1 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 2 00:00:07,380 --> 00:00:11,890 much more than that. Gravity predicts the formation of planets, explains why they are 3 00:00:11,890 --> 00:00:17,500 spherical and why the orbits of planets around the sun are elliptical. It helped us discover 4 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 5 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. 6 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 7 00:00:32,529 --> 00:00:35,440 us understand these diverse phenomena. 8 00:00:35,440 --> 00:00:39,850 This video is part of the Governing Rules video series. A small number of rules describe 9 00:00:39,850 --> 00:00:44,149 the physical and chemical interactions that are possible in our universe. 10 00:00:44,149 --> 00:00:50,519 Hello. My name is Nergis Mavalvala. I am a professor in the physics department at MIT, 11 00:00:50,519 --> 00:00:53,769 and today I'll be talking with you about gravity. 12 00:00:53,769 --> 00:00:58,890 After watching this video, you should be able to recognize several different expressions 13 00:00:58,890 --> 00:01:05,059 for gravity, and to analyze situations involving gravity in preparation for problem-solving. 14 00:01:05,059 --> 00:01:09,640 We also hope that you gain an appreciation for the universal nature of gravity and the 15 00:01:09,640 --> 00:01:12,730 many places its effects can be seen. 16 00:01:12,730 --> 00:01:17,110 There are three expressions of gravity that scientists find useful. We're going to talk 17 00:01:17,110 --> 00:01:23,120 about all three of them today: gravity near the earth's surface, Newton's universal law 18 00:01:23,120 --> 00:01:29,720 of gravity, and Einstein's gravitational field equations, which are the core of general relativity. 19 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 20 00:01:34,110 --> 00:01:39,190 the simplest item and build upward and outward from there. You should make sure that the 21 00:01:39,190 --> 00:01:42,560 first two equations are in your notes. 22 00:01:42,560 --> 00:01:48,310 Let's start with the basics: gravity near Earth's surface. In studying Newton's Laws 23 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 24 00:01:56,450 --> 00:02:02,060 gravity. The value is almost constant, so we use this small "g" constant to represent 25 00:02:02,060 --> 00:02:03,520 it. 26 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 27 00:02:10,360 --> 00:02:16,520 objects fall downward, that we have to work harder walking up a hill than down. 28 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 29 00:02:20,480 --> 00:02:28,100 experience. For instance, elevators use counterweights to ease the load on the motor. As gravity 30 00:02:28,110 --> 00:02:33,420 pulls on the counterweight, the tension it puts on the cable pulls the elevator upward 31 00:02:33,420 --> 00:02:39,480 and helps to balance the force of gravity on the elevator itself. 32 00:02:39,480 --> 00:02:46,030 Some older mountain railways also use counterbalancing, with one train car moving upward as the other 33 00:02:46,030 --> 00:02:48,280 moves down. 34 00:02:48,280 --> 00:02:53,010 Pile drivers are construction machines that rely on the pull of gravity to slam large 35 00:02:53,010 --> 00:03:00,010 weights into the ground, digging holes and driving foundations for buildings. 36 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 37 00:03:06,650 --> 00:03:11,459 the planets are spherical instead of, say, cube-shaped. It also can't explain the orbits 38 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 39 00:03:17,050 --> 00:03:21,800 gravity that can help us understand these things. 40 00:03:21,800 --> 00:03:27,110 Newton's law of universal gravitation is a powerful model that can explain many different 41 00:03:27,110 --> 00:03:31,430 phenomena. Let's dive right in. 42 00:03:31,430 --> 00:03:36,709 Unlike the most basic view of gravity, in which it pulls straight down, leaving Canadians 43 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 44 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. 45 00:03:51,050 --> 00:03:56,099 Because the gravitational force pulls equally in all directions, large bodies in space tend 46 00:03:56,099 --> 00:04:03,099 to be spherical. The Sun, all planets, and even larger moons tend towards a spherical 47 00:04:03,130 --> 00:04:04,950 shape for this reason. 48 00:04:04,950 --> 00:04:11,069 Newton's law of gravity also means that all objects are pulled toward each other, such 49 00:04:11,069 --> 00:04:16,839 as planets toward the sun. By solving the differential equations that come from this 50 00:04:16,839 --> 00:04:22,370 law, we can obtain the elliptical orbits that all planets have as they move around their 51 00:04:22,370 --> 00:04:23,219 stars. 52 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, 53 00:04:29,229 --> 00:04:36,229 to Pluto's elongated orbit, to comets that swing far out of the solar system. 54 00:04:36,479 --> 00:04:42,099 The smaller pulls that planets have toward each other can be useful too. They're what 55 00:04:42,099 --> 00:04:48,029 allowed us to discover Neptune, by looking at the disturbances in the orbit of Uranus. 56 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 57 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 58 00:05:01,439 --> 00:05:06,699 side, in a phenomenon called tidal forces. 59 00:05:06,699 --> 00:05:13,699 Our own galaxy, the Milky Way, has gravitational interactions with other smaller galaxies nearby. 60 00:05:13,999 --> 00:05:20,620 Its disc-like shape and spiral arms may have come from tearing those galaxies apart. 61 00:05:20,620 --> 00:05:25,930 We see other galaxies colliding in many other places in the universe, as gravity pulls them 62 00:05:25,930 --> 00:05:30,259 together. It actually seems to be fairly common. 63 00:05:30,259 --> 00:05:36,819 Speaking of galaxies, Newton's law also tells us how fast galaxies should rotate. We can 64 00:05:36,819 --> 00:05:41,860 predict a particular A curve for how fast the stars will be moving according to their 65 00:05:41,860 --> 00:05:48,009 distance from the center - that's curve A here. But when we measure the actual velocity 66 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 67 00:05:54,419 --> 00:05:59,990 of dark matter - some sort of substance that produces gravity but doesn't interact with 68 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 69 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! 70 00:06:13,430 --> 00:06:18,129 Physicists are still trying to figure out what this dark matter might be. 71 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 72 00:06:23,669 --> 00:06:30,669 - we can look at clusters of galaxies, superclusters, and even the entire visible universe. 73 00:06:32,060 --> 00:06:34,360 Fair enough. 74 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 75 00:06:39,529 --> 00:06:45,699 see massive structures of galaxies, like this Great Wall here, or these empty intergalactic 76 00:06:45,699 --> 00:06:48,419 voids. 77 00:06:48,419 --> 00:06:53,240 In recent years supercomputers have become powerful enough to simulate the formation 78 00:06:53,240 --> 00:06:59,210 of such structures in our universe. Here you can see the result of one such simulation, 79 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 80 00:07:05,659 --> 00:07:12,110 law of gravity, superclusters of galaxies and intergalactic voids appear naturally! 81 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 82 00:07:19,069 --> 00:07:24,249 out to some of the most distant objects we can see. 83 00:07:24,249 --> 00:07:30,270 But it couldn't handle everything, and that's why we need this next part. 84 00:07:30,270 --> 00:07:35,759 The most powerful model of gravity is described by Einstein's field equations, which are the 85 00:07:35,759 --> 00:07:41,589 core of general relativity. This equation may not make sense to you now, but later in 86 00:07:41,589 --> 00:07:47,699 your career you may learn about something called tensors, which are related to vectors. 87 00:07:47,699 --> 00:07:53,899 In this equation, tensors describe the gravitational effects of both matter and energy on all 88 00:07:53,899 --> 00:08:01,639 things around them. This equation is very hard to solve, even for experts. Some of the 89 00:08:01,649 --> 00:08:06,830 cases we know how to solve tell us about black holes and gravitational lensing, and give 90 00:08:06,830 --> 00:08:13,169 us insight into the universe when it was very young. 91 00:08:13,169 --> 00:08:18,520 Black holes were one of the first solutions to Einstein's field equations. You've probably 92 00:08:18,520 --> 00:08:24,300 heard of black holes, which are objects so massive that they warp space and time, and 93 00:08:24,300 --> 00:08:27,589 even light cannot escape their gravitational pull. 94 00:08:27,589 --> 00:08:35,078 At the center of our galaxy, and of many large galaxies, are supermassive black holes. We 95 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. 96 00:08:42,149 --> 00:08:48,060 While black holes trap light, other massive objects can have an effect too. Light bends 97 00:08:48,060 --> 00:08:52,740 in its path as it moves past heavy objects like stars. 98 00:08:52,740 --> 00:08:57,880 This can lead to gravitational lensing, in which light from a distant object is bent 99 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 100 00:09:04,240 --> 00:09:06,630 even warped images. 101 00:09:06,630 --> 00:09:13,630 Einstein's field equations also include this lambda value: the cosmological constant. 102 00:09:13,779 --> 00:09:20,259 This value can be used to describe a universe that collapses or holds steady, expands slowly, 103 00:09:20,259 --> 00:09:25,949 or expands at an accelerating rate. Astronomers are working to measure this value, and we 104 00:09:25,949 --> 00:09:32,019 seem to be in the third case - a universe that expands faster and faster. 105 00:09:32,019 --> 00:09:36,959 Einstein's theory of gravity remains one of the best-tested and most accurate theories 106 00:09:36,959 --> 00:09:43,410 in all of science. It can explain everything that Newtonian gravity can and more, things 107 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 108 00:09:48,589 --> 00:09:54,790 the universe will end. You can see why people would be interested in studying it. 109 00:09:54,790 --> 00:10:00,860 These three gravitational equations describe a huge range of phenomena in our natural world, 110 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 111 00:10:06,180 --> 00:10:11,670 motivated to learn more about them. Understanding these laws and being able to use them will 112 00:10:11,670 --> 00:10:16,160 lead you to a greater appreciation of the natural world. 113 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. 114 00:10:21,740 --> 00:10:27,550 You will need paper and something to write with for this part of the video. 115 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 116 00:10:33,339 --> 00:10:35,310 these phenomena mathematically. 117 00:10:35,310 --> 00:10:42,230 We'll be giving you some situations that can be described through gravity. Your job, working 118 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 119 00:10:47,889 --> 00:10:50,110 solve a particular problem. 120 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 121 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 122 00:11:00,339 --> 00:11:06,379 important. We might also want to double-check the value for gravity on Earth. 123 00:11:06,379 --> 00:11:13,069 That example is pretty simple. Let's do a more complicated one. Given an asteroid headed 124 00:11:13,069 --> 00:11:18,860 toward Earth, and its velocity and location, which approach would we need to find out whether 125 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? 126 00:11:25,949 --> 00:11:31,509 To understand an object's trajectory we need to know about its starting point - the position 127 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 128 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 129 00:11:42,440 --> 00:11:46,860 will factor into the force applied on the asteroid. 130 00:11:46,860 --> 00:11:52,910 Some things are arbitrary choices - for instance, we can pick any coordinate system we like. 131 00:11:52,910 --> 00:11:57,819 Since gravity pulls objects together, we might want to choose polar coordinates centered 132 00:11:57,819 --> 00:12:00,199 on the Earth to make things easier. 133 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. 134 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 135 00:12:11,529 --> 00:12:16,089 our positions and velocities from the Earth's reference frame as if it were moving with 136 00:12:16,089 --> 00:12:21,600 constant velocity? Should we track the Earth as it moves in its orbit? 137 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 138 00:12:25,959 --> 00:12:27,790 to write them down. 139 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 140 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 141 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 142 00:12:43,819 --> 00:12:48,649 it - just write down what you would need to know in order to find a solution. 143 00:12:48,649 --> 00:12:52,591 Here are the problems. Thank you for watching our video, and good luck with your class.