Copy of Kepler's Laws

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School

University of Texas *

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420

Subject

Astronomy

Date

Apr 3, 2024

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pdf

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4

Uploaded by ColonelThunderKudu36

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Kepler’s Laws OBJECTIVES To explore and understand each of Kepler’s three laws To simulate a variety of orbits and confirm each follows Kepler’s Laws EXPLORE THE SIMULATION ● (Never learned about Kepler’s Laws before? You should review this lesson first.) ● Launch the Gravity Simulator . ● Watch this brief instructor video , which shows the basic functions of the simulation. ● Experiment with the simulation yourself. Try making your own solar system. KEPLER’S FIRST LAW 1. Remove any existing planets by pressing the “Clear Spacetime” button. 2. Make sure that the “Simulation Mode” is set to Kepler’s 1st Law. In this mode, you can fling a planet in any direction you like at any speed you like. 3. Kepler’s 1st Law states that all planets orbit in an ellipse with the sun at one focus. Use the simulation to create a planet that orbits the sun in an ellipse. Take a screenshot of the planet as it orbits the sun and include it in the space below. ( How do I take a screenshot? ) 4. What is the eccentricity of the orbit you created? Use the table below to help you estimate the eccentricity of your own orbit.
e = 0.0 e = 0.2 e = 0.5 e = 0.7 The eccentricity of my orbit is approximately ______0.7______ 5. A circular orbit is simply an elliptical orbit with an eccentricity of 0. Use the simulation to create a planet that orbits the sun in a perfect circle. (You can watch this brief teacher video for some hints ). Once you’ve created a nice circular orbit, take a screenshot of the orbit and include it below. KEPLER’S SECOND LAW 6. Remove any existing planets by pressing the “Clear Spacetime” button. 7. Change the “Simulation Mode” to Kepler’s 2nd Law. In this mode, you can set the eccentricity to any value in the menu and then click to launch a planet into orbit. 8. Set the eccentricity to 0.5. 9. Launch a planet into orbit with an eccentricity of 0.5 and watch as it orbits. 10. Does the planet orbit at a constant speed? No 11. Where does the planet move the fastest? When it gets closer to the blue circle 12. Where does the planet move the slowest? When it is furthest from the blue circle 13. Remove your planet by pressing the “Clear Spacetime” button. 14. Now set the eccentricity to 0 so that we can launch planets in circular orbits.
15. Launch a planet into orbit near the sun (about two blocks away). Watch the planet orbit. 16. Does the planet orbit at a constant speed? Yes 17. Launch four more planets into circular orbits, each one further from the sun than the last. Watch them orbit. Do all the planets move at the same speed? No 18. Which planet moves the fastest? The planet closest to the blue circle 19. Which planet moves the slowest? The planet furthest from the blue circle 20. In general, comets have very elliptical orbits. Halley’s Comet, which is famous for passing by the earth every 76 years, has an eccentricity of 0.97 - it’s orbit is shown below along with the sun and the orbit of the earth for comparison. A comet can only be seen when it is near both the sun and the earth - the sun melts part of the icy comet, causing the long tail that we can observe in the night sky. When the comet is far from the sun and earth, it is only visible to the most powerful telescopes. 21. Clear spacetime and set the eccentricity to 0.9 to simulate a comet. Launch a comet far from the Sun and watch its orbital motion (if the comet falls into the sun, then you need to launch it from farther away). Notice how much faster the comet moves near the sun than when it is far away. Use your observations to explain why Halley’s Comet is only visible for about six months out of every 76 years. Halley’s comet is only visible for 6 months every 76 years because its orbit around the sun is so long that the comet only comes close to earth for 6 months before it gets sling shotted away for another 76 years. KEPLER’S THIRD LAW 22. Remove any existing planets by pressing the “Clear Spacetime” button.
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23. Make sure that the “Simulation Mode” is set to Kepler’s 3rd Law. In this mode, you can still set the eccentricity and then click to launch a planet into orbit. 24. Set the eccentricity to 0.00 for the duration of this portion of the lab. 25. Kepler’s Third Law is an equation that relates a planet’s distance from the sun (a) to its orbital period (P). The equation is P 2 = a 3 . 26. One astronomical unit (1 AU) is the distance from the earth to the sun. In our simulation, it is equal to three blocks (as shown in the image below). On this scale, the size of the planet and sun are greatly exaggerated. 27. The table below lists several imaginary planets. For each one, you are given a specific distance from the sun (a). Use Kepler’s Third Law to calculate the orbital period that you expect for each planet. Then use the simulation to measure the orbital period. Watch this teacher video for important hints on completing the table. Planet a (AU) a 3 P 2 Calculated P (Years) Measured* P (Years) Arrakis 0.33 0.035937 0.035937 0.18957 0.20 Dagobah 1.00 1.00 1.00 1.00 0.80 Cybertron 1.66 4.574296 4.574296 2.1387 1.74 Coruscant 2.33 12.649397 12.649397 3.5565 2.80 Caprica 3.00 27 27 5.1961 4.20 * The measured period should match the calculated period quite closely. If you find a significant difference, this may be due to the simulation running slowly on your computer. 28. As the size of a planet’s orbit increases, what happens to its orbital period? It increases COMPLETING THE LAB 1. Return to the course and complete the lab quiz to demonstrate your understanding. 2. Submit your completed lab document using your instructor’s online dropbox .