Media Activity 5 Orbits and Kepler’s Laws Answer Sheet (1) (1)

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Astronomy

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Apr 3, 2024

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5 Orbits and Kepler’s Laws Your goals in this tutorial are to: • understand that objects in orbit are simply falling • to be able to explain Kepler’s laws of planetary motion LESSON 1 1. What is necessary for an object to be able to escape a planet’s orbit? To achieve escape velocity 2. What effect does an object’s mass have on its orbit? Try different masses while keeping the speed constant. None 3. Explain why a feather and a hammer fall at the same rate on the Moon. In the absence of air resistance all objects accelerate towards the ground at the same rate. Since the Moon has virtually no atmosphere, there is virtually no air resistance. 4. Why do they fall at different rates on Earth? On Earth, the thick atmosphere creates a large amount of air resistance for falling objects making the feather and hammer fall at different rates. LESSON 2 5. Use the ellipse tool from Lesson 2 to prove that the semi-major axis of an ellipse is a planet’s average orbital radius: A. Orbital radius when the planet is closest to the Sun: perihelion = 5 AU B. Orbital radius when the planet is farthest from the Sun: aphelion = 15 AU C. Average of perihelion and aphelion = 10 AU D. Length of the major axis of the ellipse = 20 AU E. Length of the semi-major axis of the ellipse = 10 AU Are the average orbital radius (C) and the semi-major axis (E) equal? Yes 6. What special case of an ellipse is a cir cle? When the eccentricity of the ellipse is zero i.e. the major axis is equal to the minor axis. LESSON 3 Use the tool from Lesson 3, to answer the following questions. 7. When a comet is closer to the Sun, its orbital speed is (a) FASTER (b) SLOWER (choose one) . A This means that orbital radius and speed are (a) DIRECTLY (b) INVERSELY (choose one) pr oportional. B 8. Explain why we see Comet Halley from Earth for a few months only once every 76 years. We
only see it for a few months once every 76 years because of it's eccentric orbit. When it is closer to it's perihelion distance it's orbital speed is greater and this is the reason why we see it only a few months every 76 years. 9. Is orbital radius a more meaningful quantity for the Earth or for Comet Halley? Explain your answer . Orbital radius is a more meaningful quantity for the Earth because it has a nearly circular orbit, while Comet Halley has a highly eccentric orbit. 10. The orbital period is the amount of time a planet takes to go around the Sun. Which of the following quantities would the orbital period of a planet depend on? (choose your answers) (a) Orbital Speed (b) Orbital Radius (c) Eccentricity B LESSON 4 11. Use the tool to predict the orbital period of an asteroid that has an orbital radius of 4 AU. P = 8y . Now use Kepler’s third law, P 2 = a 3 , to check your pr ediction. a 3 = 64 . Now take the square root of the result, P = 8 . Is the orbital period the same as the answer you calculated? Yes 12. Use the tool to predict the orbital radius of an asteroid that has a period of two years. 1.5674 AU. Hint: Would it be farther or closer to the Sun than Earth? Farther Check your answer using Kepler’s third law . LAB ACTIVITY Orbits and Kepler’s L aws The goal of this activity is to test Kepler’s third law . For each semi-major axis given in the table, use the stopwatch in the tool from Lesson 4 (shown below in to time the orbital period. Then test Kepler’s third law . Semimajor Axis (in AU) Period (in y ears) P 2 (period squar ed) a 3 (semi-major axis cubed) 1 1 1 1 2 2.83 8 8 3 5.2 27.04 27 4 8 64 64 5 11.18 124.99 125 Do the squares of the periods seem to come out close to equal to the cubes of the semimajor axes? Yes Why do you think some of the squared periods and cubed semimajor axes came out very close
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