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NASA Connect Video containing six segments as described below. NASA Connect Video discovering algebra and how algebra is used in telescopes. Explores Galileo's fifteenth century telescope and the Milkyway Galaxy. NASA Connect Video involving students in
Hi, I'm Roy Zazu-Bird of the Harlem Globetrotters.
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I bet you don't know that the art created when you shoot a basketball involves mathematics.
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Hey, when I line up to shoot, I think AX squared plus BX plus C equals D. Math works, I should
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know.
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I have a business degree which requires mathematics.
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On this episode of NASA Connect, you'll learn all about algebra.
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You'll discover how NASA engineers and astronomers use algebra every day in their work and see
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how telescopes like the Hubble Space Telescope and the next generation of space telescopes
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collect data on our expanding universe.
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So sit tight as Van and Jennifer explore algebra and telescopes on this episode of NASA Connect.
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Hi, welcome to another episode of NASA Connect, the show that connects you to the world of
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math, science, technology, and NASA.
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I'm Jennifer Foley.
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And I'm Van Heers.
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We're your hosts along with Norbert.
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He's going to be helping us take you through another awesome episode of NASA Connect.
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Right.
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Every time Norbert appears, have the cue cards from the lesson guide and your brain ready
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to look for answers to the questions he gives you.
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And teachers, every time Norbert appears with a remote, that's your cue to pause the video
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and let your students consider the problems we'll give them.
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Today we're in Baltimore, Maryland, and this is the Maryland Science Center.
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It's home to the Hubble Space Telescope's National Visitor Center, and it's a lot of
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fun.
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The center has three floors of hands-on experiments to get students like you interested in astronomy.
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Let's go on in and check it out.
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Excuse me, sir.
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Today's show is called Algebra, Mirror, Mirror on the Universe, and this mirror right here,
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it's the same size as the primary mirror on the Hubble Space Telescope.
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But more on the Hubble later.
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First, let's learn about algebra.
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Algebra?
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What's algebra?
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It sounds scary.
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It's really not.
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Let me show you.
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Can you read this graph?
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I bet you didn't know that when you're reading graphs, you're doing algebra.
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Algebra is used to describe a relationship between two or more things.
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For example, in this graph, we can say that the number of pizzas is related to the number
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of people served.
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The more pizzas you have, the more people you can serve.
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That's a relationship.
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In fact, this graph shows a linear relationship.
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A linear relationship means that the points on the graph appear to form a straight line.
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Of course, there are lots of relationships in math, but since these examples don't form
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a straight line, they aren't linear.
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Got it?
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So, looking at this graph, how many people would one pizza serve?
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Let's set up a table to show the relationship we see in the graph.
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Let's label our table like this, n equals the number of pizzas and p equals the number
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of people served.
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According to our graph, one pizza serves two people.
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That means there are two servings in one pizza.
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For our purposes, this number of servings, two, doesn't change.
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It's called a constant.
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How many people would be served if you have two pizzas?
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What about three pizzas?
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You should begin to see a pattern developing.
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Now, what if you were planning a sleepover and your mom got carried away and ordered
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215 pizzas?
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How many people would you have to invite to your slumber party?
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Remember the pattern we saw in the graph and table?
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Let's use the pattern we saw in the table to set up the relationship.
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In algebra, letters called variables help us solve algebraic equations.
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Remember how we used the letters n and p in the table to represent the number of pizzas
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and the number of people being served?
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Using those variables, we can set up an equation like this.
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n, which is the number of pizzas, times the number of servings in one pizza equals p,
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which is the number of people served.
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Okay, what do we know?
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Well, remembering that there are two servings in one pizza and that your mom ordered 215
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pizzas, we can substitute those numbers like this.
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215 times 2 equals p.
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According to our graph, you will have to invite 430 people over for your slumber party.
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Better tell your mom to cool it.
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So you see, guys, algebra isn't scary at all.
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In fact, algebra is used to solve problems much tougher than the one we just did.
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And remember, there are lots of ways to do problems algebraically.
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Absolutely.
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Now that we've gotten a taste of algebra, let's learn more about telescopes.
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1608 was a happening year.
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In that year, the Italian scientist Galileo became one of the first humans to view celestial
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objects with the newly invented telescope.
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Galileo improved on the design to see objects ten times more clearly than ever before possible.
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With his primitive telescope, Galileo saw many thousands of previously invisible stars
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that make up part of our galaxy.
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The ancient Greeks named our galaxy the Milky Way because most of its visible stars appear
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overhead on a clear, dark night as a milky band of light extending across the sky.
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Hmm.
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How many galaxies do you think are in the universe?
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Maybe a couple trillion?
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Well, I know there's at least one.
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340 billion.
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Those are all good guesses.
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To get the real answer, stay tuned because later on in the show, you'll have the opportunity
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to estimate the number of galaxies in the universe with our web activity.
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During the centuries following Galileo's discoveries, scientists created telescopes of increasing
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size and complexity.
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For more information on telescopes and something called optics, let's visit Marshall Space
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Flight Center in Huntsville, Alabama.
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What is optics?
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And how is algebra used in optics?
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Optics is the study of light, what it is, how it moves through space, and how it interacts
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with objects.
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Light can be controlled with lenses and mirrors, and these elements can be combined into optical
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instruments like telescopes, lasers, and cameras, just like the one being used to take
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this picture now.
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There are two types of telescopes.
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This is a refractor telescope that has a lens in the front.
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This is a reflector telescope that has no lens, but a mirror in the bottom of it.
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The light from the object goes through the tube, is concentrated by the mirror to form
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an image which I see with my eye.
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Reflector telescopes are better for looking at faint objects like distant stars and are
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therefore better for astronomy.
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I've taken this mirror out of the telescope to show you how the light is focused down
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to a spot at the focal point.
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This distance from the spot to the mirror is called the focal length, and there's an
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algebraic expression that relates the distance of the focal length, the distance u to an
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object, and the distance v to the image formed by the mirror.
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That expression is 1 over f is equal to 1 over v plus 1 over u.
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We use this equation to test telescopes here at the X-ray Calibration Facility.
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We want to have the object source as far away from the telescope as possible, so we put
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it at the end of this tunnel, which is a third of a mile or 500 meters away.
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Then with the telescope at the other end, we measure the image formed by the mirror
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very precisely to make sure that the telescope is built properly and will focus the stars
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correctly.
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And that's how we use algebra in optics.
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Ground-based telescopes have revealed much over their nearly 400-year history, but they're
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really limited in what they can show us.
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Things like light pollution, cloud cover, and the Earth's turbulent atmosphere interfere
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with ground-based telescope observations.
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So in 1990, NASA launched the Hubble Space Telescope, an automated reflecting telescope
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which orbits the Earth every 97 minutes.
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The Hubble Telescope was named after Edwin Hubble, who discovered that the universe is
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expanding and the more distant a galaxy, the faster it appears to move away.
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Remember the graph we analyzed at the beginning of the show?
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Well, Hubble created a graph that's not too different from our pizza graph.
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Check it out.
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Hubble's graph shows a linear relationship between distance and velocity.
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Remember the linear equation we used for the pizza graph, n times 2 equals p?
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Well, the linear equation for Hubble's graph is h times d equals v.
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h is the Hubble constant.
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It is similar to the number 2 in our previous equation.
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Remember there were two servings and one pizza?
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Anyway, d is the distance of the object and v is the velocity or speed of the object.
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Hey, how would you like to create a model of our universe using something as simple
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as a balloon?
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Hi, we're from Fort Washakie School in Fort Washakie, Wyoming.
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We live on the Wind River Indian Reservation in central Wyoming.
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We enjoy spending time in the Wind River Mountains, which tower behind our home.
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Our community consists of many Native American tribes, but most of us are members of the
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Shoshone tribe.
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We are proud of our heritage and we celebrate by participating in powwows and traditional
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ceremonies.
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We also take pride in our arts and crafts that we have learned from our elders.
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NASA Connect asks us to help you understand NISHO student activity.
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In this lesson, you'll learn about our expanding universe.
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You'll also learn how scientists use models to understand observations, and you'll get
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to plot and analyze data that you'll get from taking distance measurements between
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objects in your own universe.
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You see, we'll use an analogy to try to explain a very complex concept.
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What's an analogy?
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It's simple, really.
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It's a comparison.
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For example, sometimes I say my big brother is like a vacuum cleaner when he eats.
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I use the vacuum cleaner as an analogy to try to explain his eating habit.
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You're going to use an analogy for the universe to help you understand the idea that it is
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expanding.
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When I look out into space, I really don't see anything expanding.
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It's too big.
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So we'll use something like the universe to help us understand one of its characteristics
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that we cannot easily see.
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A good analogy for the universe expanding would be a loaf of raisin bread baking in
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the oven.
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As the loaf expands, the raisins move away from each other.
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The raisins represent galaxies, and the bread represents space.
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This is kind of like what happens in the universe.
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Another analogy for the expansion of the universe is a balloon.
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Things that exist on the surface of a balloon, for example, these marks, move further apart
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as the balloon is blown up.
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In just a minute, we're going to measure the distance between points on a balloon when
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it is about the size of a grapefruit, then again when it is blown up to about the size
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of your head.
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Before we do that, here's something you must understand about an analogy.
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It's only like what it is compared to in a certain way.
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The balloon is not the universe, in other words.
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In fact, the surface of a balloon is only two-dimensional, not three-dimensional like
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the universe.
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It would be very hard to measure something inside the balloon because, well, we can't
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get inside of it.
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Because we can measure the distance between points on the surface of a balloon, that's
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what we'll do to verify what Hubble discovered about the universe.
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He found out the further away a space object is from us, the faster it is moving away from
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us.
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Now that you understand about the universe expanding and how we use models and analogies
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to describe it, you're ready to do the lesson.
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Separate into groups, then expand your balloon to about the size of a grapefruit.
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Roll the neck of the balloon making three turns toward the expanded portion.
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Secure it with a binder clip to keep air from escaping.
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Mark a point near the balloon's equator.
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Label the first point as home.
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Starting from home, measure 10 millimeter intervals along the balloon's equator and
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mark five points.
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Label each point starting with the number one.
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Measure again the distance to point number one from home.
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Be sure no air has escaped.
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Record the distance from home to each point.
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Be careful not to compress or dent the balloon while making the marks.
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Expand the balloon to about the size of your head.
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Measure the new distance from home to each point and record the results.
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Be careful not to compress or dent the balloon while making the measurements.
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Calculate the distance each point moved by subtracting its first recorded distance from
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home from the second recorded distance.
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Have someone check the calculations.
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Record the results on the data sheet.
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Now divide the distance each point traveled by the time it took or when epoch to get the
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expansion rate.
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This is the rate of expansion of your balloon.
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Record the results for each point on the data sheet.
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Now you're ready to plot your data.
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Using the data from the universe data sheet, plot the points.
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Distance traveled, expansion rate.
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Team members should verify that the points are plotted correctly on the graph.
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So, what conclusions can you make from this lesson?
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The 4-1-r graph looks just like the Hubble data graph.
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We created a pretty good model for the expansion of space.
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Our data showed a linear pattern like the Hubble data.
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That's great!
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Any other thoughts about this lesson?
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We learned how to use a metric system.
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Science is fun.
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How the universe expands.
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Way to go, guys!
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You did a great job.
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Hey, teachers, check out our NASA Connect website and download the lesson guide from
00:15:14
this program.
00:15:18
In it, you'll find this student activity, data analysis questions, extension activities,
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and tons more.
00:15:24
How do engineers take care of the Hubble Space Telescope while it's in space?
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Hey, guys, meet Patty Hanson.
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She works on the Hubble Space Telescope project.
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Today, we're at NASA Goddard Space Flight Center in Greenbelt, Maryland.
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Okay, Patty, so far we've learned about algebra, optics, telescopes,
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and a little about the Hubble Space Telescope.
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Now, what is NASA Goddard doing to protect the Hubble while it's orbiting around the Earth?
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Yeah, and how do engineers like you use algebra in your jobs?
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Whoa, those are a lot of questions.
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Here at Goddard, we're actually the servicing part of the Hubble Space Telescope project.
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We actually prepare scientific instruments, computers, tape recorders,
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to go up on the shuttle, rendezvous with Hubble, and perform servicing of the telescope.
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Astronauts go out into the payload bay, get the new equipment out of carriers,
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and install it on the telescope, and we bring the old hardware home.
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Now, when we're getting ready for a servicing mission, we have our instruments in our clean room.
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And in the clean room, we want to make sure we control contamination
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by having everyone get dressed in what we call bunny suits.
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And you'll see that everybody in the clean room is dressed head to toe in white.
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And what this does is it controls all the contamination from your clothing,
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which is lint, your hair.
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We don't want any dropped hairs on our science instruments.
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And our skin flakes.
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Here on Hubble, we're really worried about both particulate and molecular contamination
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accumulating on the primary and secondary mirrors.
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Particulate contamination is like a fine layer of dust that scatters the light
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and doesn't allow it to transmit through the optic and gather into the detector very well.
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Molecular contamination is a thin film similar to the condensation that you see on this mirror
00:17:08
when I squirt it with the nitrogen cleaner.
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This doesn't allow the light to be transmitted very well through the optic.
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Okay, Van, to get back to your question about how I use algebra in my job,
00:17:21
is that I have an end-of-life requirement for the amount of contamination
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I can accumulate on flight optics.
00:17:28
Now, for Hubble, that's the primary and secondary mirrors.
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End-of-life is the amount of contamination that we can accumulate
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from the time it was launched until the time that we no longer expect to take science.
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And for Hubble, that's 20 years.
00:17:41
So you're saying that in 20 years, you will accumulate some type of contamination on Hubble's mirrors.
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That is correct.
00:17:48
And what we do is we take periodic measurements
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and we compare that to our end-of-life requirement.
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Okay, let's look at the algebra Patty is talking about.
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NASA engineers know the total amount of contamination on the Hubble has to be less than 5%
00:17:58
or the telescope won't work the way it should.
00:18:04
Before Hubble was launched, three measurements for contamination were taken.
00:18:06
The first was 8 tenths of a percent.
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The second was six tenths of a percent.
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And the third was one tenth of a percent.
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The total amount of contamination on the Hubble consists of
00:18:16
the amount of contamination measured on Earth
00:18:20
plus the amount of contamination that it collects on orbit.
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If we substitute the values we know into the inequality,
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we find that the amount of contamination the Hubble can collect on orbit
00:18:30
has to be less than 3.5%.
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Using algebra, you can see that we have plenty of on-orbit margin left
00:18:37
to accumulate contamination on both the primary and secondary optics.
00:18:40
Hey check it, did you know that the Hubble Space Telescope
00:18:44
is about the same size as this school bus?
00:18:47
This is where all of the data from the Hubble Space Telescope
00:18:50
is continuously being collected.
00:18:54
Back in 1995, NASA Goddard collected images from the Hubble Deep Field.
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A few thousand never-before-seen galaxies are visible
00:19:01
in this deepest-ever view of the universe.
00:19:04
Hey, how would you like to use the web and real images
00:19:07
from the Hubble Space Telescope
00:19:11
to estimate the number of galaxies in the universe?
00:19:13
And then compare your findings with those made by real astronomers.
00:19:16
Dr. Shelley Canright has the scoop.
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I'm here at the Science Museum of Virginia in Richmond,
00:19:24
home of the Ethel Corporation IMAX Dome and Planetarium.
00:19:27
This is a wonderful place to visit.
00:19:31
It has over 250 hands-on interactive exhibits
00:19:34
where visitors will find that learning science is a whole lot of fun.
00:19:37
But you know what? If we go inside the museum,
00:19:41
we're going to find a computer lab where some students are waiting for us,
00:19:44
where they're going to share with us the featured online activity for NASA Connect.
00:19:47
Come on, let's go inside.
00:19:51
As we have learned how these students use the Internet to explore new knowledge,
00:19:55
with the Hubble Space Telescope,
00:19:59
scientists can now begin exploring the outer reaches of the universe.
00:20:01
In December 1995, a dark section of the sky near the Big Dipper
00:20:05
was selected for a prolonged observation using cameras located on the telescope.
00:20:09
For 100 hours over a 10-day period,
00:20:14
the telescope was pointed at this part of the sky.
00:20:16
We called this the Hubble Deep Field.
00:20:19
What the Hubble saw were thousands of stars and galaxies
00:20:22
beyond what we could see with our own eyes.
00:20:25
In other words, it confirmed the idea that the universe is a really, really big place.
00:20:27
In this show, we are featuring the Hubble Deep Field Academy,
00:20:32
produced by the Space Telescope Science Institute.
00:20:36
The Academy consists of five sections.
00:20:39
The first one gets you oriented to the website and to your mission,
00:20:42
to explore the galaxies of the Hubble Deep Field
00:20:46
and fulfill one of humankind's long-time goals
00:20:49
of seeing as far as possible into the universe
00:20:52
in an attempt to understand our origins.
00:20:55
The first activity, called Stellar Statistician,
00:20:58
introduces you to an estimating technique scientists use called representative sampling.
00:21:02
By counting the number of space objects in a small section of the deep field photograph,
00:21:08
then multiplying that by the number of total sections,
00:21:13
you'll get an estimate of the number of objects in the whole deep field.
00:21:17
Activity 2 lets you classify selected objects based on their color and shape.
00:21:22
You'll choose a camera, then try to classify the 15 numbered objects in the picture.
00:21:27
Then you will see how your choices compare with those made by astronomers.
00:21:32
Activity 3 presents you with the problem of determining the distances between Earth and objects in space.
00:21:37
You'll look at six objects and determine by observation what their relative distances are from the Earth.
00:21:44
Then you'll get to compare your answers with those of the astronomers.
00:21:51
The last activity is a review of what you learned.
00:21:56
You'll answer questions like, what is the difference between a galaxy and a star?
00:21:59
Why isn't a galaxy's size alone useful in determining its distance from Earth?
00:22:04
We've just scratched the surface of this website.
00:22:09
Along the way, you'll get to view animations and see diagrams
00:22:12
that further explain facts and concepts related to the Hubble Deep Field.
00:22:16
I'm sure you'll find it to be a fascinating extension to what you've already learned in today's program.
00:22:20
And speaking of extensions, let me introduce you to another exciting website, space.com.
00:22:26
It's devoted to space news with a special portal to spacekids.com.
00:22:32
There you will find an interactive photo gallery of Hubble images.
00:22:37
You can compare galaxies, contrast different kinds of images of the same exploding star,
00:22:40
find out about the astronomer Edwin Hubble,
00:22:46
and follow the drama of scientists and astronauts who fixed the telescope when it broke.
00:22:48
Both the Hubble Academy and spacekids.com can be accessed through Norfolk's lab on the NASA Connect website.
00:22:53
Oh, and special thanks to the Science Museum of Virginia
00:23:00
and our AIAA student mentor from Old Dominion University in Norfolk, Virginia.
00:23:03
So, you see, the data from the Hubble is being used now,
00:23:08
but there is a need for even bigger telescopes that can see even deeper into space and collect more information.
00:23:11
Compare and contrast the Hubble Space Telescope and the Next Generation Space Telescope.
00:23:19
Hey guys, Van and I are with Dr. Eric Smith. He's an astronomer at NASA Goddard.
00:23:25
So, Dr. Smith, what is a Next Generation Space Telescope?
00:23:30
Well, the NGST, or Next Generation Space Telescope, is the logical successor to the Hubble Space Telescope, or HST.
00:23:34
NGST is designed to see the first stars and galaxies that light up in the universe.
00:23:41
To do this, we need to work in the infrared part of the spectrum.
00:23:46
So that's one very important difference.
00:23:50
Another important difference is just how the telescope looks.
00:23:52
HST looks like a very familiar telescope to most people.
00:23:55
It's a tube, it's got a mirror at one end of it.
00:23:58
NGST, because it is so large, four times the size of HST, is going to have to be cut up and folded in a rocket,
00:24:01
and then it will be launched into space, and it will sort of bloom like a flower,
00:24:08
and then it will have a sunshade to block light from the sun and protect its optics.
00:24:12
That sunshade is about the size of a tennis court.
00:24:17
It's huge!
00:24:19
It is.
00:24:20
Yeah. Now, one of the other important differences between HST and NGST is where it will be.
00:24:21
HST is about 200 miles above our heads orbiting the Earth.
00:24:27
NGST will be about 1.5 million kilometers from the Earth, farther than the moon.
00:24:30
It's being put there so that it can be in a very cold environment,
00:24:36
which, again, is good for telescopes that have to work in the infrared.
00:24:40
It also means that no one will service the NGST.
00:24:43
How do astronomers, like you, use algebra when you're designing or dealing with the NGST?
00:24:47
Well, algebra is used at all stages in the design and construction of a telescope.
00:24:53
Astronomers used algebra at the very beginning when they decided how they wanted to optimize it.
00:24:57
I mentioned you wanted to optimize for the infrared.
00:25:03
Well, you can use algebra to tell exactly where you want to optimize this telescope to work,
00:25:05
and you do that by studying galaxies and knowing where they emit their radiation.
00:25:10
Now, you said that the NGST has a sunshield that's the size of a tennis court?
00:25:15
Right, and the reason it has a sunshield is to protect the telescope optics from getting sunlight on them.
00:25:20
Wow. Okay, now, so are you guys working here at NASA Goddard on the sunshield?
00:25:27
A little bit, but a lot of work on the materials are being done at NASA Langley.
00:25:31
Hey, that's where we're from.
00:25:34
Why don't we head down to Hampton, Virginia and meet John Connell and find out more about the sunshield?
00:25:36
Here at the NASA Langley Research Center,
00:25:41
we're working on a number of technologies that are relevant to the Next Generation Space Telescope.
00:25:43
The sunshield is comprised primarily of polymeric films.
00:25:47
Polymer is a term that means many repeat units of the same structure.
00:25:51
Common examples of polymers that you would encounter in everyday life would include things such as saran wrap,
00:25:56
food packaging material, milk jugs, compact discs, things of this nature.
00:26:01
The materials we are developing are primarily for the outermost shield of the Next Generation Space Telescope.
00:26:07
As you recall, this shield is designed to keep the optics as cold as possible,
00:26:14
so the shield has to be very reflective.
00:26:19
The outermost layer in particular has to be very reflective and be resistant to the radiation environment.
00:26:21
As you can see, the material looks much like the mylar balloon
00:26:27
that you might encounter at a birthday party or other type of event.
00:26:30
The chemistry of them is such that they are much different
00:26:33
and they will be resistant to the radiation present in space.
00:26:37
Polymer chemists use algebra in their everyday working activities
00:26:40
in the calculation of the recipes necessary to make these advanced polymers.
00:26:43
Well, that about wraps up this episode of NASA Connect.
00:26:48
It was a blast, wasn't it, Van?
00:26:52
Oh yeah, it sure was.
00:26:53
Jennifer and I would like to thank everyone who helped contribute to this episode.
00:26:54
We sure would, and you know, Van and I would love to hear from you
00:26:58
with your comments, your questions, your suggestions or ideas.
00:27:00
So just write us at NASA Connect, NASA Langley Research Center, Mail Stop 400,
00:27:03
Hampton, Virginia, 23681.
00:27:08
Or you know, you can find us on the web at connect at edu.larc.nasa.gov.
00:27:10
Hey teachers, if you would like a videotape copy of this NASA Connect show and the teacher's guide,
00:27:17
contact CORE, the NASA Central Operation of Resources for Educators,
00:27:22
or check out this website to locate your local NASA Educator Resource Center.
00:27:27
All this information and more is located on the NASA Connect website.
00:27:32
For the NASA Connect series, I'm Jennifer Pulley.
00:27:37
And I'm Van Hughes.
00:27:39
See you next time. Bye.
00:27:40
Bye-bye.
00:27:42
Have fun.
00:27:43
I have the amount of contamination that I can accumulate.
00:27:44
Don't start laughing, you're going to make me laugh.
00:27:47
We're heading out to La Labrie.
00:27:51
Easy.
00:27:54
Easy, it's easy.
00:27:55
The invention of the telescope came about by accident.
00:27:57
A Dutch spectacle maker had an apprentice who was playing with lenses one day
00:28:00
and found that if he held two lenses in front of his eyes, he saw things considerably closer than they were.
00:28:04
Yah!
00:28:09
Immediately, the spectacle maker grasped the importance of the discovery.
00:28:11
And in 1608, Hans Lippershey mounted the lenses in a tube and invented the telescope.
00:28:14
Did you know that telescopes were first called Dutch trunks?
00:28:20
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- Idioma/s:
- Materias:
- Matemáticas
- Niveles educativos:
- ▼ Mostrar / ocultar niveles
- Nivel Intermedio
- Autor/es:
- NASA LaRC Office of Education
- Subido por:
- EducaMadrid
- Licencia:
- Reconocimiento - No comercial - Sin obra derivada
- Visualizaciones:
- 368
- Fecha:
- 28 de mayo de 2007 - 16:52
- Visibilidad:
- Público
- Enlace Relacionado:
- NASAs center for distance learning
- Duración:
- 28′ 30″
- 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.
- Resolución:
- 480x360 píxeles
- Tamaño:
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