1 00:00:00,000 --> 00:00:07,560 Hi, I'm Jennifer Pulley, and welcome to NASA Connect, the show that connects you to math, 2 00:00:07,560 --> 00:00:10,680 science, technology, and NASA. 3 00:00:10,680 --> 00:00:15,520 Today, we are at NASA Kennedy Space Center on the east coast of Florida, and behind me 4 00:00:15,520 --> 00:00:19,000 is the Vehicle Assembly Building, or VAB. 5 00:00:19,000 --> 00:00:23,400 This is where NASA assembles all the components of the space shuttle system. 6 00:00:23,400 --> 00:00:28,600 Kennedy Space Center is also a site where NASA launches satellites that study the Earth 7 00:00:28,600 --> 00:00:30,120 and our solar system. 8 00:00:30,120 --> 00:00:35,960 In fact, the satellite Voyager 1, which was launched right here back in 1977, is very 9 00:00:35,960 --> 00:00:38,240 close to leaving our solar system. 10 00:00:38,240 --> 00:00:43,200 It's over 13 billion kilometers, or 8 billion miles, from Earth. 11 00:00:43,200 --> 00:00:44,680 Can you imagine that? 12 00:00:44,680 --> 00:00:46,680 Thirteen billion kilometers? 13 00:00:46,680 --> 00:00:47,680 Whew! 14 00:00:47,680 --> 00:00:49,880 It would be hard to count that high. 15 00:00:49,880 --> 00:00:57,320 Just look at all the digits that 13 billion represents. 16 00:00:57,320 --> 00:01:03,720 I don't know about you, but it's hard for me to imagine just how far away 13 billion 17 00:01:03,720 --> 00:01:04,920 kilometers is. 18 00:01:04,920 --> 00:01:10,680 I mean, how large is the solar system? 19 00:01:10,680 --> 00:01:19,080 It would probably make more sense to us if we could see a scale model of the solar system. 20 00:01:19,080 --> 00:01:23,960 This would give a better understanding of how far away Voyager 1, or the other planets 21 00:01:23,960 --> 00:01:28,160 in the solar system, are from Earth. 22 00:01:28,160 --> 00:01:33,920 The focus of today's program is to learn why we use scale models to determine the size 23 00:01:33,920 --> 00:01:37,960 and distance of objects in our solar system and beyond. 24 00:01:37,960 --> 00:01:43,680 In order to learn how to scale the solar system, we must first understand the concept of scaling. 25 00:01:43,680 --> 00:01:48,720 During the course of the program, you will be asked to answer several inquiry-based questions. 26 00:01:48,720 --> 00:01:52,620 After the questions appear on the screen, your teacher will pause the program to allow 27 00:01:52,620 --> 00:01:55,740 you time to answer and discuss the questions. 28 00:01:55,740 --> 00:01:59,340 This is your time to explore and become critical thinkers. 29 00:01:59,340 --> 00:02:04,460 Students working in groups, take a few minutes to answer the following questions. 30 00:02:04,460 --> 00:02:08,140 What does it mean to scale? 31 00:02:08,140 --> 00:02:14,260 Why is it sometimes necessary to use scale models or drawings? 32 00:02:14,260 --> 00:02:19,300 List some math terms associated with scale models or drawings. 33 00:02:19,300 --> 00:02:23,260 It's now time to pause the program and answer the questions. 34 00:02:23,260 --> 00:02:30,780 A scale model or drawing is used to represent an object that is too large or too small to 35 00:02:30,780 --> 00:02:34,340 be drawn or built at actual size. 36 00:02:34,340 --> 00:02:40,100 The scale gives the ratio of the measurements in the model or drawing to the measurements 37 00:02:40,100 --> 00:02:42,100 of the actual object. 38 00:02:42,100 --> 00:02:48,100 Remember guys, a ratio is a fraction that is used to compare the size of two numbers 39 00:02:48,100 --> 00:02:49,100 to each other. 40 00:02:49,100 --> 00:02:50,700 Let's take a look at an example. 41 00:02:50,700 --> 00:02:54,780 One of the most common types of scale drawings is a map. 42 00:02:54,780 --> 00:03:00,260 Maps are very useful when planning a trip, whether it is across town or across the country. 43 00:03:00,260 --> 00:03:05,740 Norbert and Zot are planning to drive from NASA Kennedy Space Center to Washington, D.C. 44 00:03:05,740 --> 00:03:10,140 Norbert wants to estimate the distance he and Zot will travel. 45 00:03:10,140 --> 00:03:16,140 The scale on Norbert's map reads 1 centimeter equals 100 kilometers. 46 00:03:16,180 --> 00:03:21,660 How can he estimate the distance in kilometers from Kennedy Space Center to Washington, D.C. 47 00:03:21,660 --> 00:03:23,540 using the given scale? 48 00:03:23,540 --> 00:03:29,540 The scale can be written as the fraction 1 centimeter over 100 kilometers. 49 00:03:29,540 --> 00:03:36,460 The first number, 1 centimeter, represents the map distance and the second number, 100 50 00:03:36,460 --> 00:03:39,740 kilometers, represents the actual distance. 51 00:03:39,740 --> 00:03:45,700 First, using a metric ruler and the given map, measure the linear distance from Kennedy 52 00:03:45,700 --> 00:03:48,700 Space Center to Washington, D.C. 53 00:03:48,700 --> 00:03:54,900 On Norbert's map, this distance is approximately 13 and a half centimeters. 54 00:03:54,900 --> 00:03:59,220 Now we have all the information we need to set up our proportion. 55 00:03:59,220 --> 00:04:04,260 Remember guys, a proportion is a pair of equal ratios. 56 00:04:04,260 --> 00:04:11,180 The first ratio is the map scale and the second ratio is the distance from Kennedy Space Center 57 00:04:11,180 --> 00:04:13,180 to Washington, D.C. 58 00:04:13,500 --> 00:04:17,660 Let's set these two ratios equal to each other. 59 00:04:17,660 --> 00:04:21,620 N represents the distance that we are trying to calculate. 60 00:04:21,620 --> 00:04:29,460 This proportion can be read as 1 centimeter is to 100 kilometers, as 13 and a half centimeters 61 00:04:29,460 --> 00:04:32,420 is to N kilometers. 62 00:04:32,420 --> 00:04:37,940 In a proportion, the cross products of the two ratios are equal. 63 00:04:37,940 --> 00:04:44,860 In other words, the product of the top value from the first ratio and the bottom value 64 00:04:44,860 --> 00:04:52,260 from the second ratio is equal to the product of the top value of the second ratio and the 65 00:04:52,260 --> 00:04:55,380 bottom value from the first ratio. 66 00:04:55,380 --> 00:05:03,060 We can write the cross product as 1 centimeter times N kilometers equals 100 kilometers times 67 00:05:03,060 --> 00:05:05,940 13 and a half centimeters. 68 00:05:05,940 --> 00:05:11,340 In multiplication, Norbert calculated the actual distance between Kennedy Space Center 69 00:05:11,340 --> 00:05:16,420 and Washington, D.C. to be about 1,350 kilometers. 70 00:05:16,420 --> 00:05:20,940 Students, here is an important point for you to remember. 71 00:05:20,940 --> 00:05:25,020 Proportions often include different units of measurements. 72 00:05:25,020 --> 00:05:32,500 Units must be the same across the top and bottom or down the left and right sides. 73 00:05:32,740 --> 00:05:39,580 If the units only match diagonally, then the ratios do not form a proportion. 74 00:05:39,580 --> 00:05:42,820 So guys, are you still having trouble trying to understand scaling? 75 00:05:42,820 --> 00:05:48,300 Okay, well, let's look at another example, this time using a scale model. 76 00:05:48,300 --> 00:05:52,580 Right behind me is a replica of the Space Shuttle and this right here, this is a scale 77 00:05:52,580 --> 00:05:54,220 model of the Space Shuttle. 78 00:05:54,220 --> 00:06:04,180 The actual Space Shuttle has a length of 37.2 meters, a height of 17.3 meters, and 79 00:06:04,180 --> 00:06:09,820 a width or wingspan of 23.8 meters. 80 00:06:09,820 --> 00:06:14,860 Now this shuttle model is a 1-100 scale of the actual Space Shuttle. 81 00:06:14,860 --> 00:06:19,100 Now that is 1 meter equals 100 meters. 82 00:06:19,140 --> 00:06:24,500 So using that scale, let's set up a proportion to calculate the length of this Space Shuttle 83 00:06:24,500 --> 00:06:25,940 model. 84 00:06:25,940 --> 00:06:31,420 The first ratio is the model scale and the second ratio is the length of the model to 85 00:06:31,420 --> 00:06:34,300 the actual shuttle length. 86 00:06:34,300 --> 00:06:37,580 N represents the length of the shuttle model. 87 00:06:37,580 --> 00:06:41,020 We set these two ratios equal to each other. 88 00:06:41,020 --> 00:06:47,420 Now remember, in a proportion, the cross products of the two ratios are equal. 89 00:06:47,420 --> 00:06:58,140 We write the cross product as 1 meter times 37.2 meters equals 100 meters times N meters. 90 00:06:58,140 --> 00:07:05,980 Dividing 37.2 by 100 gives us the length of the shuttle model, which is 0.372 meters or 91 00:07:05,980 --> 00:07:07,980 approximately 14 and a half inches. 92 00:07:07,980 --> 00:07:09,980 Well, that wasn't too bad, was it? 93 00:07:09,980 --> 00:07:13,260 Do you think you can handle the other two dimensions? 94 00:07:13,260 --> 00:07:22,900 So now it's your turn to calculate the height and the width or wingspan of the shuttle model 95 00:07:22,900 --> 00:07:24,380 using the given scale. 96 00:07:24,380 --> 00:07:29,540 Remember, the height of the actual shuttle is 17.3 meters. 97 00:07:29,540 --> 00:07:39,420 The width or wingspan is 23.8 meters and the scale is 1 meter equals 100 meters. 98 00:07:39,420 --> 00:07:45,540 It's now time to pause the program to calculate the height and width of the shuttle model. 99 00:07:45,540 --> 00:07:47,740 So guys, how did you do? 100 00:07:47,740 --> 00:07:50,380 Let's check your answers with mine. 101 00:07:50,380 --> 00:07:57,100 Earlier we calculated the length of the shuttle model to be 0.372 meters. 102 00:07:57,100 --> 00:08:04,660 I calculated the height of the model to be 0.173 meters or approximately 7 inches and 103 00:08:04,780 --> 00:08:11,860 the width or wingspan to be 0.238 meters or approximately 9 and a half inches. 104 00:08:11,860 --> 00:08:13,580 Did you get the same answers? 105 00:08:13,580 --> 00:08:15,580 If you did, great job. 106 00:08:15,580 --> 00:08:17,940 And if you didn't, don't be discouraged. 107 00:08:17,940 --> 00:08:20,740 Just go back and check over your work carefully. 108 00:08:20,740 --> 00:08:25,140 Make sure you set up your proportions and multiplied correctly. 109 00:08:25,140 --> 00:08:29,380 You know, scientists and engineers learn a great deal from making mistakes.