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NASA Connect Video containing six segments as described below. NASA Connect segment explaining how scientists determined the distance between the earth and the sun. The video also explores the geometric technique called parallax. NASA Connect segment involving students in a classroom activity that uses graphing, measurement, and ratios to construct a scaled model of the Solar System. NASA Connect segment exploring what it means to scale and why scientists use scale models and drawings. The video also explores math terms that are associated with scale models and drawings. NASA Connect segment that explores how astronomers and scientists use astronomical units in measuring distances in the Solar System. NASA Connect segment that challenges students to participate in an activity to scale the universe. The video involves students in a proposal to determine a new baseline distance to use for an astronomical unit. NASA Connect segment that explains the Venus Transit and compares it to a solar eclipse.
Hi, I'm Christy Carlson Romano.
00:00:00
You know me as Wren Stevens from Disney Channel's hit TV series, Even Stevens.
00:00:13
On this episode of NASA Connect, you'll learn about the concept of scaling and the math
00:00:17
principles associated with it.
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You'll also learn about the transit of Venus, an astronomical event that is way cool.
00:00:23
So stay tuned, because Jennifer Pulley, your host, is going to take you on another exciting
00:00:27
episode of NASA Connect.
00:00:31
Hi, I'm Jennifer Pulley, and welcome to NASA Connect, the show that connects you to math,
00:00:57
science, technology, and NASA.
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Today, we are at NASA Kennedy Space Center on the east coast of Florida, and behind me
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is the Vehicle Assembly Building, or VAB.
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This is where NASA assembles all the components of the space shuttle system.
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Kennedy Space Center is also a site where NASA launches satellites that study the Earth
00:01:24
and our solar system.
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In fact, the satellite Voyager 1, which was launched right here back in 1977, is very
00:01:31
close to leaving our solar system.
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It's over 13 billion kilometers, or 8 billion miles, from Earth.
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Can you imagine that?
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Thirteen billion kilometers?
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Whew, it would be hard to count that high.
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But look at all the digits that 13 billion represents.
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I don't know about you, but it's hard for me to imagine just how far away 13 billion
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kilometers is.
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I mean, how large is the solar system?
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It would probably make more sense to us if we could see a scale model of the solar system.
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This would give a better understanding of how far away Voyager 1 or the other planets
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in the solar system are from Earth.
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The focus of today's program is to learn why we use scale models to determine the size
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and distance of objects in our solar system and beyond.
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In order to learn how to scale the solar system, we must first understand the concept of scaling.
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During the course of the program, you will be asked to answer several inquiry-based questions.
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After the questions appear on the screen, your teacher will pause the program to allow
00:02:49
you time to answer and discuss the questions.
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This is your time to explore and become critical thinkers.
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Students working in groups take a few minutes to answer the following questions.
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What does it mean to scale?
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Why is it sometimes necessary to use scale models or drawings?
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List some math terms associated with scale models or drawings.
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It's now time to pause the program and answer the questions.
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A scale model or drawing is used to represent an object that is too large or too small to
00:03:24
be drawn or built at actual size.
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The scale gives the ratio of the measurements in the model or drawing to the measurements
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of the actual object.
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Remember guys, a ratio is a fraction that is used to compare the size of two numbers
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to each other.
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Let's take a look at an example.
00:03:50
One of the most common types of scale drawings is a map.
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Maps are very useful when planning a trip, whether it is across town or across the country.
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Norbert and Zot are planning to drive from NASA Kennedy Space Center to Washington, D.C.
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Norbert wants to estimate the distance he and Zot will travel.
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The scale on Norbert's map reads 1 centimeter equals 100 kilometers.
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How can he estimate the distance in kilometers from Kennedy Space Center to Washington, D.C.
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using the given scale?
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The scale can be written as the fraction 1 centimeter over 100 kilometers.
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The first number, 1 centimeter, represents the map distance and the second number, 100
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kilometers, represents the actual distance.
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First, using a metric ruler and the given map, measure the linear distance from Kennedy
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Space Center to Washington, D.C.
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On Norbert's map, this distance is approximately 13 and a half centimeters.
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Now we have all the information we need to set up our proportion.
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Remember guys, a proportion is a pair of equal ratios.
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The first ratio is the map scale and the second ratio is the distance from Kennedy
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Space Center to Washington, D.C.
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Let's set these two ratios equal to each other.
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N represents the distance that we are trying to calculate.
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This proportion can be read as 1 centimeter is to 100 kilometers as 13 and a half centimeters
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is to N kilometers.
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In a proportion, the cross products of the two ratios are equal.
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In other words, the product of the top value from the first ratio and the bottom value
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from the second ratio is equal to the product of the top value of the second ratio and the
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bottom value from the first ratio.
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We can write the cross product as 1 centimeter times N kilometers equals 100 kilometers times
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13 and a half centimeters.
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Using multiplication, Norbert calculated the actual distance between Kennedy Space Center
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and Washington, D.C. to be about 1,350 kilometers.
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Students, here is an important point for you to remember.
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Proportions often include different units of measurements.
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Units must be the same across the top and bottom or down the left and right sides.
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If the units only match diagonally, then the ratios do not form a proportion.
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So guys, are you still having trouble trying to understand scaling?
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Okay, well let's look at another example, this time using a scale model.
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Right behind me is a replica of the space shuttle and this right here, this is a scale
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model of the space shuttle.
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The actual space shuttle has a length of 37.2 meters, a height of 17.3 meters, and
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a width or wingspan of 23.8 meters.
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Now this shuttle model is a 1,100 scale of the actual space shuttle.
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Now that is 1 meter equals 100 meters.
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So using that scale, let's set up a proportion to calculate the length of this space shuttle
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model.
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The first ratio is the model scale and the second ratio is the length of the model to
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the actual shuttle length.
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N represents the length of the shuttle model.
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We set these two ratios equal to each other.
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Now remember, in our proportion, the cross products of the two ratios are equal.
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We write the cross product as 1 meter times 37.2 meters equals 100 meters times N meters.
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Dividing 37.2 by 100 gives us the length of the shuttle model, which is 0.372 meters or
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approximately 14 and a half inches.
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Well, that wasn't too bad, was it?
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Do you think you can handle the other two dimensions?
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So now it's your turn to calculate the height and the width or wingspan of the shuttle model
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using the given scale.
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Remember, the height of the actual shuttle is 17.3 meters.
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The width or wingspan is 23.8 meters, and the scale is 1 meter equals 100 meters.
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It's now time to pause the program to calculate the height and width of the shuttle model.
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So guys, how did you do?
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Let's check your answers with mine.
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Earlier, we calculated the length of the shuttle model to be 0.372 meters.
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I calculated the height of the model to be 0.173 meters or approximately 7 inches and
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the width or wingspan to be 0.238 meters or approximately 9 and a half inches.
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Did you get the same answers?
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If you did, great job.
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And if you didn't, don't be discouraged.
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Just go back and check over your work carefully.
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Make sure you set up your proportions and multiplied correctly.
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You know, scientists and engineers learn a great deal from making mistakes.
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Now that you have a better understanding of scaling, let's turn our attention to the focus
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of today's program, which is scaling the solar system.
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Dr. Stan Odenwald, an astronomer and scientist at NASA Goddard Space Flight Center, has a scoop.
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Thanks, Jennifer.
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When we talk about the distances between points of interest, we instinctively use units that
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make sense to us and that are convenient.
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For example, what unit of measure would you use to describe the distance from Washington,
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D.C. to Los Angeles, California?
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Would you use miles, inches, kilometers, or meters?
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What about your height?
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Would you measure it in inches or feet?
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And how about the width of your classroom?
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Do you use kilometers, meters, or feet?
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You can choose any unit of measure you wish, as long as it's convenient for everyone to
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understand.
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When describing distances at the scale of the solar system, even units like miles and
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kilometers lead to numbers that are in the millions or the billions, and that makes it
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very hard to understand them.
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For example, the distance between the Earth and the Sun is about 149 million kilometers.
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Between the Sun and Pluto, the distance is about 5.9 billion kilometers.
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But suppose we wanted to compare these two numbers.
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It's not easy to see that Pluto is about 40 times as far from the Sun as Earth is.
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It would make sense to use a smaller scale in order to get a better idea of the distances
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between the planets.
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To come up with that scale, we have to define a baseline.
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The baseline that astronomers use is the distance between the Earth and the Sun.
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This distance is known as the astronomical unit.
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The astronomical unit, or AU, represents the distance between the Earth and the Sun, which
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is about 93 million miles.
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The astronomical unit is the baseline that astronomers use to determine the distances
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to the planets in our solar system and to the stars beyond.
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So let's have a look at the scale of the solar system, where one astronomical unit equals
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93 million miles.
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Based on the astronomical unit, it's easy to compare the distances between all the other
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objects in the solar system.
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The accompanying chart shows the distances to the planets from the Sun in terms of astronomical
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units.
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Let's look at Mars.
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We can quickly see that Mars is one and a half times further away from the Sun than
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Earth is.
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So how far is Mars from the Sun in miles?
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Remember the process Jennifer demonstrated earlier in the program to solve problems involving
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scaling?
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We can solve the Mars distance problem using a proportion.
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The first ratio is the scale, and the second ratio is the distance of Mars to the Sun.
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And miles represents the distance from Mars to the Sun.
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After setting these ratios equal to each other, let's find the cross products.
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The equation becomes 1 times n equals 93 million times 1.52.
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Multiplying, we get the distance from Mars to the Sun to be approximately 141 million
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miles.
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Using the astronomical unit instead of the mile or the kilometer makes it easier to compare
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the distances between the planets and the Sun.
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For example, it's easier to remember that Mars is one and a half times further away
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from the Sun than the Earth than it is to remember that it's 48 million miles farther
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away from the Sun than the Earth.
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If you recall from earlier in the program, the Voyager spacecraft is 8 billion miles
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or 13 billion kilometers from the Earth.
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It's at the far edge of our solar system, ready to head out into interstellar space.
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Based on what you've learned about scaling and the astronomical unit, can you estimate
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the distance of Voyager 1 from the Earth in astronomical units?
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Working with a partner, take a few minutes and see if you can solve this problem.
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Voyager 1 is over 8 billion miles away from Earth.
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Guess how far, in astronomical units, Voyager 1 is from the Earth.
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Remember the scale is 1 astronomical unit equals 93 million miles.
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Teachers, you may now pause the program so students can answer the problem.
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Okay, so what did you come up with?
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If you said that Voyager was 86 astronomical units away from the Earth, you're correct.
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Do you have a sense for how far that is?
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The planet Pluto is 40 astronomical units away from the Earth, so that means Voyager
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is twice as far away from the Earth as the planet Pluto.
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Suppose that Voyager 1 were stationary and you were able to ride in a car traveling at
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55 miles per hour to get to it.
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The trip would take you over 16,000 years just to reach the satellite.
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That would be quite a lengthy and expensive vacation.
00:14:00
Jennifer, I think the students are ready for that hands-on activity now.
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Could you send them back to me when you're finished?
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I have a real tough question for them to answer.
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Thanks, Sten.
00:14:13
We'll get back to you a little later in the program.
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But first, students from Brewster Middle School at Camp Lejeune, North Carolina, will preview
00:14:17
this program's hands-on activity.
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Hi, NASA Connect has asked us to show you this program's hands-on activity.
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In this activity, you will use graphing, measurement, and ratios to construct a scaled model of
00:14:31
the solar system and relate each planet to the sun.
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And you will explore the scales needed to represent the size of the planets and the
00:14:42
distances to the sun.
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You can download a copy of the educator guide containing directions and a materials list
00:14:49
from the NASA Connect website.
00:14:53
Working in groups, students will complete the activity by using the scale model chart
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and the planet templates.
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Each group will be assigned a planet.
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Cut out your assigned planet using the planet template.
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The scale for this activity is 1 toilet paper sheet equals 30,102,900 kilometers.
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Using the scale, students complete column 4 on the scale model chart.
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Remember the math concepts you learned earlier in the program?
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This is your chance to put your math skills to the test.
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Next, you will complete column 5 on the scale model chart.
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The scale needed to complete this column is 1 AU or astronomical unit equals 5 toilet
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paper sheets.
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Groups should check each other's work to make sure all values are correct.
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After completing the scale model chart, each group should roll out the number of toilet
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paper sheets needed for its assigned planet.
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Now it's time to head to the staging area.
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This could be in a gym, hallway, or even outside.
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Place the sun in a central position.
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Students attach your pre-measured toilet paper strip to the sun and let it extend outward
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in various directions.
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Don't forget to tape your assigned planet on the end of the strip.
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You will need about 23 meters or 75 feet in one direction.
00:16:12
Based on your solar system model, you will be asked to answer several critical thinking
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questions.
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Graphing is a great way to visually represent data.
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Each group will construct and analyze two graphs using an appropriate type of graph
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and scale of your choice.
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Be careful with the type of graph you choose.
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Don't forget to check out the web activity for this program.
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You can download it from the NASA Connect website.
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Great job Brewster Middle School.
00:16:46
Okay, now that you guys have a preview of this program's hands-on activity, now it's
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time to pause the program and see if you can construct a scale model of the solar system.
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So how was the activity?
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Hopefully it helped reinforce the math concepts you learned earlier in today's program.
00:17:01
Now let's review.
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In the beginning of the program, we talked about the importance of scaling, especially
00:17:08
when it comes to maps and models.
00:17:12
You learned that fractions, decimals, ratios, and proportions are all important math concepts
00:17:15
when dealing with scales.
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STEN introduced you to the astronomical unit, the unit used to scale the solar system.
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Later in the program, I have an interesting challenge for you.
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But before we get to that, STEN has a few more questions for you.
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Let's head back to STEN now and learn more about scaling the solar system.
00:17:37
Hey, it's great to have you back.
00:17:43
In the last segment, we introduced the scale of the solar system and the astronomical unit.
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Believe it or not, astronomers once knew only what the distances were in astronomical
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units, not in actual miles.
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Recall the following chart that shows the distances of the planets to the sun.
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Between 1609 and 1619, the astronomer Johannes Kepler used precise measurements of the planets
00:18:03
in the sky to determine their orbits.
00:18:10
But his geometric model was based on the scale of the Earth's orbit, not on its actual diameter
00:18:12
in kilometers or miles.
00:18:17
He determined the ratio of the distance of each planet to the sun relative to Earth's
00:18:19
distance to the sun.
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His baseline unit, the distance from Earth to the sun, was designated as exactly 1 AU,
00:18:24
or 1 astronomical unit.
00:18:30
The problem is that Kepler could not accurately determine the distance between the Earth and
00:18:32
the sun.
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The best estimates at that time ranged from 50 million miles to over 200 million miles.
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But by the 1890s, astronomers began to know that number very precisely.
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How did scientists without modern space technology and rockets do this?
00:18:48
You can't just send a spacecraft to the sun and back to determine the distance.
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Human life, including Norbert and Zott, couldn't survive the intense heat produced by the sun.
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So the question for this segment of the program is, how do we determine that the Earth is
00:19:02
93 million miles, or 149 million kilometers, from the sun?
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This would be a good time to pause the program and discuss the question with your teacher
00:19:11
and your peers.
00:19:15
So did you come up with any good ideas?
00:19:17
If you didn't, don't worry about it.
00:19:19
After all, it took astronomers about 2,000 years to figure out how to do it.
00:19:20
The answer is that astronomers used a geometric technique called parallax to determine the
00:19:27
distance between the Earth and the sun.
00:19:31
Parallax is the apparent change in position of an object when you look at it from two
00:19:33
different stations or points of view.
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It sounds mysterious, but you use this technique all the time.
00:19:39
For example, let me show you how parallax works by using my thumb and that rocket in
00:19:43
the background.
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First, hold your thumb out at arm's length.
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Now look at your thumb with your left eye open and your right eye closed.
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What do you notice about the position of your thumb?
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There seems to be an apparent change in position of your thumb from two points of view, your
00:19:58
left eye and your right eye.
00:20:03
Your brain uses this information to figure out how far away things are from you.
00:20:05
General parallax calculations can be quite complicated, but here's an example of how
00:20:10
we can determine the distance to that rocket using many of the same geometric principles.
00:20:14
Suppose we wanted to approximate the distance between where I'm standing right here and
00:20:19
that rocket over there.
00:20:23
And suppose also that there was a body of water in between that we couldn't get across.
00:20:24
Would you believe that we could do that by just using a pencil, a piece of paper, a ruler,
00:20:29
a piece of rope and a protractor?
00:20:34
The first thing we do is to lay our rope in a straight line.
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The rope will serve as our baseline and is 10 meters in length.
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Standing on the left end of the rope, which we will call position A, hold the protractor
00:20:44
so that it is parallel to the baseline.
00:20:49
Place the pencil on the inside of the protractor and move it along the curve until it lines
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up with the object.
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Being careful not to move your pencil, have a partner read and record the angle measurement.
00:20:57
We then need to repeat the same procedure on the other side of the rope.
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We will call this position B.
00:21:06
We now have two angle measurements and our baseline measurement, which is 10 meters,
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the length of our rope.
00:21:13
On a sheet of paper along the bottom, we draw a line 10 centimeters long to represent our
00:21:14
baseline.
00:21:19
For this exercise, let the scale be 1 meter equals 1 centimeter.
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Mark one end of the drawn line as point A and the other end as point B.
00:21:27
Using our protractor at point A, we measure an angle that is the same number of degrees
00:21:33
as the angle we measured outside for point A.
00:21:38
Let's mark and draw the angle.
00:21:42
At point B, we do the same thing.
00:21:45
Now measure an angle that is the same number of degrees as the angle we measured outside
00:21:48
for point B.
00:21:52
As you can see, the two lines intersect.
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We mark the point of intersection as point C.
00:21:57
Now we draw a line perpendicular from point C to the baseline.
00:22:02
Using our metric ruler, we can measure the distance of this perpendicular line.
00:22:06
Finally, using the scale 1 meter equals 1 centimeter, we can approximate the distance
00:22:11
the actual object was from the baseline.
00:22:16
For our case, the object is approximately 20 meters away.
00:22:19
In this example, we used a geometric technique called triangulation, which assumes that we
00:22:24
know the baseline length and the two base angles.
00:22:28
When astronomers use parallax, they measure the baseline length and the vertex angle.
00:22:31
It is hard to use the parallax method in the classroom because you can't measure the vertex
00:22:36
angle exactly.
00:22:40
With proper measuring technology, this is not a problem for astronomers.
00:22:42
To refine the actual Sun-Earth distance, parallax observations of the transit of Venus were
00:22:46
made between 1761 and 1882.
00:22:51
The transit of Venus occurs whenever the planet Venus passes in front of the Sun as viewed
00:22:55
from the Earth.
00:22:59
By observing the apparent shift in position of Venus against the background of the solar
00:23:01
disk as seen from two different places on Earth, astronomers were able to use this parallax
00:23:05
shift to determine the distance from the Earth to the Sun.
00:23:10
The last Venus transit occurred in 1882, and we are fortunate to have another transit of
00:23:13
Venus happening on Tuesday, June 8, 2004.
00:23:17
This is an historic event because no one alive today was around when the last one occurred.
00:23:21
To learn more about the transit of Venus, let's visit Dr. Janet Luhmann at the University
00:23:26
of California's Space Science Lab in Berkeley, California.
00:23:31
Thanks, Jen.
00:23:36
A Venus transit occurs when Venus crosses the disk of the Sun as seen by an observer.
00:23:38
It's like a solar eclipse in that Venus is located on the line between the Sun and the
00:23:44
Earth, and therefore blocks some of the Sun's light.
00:23:48
However, in a Venus transit, the amount of sunlight blocked is very small compared to
00:23:51
a solar eclipse, and so the observer who is unaware will never notice it.
00:23:56
Venus's circular shadow is much, much smaller than our Moon's shadow.
00:24:01
Even though Venus is nearly the size of the Earth, it is much farther away than the Moon.
00:24:05
In clear weather, Venus transits are visible with the naked eye or with a small telescope,
00:24:09
which is why they became popular in the 1600s.
00:24:14
Before the advent of radar, Venus transits were used mainly for the measurement of the
00:24:18
astronomical unit, or the Sun-Earth distance, as you've heard earlier.
00:24:22
The biggest activity surrounding the June 2004 Venus transit will be the International
00:24:27
Network of Amateur Astronomers.
00:24:31
These astronomers will measure the astronomical unit with the Venus transit using the same
00:24:35
techniques as used by the early observers.
00:24:39
An innovative aspect this time, however not available in 1882, is the widespread use of
00:24:41
the Internet to organize international participation and the ease of access to the tools needed
00:24:47
to make the parallax calculations.
00:24:52
There also will be a few astronomical researchers who will try to exploit state-of-the-art observing
00:24:54
tools to see what can be learned about the use of transits to investigate planets around
00:24:59
other stars.
00:25:04
Transits are currently being used to search for such planets.
00:25:05
Perhaps this Venus transit will lead to some new technique or measurement that will allow
00:25:08
future researchers to further study the terrestrial planets during long-range planet-finding missions.
00:25:12
The Venus transit will also serve to remind us of Earth's place in the cosmos.
00:25:19
The tiny dot crossing the solar disk is a terrestrial planet with an atmosphere, and
00:25:23
yet it is far from an Earth.
00:25:27
Venus was once called a twin Earth, in part because of its similar size and distance from
00:25:29
the Sun.
00:25:34
It is now known to be a place that is extremely hostile to life for reasons that are still
00:25:35
under study.
00:25:39
One can speculate how our own pale blue dot would look to some distant alien astronomer
00:25:40
as it passed across the Sun in transit, and whether it has ever been so observed.
00:25:45
Maybe one day humans will be able to observe the Earth transit.
00:25:50
To learn more about the planet Venus and the Venus transit, check out the Sun-Earth Connection
00:25:53
Education Forum website.
00:25:58
Take it away, Jennifer.
00:26:00
They say you learn something new every day, and I sure did.
00:26:05
I'd never heard of transits before, and how astronomers and scientists use them to determine
00:26:08
the astronomical unit.
00:26:13
Thanks, Janet.
00:26:15
Okay, guys, remember earlier in the program when I said I had an interesting challenge
00:26:16
for you?
00:26:20
Well, it's now time for Scaling the Solar System.
00:26:21
Now, the astronomical unit, or AU, currently in use is derived from the average mean distance
00:26:25
between the Earth and the Sun, which is approximately 93 million miles.
00:26:31
Working in groups, your task is to make a proposal that uses the average mean distance
00:26:35
between the Sun and another planet in our solar system as the basis for determining
00:26:42
the astronomical unit.
00:26:47
In other words, is there a better baseline distance to use rather than the Sun-Earth
00:26:49
baseline?
00:26:54
What about using a Sun-Jupiter baseline or a Sun-Pluto baseline?
00:26:55
Once you choose another planet, you will have to recalculate the scale of the solar system
00:27:01
using your new chosen baseline and then explain why your new baseline is a better choice than
00:27:06
the Sun-Earth baseline.
00:27:12
What are the advantages and disadvantages to your new scale?
00:27:13
Detailed instructions and tips on how to make your proposal can be located at the NASA Connect
00:27:17
website.
00:27:23
From the website, we encourage you to submit your proposal.
00:27:24
Your proposal will be seen by millions of students across the country.
00:27:28
We look forward to your submittals.
00:27:31
Well guys, that wraps up another episode of NASA Connect.
00:27:34
I hope you have a better understanding of how and why astronomers and scientists use
00:27:37
scale models of the solar system.
00:27:42
We'd like to thank everyone who helped make this program possible.
00:27:45
So until next time, stay connected to math, science, technology, and NASA.
00:27:48
Bye from sunny Florida.
00:27:54
Captioning funded by the NAC Foundation of America.
00:28:03
NASA Jet Propulsion Laboratory, California Institute of Technology
00:28:33
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- Fecha:
- 28 de mayo de 2007 - 16:52
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- Enlace Relacionado:
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- Relación de aspecto:
- 4:3 Hasta 2009 fue el estándar utilizado en la televisión PAL; muchas pantallas de ordenador y televisores usan este estándar, erróneamente llamado cuadrado, cuando en la realidad es rectangular o wide.
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