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Download Unit 3 - Section 9.1 2011 Distances in Space0
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Grade 9 Academic Science – Unit 3 Space Measuring Distance in Space Section 9.1 Pages 365-369 Our Sun is about 1.5 X 108 km away…or 150,000,000 km. The next nearest star is Proxima Centauri at 4.01 X 1013 km away (about 40 trillion km). These distances are very hard to imagine. What does 40 trillion km look like? To bring it into the realm of our reality, we measure the vast distances in space by other methods. Astronomical Unit (AU) is a relative measure. The distance from Earth to the Sun is 1 AU. If Neptune is 30 AUs from the Sun, Neptune is 30X further from the Sun than Earth. An AU is a practical measuring unit inside our Solar System. Outside our Solar System, Light Years (ly) is the measurement unit. A ly is not a measurement of time; rather, it is a measurement of distance. A ly is the distance that light travels in a vacuum (i.e., empty space) in one year. Light travels at a constant speed of about 300,000 km/s. Thus, light can travel 9.46 X 10 12 km in one year (300,000 km X 31,558,464 s/yr). The formula is 1 ly = 9.46 X 1012 km Examples The Andromeda Galaxy is 2.4596 X 1019 km from Earth. How many ly is the Andromeda Galaxy away? Distance is 2.4596 X 1017 km One ly = 9.46 X 1012 km 2.4596 X 1017 / 9.46 X 1012 = 2.6 X 106 The Andromeda Galaxy is 2.6 X 106 or 2,600,000 ly from Earth The star Polaris is 400 ly from Earth. What is the distance in kilometers? Distance is 400 ly One ly = 9.46 X 1012 km 400 X 9.46 X 1012 = 3.784 X 1015 The star Polaris is 3.784 X 1015 km from Earth It makes intuitive sense that the farther a star is from Earth, the longer it takes light from the star to reach Earth. The star Polaris is 400 ly from Earth. In other words, it takes light from Polaris 400 years to reach Earth. The light that we see when we look at Polaris is 400 years old. We are actually looking back in time. For ease of understanding, a ly can be converted into a light-second (ls) 1 ly = (60 X 60 X 24 X 364.26) ls = 3.15 X 107 ls Challenge – How many kilometers are there in 1 ls? Parallax – The apparent change in position of an object as viewed from two different locations that are not on a line with the object. To determine the distance to a star, you measure the apparent change of the star’s position over one year. As the Earth orbits the Sun, you take measurements at the opposite sides of the Earth's orbit. You will observe an apparent movement of the star compared to more distant stars. The closer a star is to the Earth the greater the observed parallax. As shown in the diagram, the lines of sight and the line connecting the observer's position form a triangle with the star at the apex. NOTE: Star A and Star B in the diagram are the same star. The difference is the apparent movement of the star due to the movement of the viewer on Earth. The parallax of the star is equal to the angular radius of the Earth's orbit as seen from the star. The distance to the star (D) is equal to the reciprocal of the parallax angle (measurement units are arc-seconds). The formula is TanӨ = R/D A little fun… Star Proxima Centauri Sirius Parallax Angle Distance (parseconds) Light Years 0.77233 1.29478 4.233 0.379 2.6385 8.606 This is one of the basic problems in trigonometry: Determining the distance of some far away point C given the direction that C appears from two ends of a baseline AB (see illustration). The problem is simplified by three ideas. 1. The baseline is perpendicular (i.e., 90O) to a line draw from the middle of AB to point C. Thus, the triangle ABC is symmetric. If we call the drawn line r, then AC = BC = r 2. The length of AB is less than r. This means that the angle between AC and AB is small. This is the parallax of C as viewed from AB 3. We do not require great accuracy (i.e., within 1% of the approximate distance). Return to the diagram above The diameter of the Earth’s orbit around the Sun is 300,000,000 kilometers. (Question: How do I know that distance?) On dates separated by half-a-year, the Earth position…and where you are relative to the star between viewed…is 300,00,000 kilometers apart. The stars do not shift very little when viewed from 300,000,000 kilometers apart A circle has 360O and each degree can be divided into 60 minutes…called “minutes of arc” so they are distinguished from a minute of time. Moreover, each minute of arc contains 60 “seconds of arc.” A parsecond (…or parsec…) is the distance to a star whose yearly parallax is 1 second of arc. One parsecond equals 3.26 light years. Practice Questions / Homework Page 369, Questions 2, 3, 5,7,10,11