WEBVTT 00:00:02.550 --> 00:00:07.380 You know gravity as the force that keeps us from falling off this planet. But it's so 00:00:07.380 --> 00:00:11.890 much more than that. Gravity predicts the formation of planets, explains why they are 00:00:11.890 --> 00:00:17.500 spherical and why the orbits of planets around the sun are elliptical. It helped us discover 00:00:17.500 --> 00:00:22.689 one of the planets in our own solar system, and the formation of Saturn’s rings. Gravity 00:00:22.689 --> 00:00:28.470 can bend and even trap light, and it governs some of the behavior of the universe itself. 00:00:28.470 --> 00:00:32.529 In this video, we’ll look at the different models of gravity and explore how each helps 00:00:32.529 --> 00:00:35.440 us understand these diverse phenomena. 00:00:35.440 --> 00:00:39.850 This video is part of the Governing Rules video series. A small number of rules describe 00:00:39.850 --> 00:00:44.149 the physical and chemical interactions that are possible in our universe. 00:00:44.149 --> 00:00:50.519 Hello. My name is Nergis Mavalvala. I am a professor in the physics department at MIT, 00:00:50.519 --> 00:00:53.769 and today I'll be talking with you about gravity. 00:00:53.769 --> 00:00:58.890 After watching this video, you should be able to recognize several different expressions 00:00:58.890 --> 00:01:05.059 for gravity, and to analyze situations involving gravity in preparation for problem-solving. 00:01:05.059 --> 00:01:09.640 We also hope that you gain an appreciation for the universal nature of gravity and the 00:01:09.640 --> 00:01:12.730 many places its effects can be seen. 00:01:12.730 --> 00:01:17.110 There are three expressions of gravity that scientists find useful. We're going to talk 00:01:17.110 --> 00:01:23.120 about all three of them today: gravity near the earth's surface, Newton's universal law 00:01:23.120 --> 00:01:29.720 of gravity, and Einstein's gravitational field equations, which are the core of general relativity. 00:01:29.720 --> 00:01:34.110 We'll be spending most of our time with the second one, but we're going to start with 00:01:34.110 --> 00:01:39.190 the simplest item and build upward and outward from there. You should make sure that the 00:01:39.190 --> 00:01:42.560 first two equations are in your notes. 00:01:42.560 --> 00:01:48.310 Let's start with the basics: gravity near Earth's surface. In studying Newton's Laws 00:01:48.310 --> 00:01:55.310 we all learn that F = ma. Near Earth's surface, that "a," acceleration, is provided by Earth's 00:01:56.450 --> 00:02:02.060 gravity. The value is almost constant, so we use this small "g" constant to represent 00:02:02.060 --> 00:02:03.520 it. 00:02:03.520 --> 00:02:10.360 We're all familiar with the most basic applications of gravity - that we stay on the ground, that 00:02:10.360 --> 00:02:16.520 objects fall downward, that we have to work harder walking up a hill than down. 00:02:16.520 --> 00:02:20.480 There are also many applications of gravity that are hidden from us in our day-to-day 00:02:20.480 --> 00:02:28.100 experience. For instance, elevators use counterweights to ease the load on the motor. As gravity 00:02:28.110 --> 00:02:33.420 pulls on the counterweight, the tension it puts on the cable pulls the elevator upward 00:02:33.420 --> 00:02:39.480 and helps to balance the force of gravity on the elevator itself. 00:02:39.480 --> 00:02:46.030 Some older mountain railways also use counterbalancing, with one train car moving upward as the other 00:02:46.030 --> 00:02:48.280 moves down. 00:02:48.280 --> 00:02:53.010 Pile drivers are construction machines that rely on the pull of gravity to slam large 00:02:53.010 --> 00:03:00.010 weights into the ground, digging holes and driving foundations for buildings. 00:03:00.709 --> 00:03:06.650 As useful as this simple view of gravity is, it's fairly limited - it can't explain why 00:03:06.650 --> 00:03:11.459 the planets are spherical instead of, say, cube-shaped. It also can't explain the orbits 00:03:11.459 --> 00:03:17.050 of the planets, or the action of the tides. Let's move to a more complex expression for 00:03:17.050 --> 00:03:21.800 gravity that can help us understand these things. 00:03:21.800 --> 00:03:27.110 Newton's law of universal gravitation is a powerful model that can explain many different 00:03:27.110 --> 00:03:31.430 phenomena. Let's dive right in. 00:03:31.430 --> 00:03:36.709 Unlike the most basic view of gravity, in which it pulls straight down, leaving Canadians 00:03:36.709 --> 00:03:42.790 to wonder why penguins don't fall off the planet, Newton's gravity shows that all objects 00:03:42.790 --> 00:03:49.790 are pulled toward each other's centers. Thus, we all stay firmly planted on Earth's surface. 00:03:51.050 --> 00:03:56.099 Because the gravitational force pulls equally in all directions, large bodies in space tend 00:03:56.099 --> 00:04:03.099 to be spherical. The Sun, all planets, and even larger moons tend towards a spherical 00:04:03.130 --> 00:04:04.950 shape for this reason. 00:04:04.950 --> 00:04:11.069 Newton's law of gravity also means that all objects are pulled toward each other, such 00:04:11.069 --> 00:04:16.839 as planets toward the sun. By solving the differential equations that come from this 00:04:16.839 --> 00:04:22.370 law, we can obtain the elliptical orbits that all planets have as they move around their 00:04:22.370 --> 00:04:23.219 stars. 00:04:23.219 --> 00:04:29.229 We can get all sorts of ellipses, from the near-circles we see in the inner planets, 00:04:29.229 --> 00:04:36.229 to Pluto's elongated orbit, to comets that swing far out of the solar system. 00:04:36.479 --> 00:04:42.099 The smaller pulls that planets have toward each other can be useful too. They're what 00:04:42.099 --> 00:04:48.029 allowed us to discover Neptune, by looking at the disturbances in the orbit of Uranus. 00:04:48.029 --> 00:04:55.029 Newton's law of gravity also gave us new insight into events on Earth, like our tides. Objects 00:04:56.449 --> 00:05:01.439 on one side of the Earth are pulled more strongly toward the moon than objects on the other 00:05:01.439 --> 00:05:06.699 side, in a phenomenon called tidal forces. 00:05:06.699 --> 00:05:13.699 Our own galaxy, the Milky Way, has gravitational interactions with other smaller galaxies nearby. 00:05:13.999 --> 00:05:20.620 Its disc-like shape and spiral arms may have come from tearing those galaxies apart. 00:05:20.620 --> 00:05:25.930 We see other galaxies colliding in many other places in the universe, as gravity pulls them 00:05:25.930 --> 00:05:30.259 together. It actually seems to be fairly common. 00:05:30.259 --> 00:05:36.819 Speaking of galaxies, Newton's law also tells us how fast galaxies should rotate. We can 00:05:36.819 --> 00:05:41.860 predict a particular A curve for how fast the stars will be moving according to their 00:05:41.860 --> 00:05:48.009 distance from the center - that's curve A here. But when we measure the actual velocity 00:05:48.009 --> 00:05:54.419 of those stars, we get B curve B instead. This was our first indication of the existence 00:05:54.419 --> 00:05:59.990 of dark matter - some sort of substance that produces gravity but doesn't interact with 00:05:59.990 --> 00:06:06.710 light. We couldn't see it, but we could see its effects. Dark matter surrounds and is 00:06:06.710 --> 00:06:13.430 part of every galaxy. In fact, there's so much that it makes up most of the galaxy! 00:06:13.430 --> 00:06:18.129 Physicists are still trying to figure out what this dark matter might be. 00:06:18.129 --> 00:06:23.669 We can also use Newton's law of gravity to look beyond the structure of individual galaxies 00:06:23.669 --> 00:06:30.669 - we can look at clusters of galaxies, superclusters, and even the entire visible universe. 00:06:32.060 --> 00:06:34.360 Fair enough. 00:06:34.369 --> 00:06:39.529 When we do look at things on that scale, where individual galaxies become just dots, we can 00:06:39.529 --> 00:06:45.699 see massive structures of galaxies, like this Great Wall here, or these empty intergalactic 00:06:45.699 --> 00:06:48.419 voids. 00:06:48.419 --> 00:06:53.240 In recent years supercomputers have become powerful enough to simulate the formation 00:06:53.240 --> 00:06:59.210 of such structures in our universe. Here you can see the result of one such simulation, 00:06:59.210 --> 00:07:05.659 with each speck of light representing a galaxy worth of stars or dark matter. Using Newton's 00:07:05.659 --> 00:07:12.110 law of gravity, superclusters of galaxies and intergalactic voids appear naturally! 00:07:12.110 --> 00:07:19.069 A real triumph of Newton's approach was that it worked for everything from people on Earth 00:07:19.069 --> 00:07:24.249 out to some of the most distant objects we can see. 00:07:24.249 --> 00:07:30.270 But it couldn't handle everything, and that's why we need this next part. 00:07:30.270 --> 00:07:35.759 The most powerful model of gravity is described by Einstein's field equations, which are the 00:07:35.759 --> 00:07:41.589 core of general relativity. This equation may not make sense to you now, but later in 00:07:41.589 --> 00:07:47.699 your career you may learn about something called tensors, which are related to vectors. 00:07:47.699 --> 00:07:53.899 In this equation, tensors describe the gravitational effects of both matter and energy on all 00:07:53.899 --> 00:08:01.639 things around them. This equation is very hard to solve, even for experts. Some of the 00:08:01.649 --> 00:08:06.830 cases we know how to solve tell us about black holes and gravitational lensing, and give 00:08:06.830 --> 00:08:13.169 us insight into the universe when it was very young. 00:08:13.169 --> 00:08:18.520 Black holes were one of the first solutions to Einstein's field equations. You've probably 00:08:18.520 --> 00:08:24.300 heard of black holes, which are objects so massive that they warp space and time, and 00:08:24.300 --> 00:08:27.589 even light cannot escape their gravitational pull. 00:08:27.589 --> 00:08:35.078 At the center of our galaxy, and of many large galaxies, are supermassive black holes. We 00:08:35.078 --> 00:08:42.078 can see their effects as stars near the center of the galaxy whip around them at high speed. 00:08:42.149 --> 00:08:48.060 While black holes trap light, other massive objects can have an effect too. Light bends 00:08:48.060 --> 00:08:52.740 in its path as it moves past heavy objects like stars. 00:08:52.740 --> 00:08:57.880 This can lead to gravitational lensing, in which light from a distant object is bent 00:08:57.880 --> 00:09:04.240 around both sides of a heavy object. This lets us see multiple views of an object, or 00:09:04.240 --> 00:09:06.630 even warped images. 00:09:06.630 --> 00:09:13.630 Einstein's field equations also include this lambda value: the cosmological constant. 00:09:13.779 --> 00:09:20.259 This value can be used to describe a universe that collapses or holds steady, expands slowly, 00:09:20.259 --> 00:09:25.949 or expands at an accelerating rate. Astronomers are working to measure this value, and we 00:09:25.949 --> 00:09:32.019 seem to be in the third case - a universe that expands faster and faster. 00:09:32.019 --> 00:09:36.959 Einstein's theory of gravity remains one of the best-tested and most accurate theories 00:09:36.959 --> 00:09:43.410 in all of science. It can explain everything that Newtonian gravity can and more, things 00:09:43.410 --> 00:09:48.589 we wouldn't otherwise be able to predict or understand, it can even make predictions about how 00:09:48.589 --> 00:09:54.790 the universe will end. You can see why people would be interested in studying it. 00:09:54.790 --> 00:10:00.860 These three gravitational equations describe a huge range of phenomena in our natural world, 00:10:00.860 --> 00:10:06.180 from things in our own home to the farthest objects we can see. I hope that you will be 00:10:06.180 --> 00:10:11.670 motivated to learn more about them. Understanding these laws and being able to use them will 00:10:11.670 --> 00:10:16.160 lead you to a greater appreciation of the natural world. 00:10:16.160 --> 00:10:21.740 Now it's time to take some of the examples we saw and examine them in a different way. 00:10:21.740 --> 00:10:27.550 You will need paper and something to write with for this part of the video. 00:10:27.550 --> 00:10:33.339 Knowing that gravity causes a particular phenomenon is good, but we also want to know how to describe 00:10:33.339 --> 00:10:35.310 these phenomena mathematically. 00:10:35.310 --> 00:10:42.230 We'll be giving you some situations that can be described through gravity. Your job, working 00:10:42.230 --> 00:10:47.889 in pairs or groups of three, is to determine what information you would want in order to 00:10:47.889 --> 00:10:50.110 solve a particular problem. 00:10:50.110 --> 00:10:55.319 For instance, let's say that we drop a rock and want to know how long it would take to 00:10:55.319 --> 00:11:00.339 fall. We would want to know the rock's initial height and whether air resistance would be 00:11:00.339 --> 00:11:06.379 important. We might also want to double-check the value for gravity on Earth. 00:11:06.379 --> 00:11:13.069 That example is pretty simple. Let's do a more complicated one. Given an asteroid headed 00:11:13.069 --> 00:11:18.860 toward Earth, and its velocity and location, which approach would we need to find out whether 00:11:18.860 --> 00:11:25.860 the asteroid will hit the Earth, and if so, how long it will be before the impact? 00:11:25.949 --> 00:11:31.509 To understand an object's trajectory we need to know about its starting point - the position 00:11:31.509 --> 00:11:37.949 of the asteroid as compared to Earth. We also want to know how fast it's moving and in what 00:11:37.949 --> 00:11:42.440 direction. We'll need to know the mass of the Earth and of the asteroid, because both 00:11:42.440 --> 00:11:46.860 will factor into the force applied on the asteroid. 00:11:46.860 --> 00:11:52.910 Some things are arbitrary choices - for instance, we can pick any coordinate system we like. 00:11:52.910 --> 00:11:57.819 Since gravity pulls objects together, we might want to choose polar coordinates centered 00:11:57.819 --> 00:12:00.199 on the Earth to make things easier. 00:12:00.199 --> 00:12:05.769 Finally, there are some things that we'll want to know that are of a more general nature. 00:12:05.769 --> 00:12:11.529 For instance, how do we take into account gravity from the Sun? Can we measure all of 00:12:11.529 --> 00:12:16.089 our positions and velocities from the Earth's reference frame as if it were moving with 00:12:16.089 --> 00:12:21.600 constant velocity? Should we track the Earth as it moves in its orbit? 00:12:21.600 --> 00:12:25.959 These are things we might not know when we start to solve a problem, and it's important 00:12:25.959 --> 00:12:27.790 to write them down. 00:12:27.790 --> 00:12:33.230 Now it's your turn. We'll put four problems on the screen. Your instructor will assign 00:12:33.230 --> 00:12:38.529 problems to different groups. Each group's job is to write up a list of what information 00:12:38.529 --> 00:12:43.819 you would need in order to solve the problem. Remember, you don't need to actually solve 00:12:43.819 --> 00:12:48.649 it - just write down what you would need to know in order to find a solution. 00:12:48.649 --> 00:12:52.591 Here are the problems. Thank you for watching our video, and good luck with your class.