Music] but there are times and places in the universe where conditions are so extreme that only Einstein's theory can explain them for example when a very large star much larger than the sun exhausts its nuclear fuel it starts to collapse under its own gravity some of the masses blasted away in a violent explosion with no Force strong enough to oppose the collapse the inward fall of the rest continues until gravity becomes so intense that space-time itself is stretched and warped into a point of infinite curvature called a black hole like an ordinary projectile falling back to Earth light itself and absolutely anything else is drawn back by that awesome concentration of mass it takes an immense amount of mass crowded into a tiny space to create a black hole if black holes exist they are either remnants of collapsed giant stars or they may be primeval left over from the Big Bang the instant when the universe began of course it's tantalizing to try to imagine what it would be like to be inside of a black hole but we'll never know that is the ultimate impossibility oh you might arrange to fall into one if you really tried but then even if you survived there would be no way for you to let us know what you found once you got inside but here's something to think about when the universe was created in the Big Bang it started to expand rapidly clumps of matter condensed into galaxies but those galaxies are flying away from each other at great speed even today but that expansion does slow down with time after all the galaxies do attract each other by means of gravity in fact if the density of matter in the universe is high enough that expansion will not continue forever Sunday the universe will start Contracting again it'll become smaller and smaller approaching another cataclysmic event which is the exact reverse of the Big Bang that event has a name in cosmology too it's called the Big Crunch now we don't know if there's enough matter in the universe to cause that to happen but let's suppose that there is in that case nothing will ever escape that contraction not even light itself but if nothing not even light can escape why that's exactly the way we describe the inside of a black hole it's possible that we already are inside a black hole it's possible that our entire universe is the inside of a black hole in somebody else's Universe now it seems to me that that's a big enough idea to keep you busy until the next time I see you Stein's general theory of relativity replaces Gravity by the curvature of space-time The more mass of an object the greater the curvature of space-time around an object a black hole is an object for which space-time is so worked that nothing can escape from it the time has come the teacher said to tie up many threads how Tico's Claws and Kepler's laws just tore the Greeks to shreds why Einstein's space in Newton's place is loose in many heads [Music] foreign [Music] Annenberg media for information about this and other Annenberg media programs call 1-800 learner and visit us at www.learner.org