inclass work 10 - rings of saturn

Name Date Section The Clearing and Herding of Saturn's Ring Particles Learning Goals In this activity you will use Kepler's and Newton’s laws to analyze the behavior of ring patterns in the rings of Saturn. After completing this activity you will be able to: 1. Apply Kepler's third law to sections of the ring system of Saturn. 2. Summarize the process by which a single moon will clear a gap in a ring system like Saturn’s. 3. Summarize how the two shepherd moons manage to keep the particles that orbit between their orbits tightly confined within a narrow ring. Step 1—Applying Kepler’s Laws to Rings and Satellites Figure 14.1 shows an image of part of Saturn’s rings taken by the Cassini spacecraft. The rings are made up of millions of icy chunks. These ring particles follow Kepler’s laws, each in its own orbit. From this image: 1. Which set of particles will be traveling fastest? (Check one.) A B C 2. Which set will be traveling the slowest? (Check one.) A B C FIGURE 14.1 59

60 ACTIVITY 14 o The Clearing and Herding of Saturn’s Ring Particles Figure 14.2 shows a Cassini image of Pandora, the F Ring, Prometheus, and the outer part of the A Ring of Saturn. 3. Rank the following objects in order of orbiting Saturn the fastest (1) to orbiting Saturn the slowest (4): Pandora A Ring F Ring Prometheus 4. Explain your logic in ranking the objects. Figure 14.3 depicts a possible approach of the space shuttle to a satellite in Earth orbit (Figure 14.3a). (Earth is at the bottom of the figure.) The shuttle has to capture the satellite to prevent it from falling out of orbit and burning up in Earth’s atmosphere. The satellite is orbiting at a height of 250 km. The space shuttle is getting ready to adjust its orbit in order to catch up to the satellite, and there are three possible approaches (Figure 14.3b). FIGURE 14.3 Prometheus Pandora FIGURE 14.2

62 ACTIVITY 14 o The Clearing and Herding of Saturn’s Ring Particles 14. Now, draw arrows on Figure 14.4 that indicate the direction each particle will go in its orbit 15. 16. when affected by the single moon. Label these arrows to distinguish them from the arrows representing the gravitational forces. As a particle falls “down” toward the planet, it will gain a little speed. This will stabilize it in a new, lower orbit. The outer particles, however, speed as they move away from the planet, so they stabilize in a new, orbit, Summarize the process by which a single moon will clear a gap in a ring system like Saturrs. Step 3—How Two Moons Shepherd Ring Particles Figure 14.5 shows a ring interacting with two moons. The inner shepherd moon will have a slightly higher speed and the outer shepherd moon will have a slightly lower speed than the ring particles, as indicated by the sizes of the arrows pointing in the direction of the moons’ orbits. We once again need to consider Kepler’s third law. 17. 18. 19. 20. 21. Do the stray ring particles move faster or slower than the outer shepherd moon? Do the stray ring particles move faster or slower than the inner shepherd moon? The moons have a strong gravitational effect on the stray ring particles. Draw arrows on Fig- ure 14.5 that represent the direction in which each moon’s gravity will act on the stray ring Outer shepherd moon —— —_— ~— - \S’(ray ring ?rticles ' > e — -~ —— ~— Inner shepherd moon FIGURE 14.5 particle closest to it. Label these arrows to distinguish them from the arrows representing the speeds of the moons. Now, consider your answers from the previous section, and draw arrows on Figure 14.5 that indicate the direction each stray ring particle will go in its orbit after being affected by the shepherd moon closest to it. Label these arrows to distinguish them from the arrows repre- senting the gravitational forces. Summarize how the two shepherd moons manage to keep the particles that orbit between their orbits tightly confined within a narrow ring.