Use the Stary Night Enthusiast \({ }^{\text {TM }}\) program to observe the five large satellites of Uranus. Open the Favourites pane and click on Guides \(>\) Atlas to display the entire celestial sphere. Open the Find pane and double- click the entry for Uranus to center this planet in the view. (Clicking once on the Space bar will speed up this centering). You can reduce the confusion in this view by removing the background stars by clicking on View \(>\) Stars \(>\) Stars and by ensuring that the celestial grid is removed by clicking on View > Celestial Grid. Using the controls at the right-hand end of the toolbar, zoom in to a field of view of about \(2^{\prime} \times 1^{\prime}\). In the toolbar, set the year to 1986 and the Time Flow Rate to 1 hour. Then click on the Run Time Forward button, the right-pointing triangle on the toolbar. You can scroll on and off the labels for the moons by clicking on Labels > Planets-Moons. (a) Describe how the satellites move, and relate your observations to Kepler's third law (see Sections 4-4 and 4-7). (b) Set the year to 2007 and again click on the Run Time Forward button. How do the orbits look different than in (a)? Explain any differences.

Step by step solution

01

Initial Observation

Open the Starry Night Enthusiast program, then open the Favourites pane and click on Guides > Atlas to display the celestial sphere. Then, in the Find pane, double-click the entry for Uranus to center this planet in the view. Adjust visibility settings by removing background stars and the celestial grid. Zoom in for a close-up view of about \(2' \times 1'\). Now, you should see Uranus and its satellites.

02

Observe and Describe Motion for the year 1986

Set the year to 1986 and the Time Flow Rate to 1 hour, then click on the Run Time Forward button. Carefully observe the motion of the satellites, taking note of their movement patterns, speed, and distance from Uranus. Write down the observations.

03

Tie Observations to Kepler's Third Law

Look for ways that the observed satellite motions align with Kepler's third law, which states that the square of the period of a planet's orbit is proportional to the cube of the semi-major axis of its orbit. Use the observed motion and structures of the satellites' orbits to discuss how they support or contradict this principle, and include specific examples based on observations.

04

Observations for the Year 2007

Now, set the year to 2007 and run the time forward again. Observe how the satellites' orbits have changed over the years. Look for clues in the motion, direction, and structure of the orbits to understand the differences.

05

Explain Differences Observed

Finally, discuss and explain the differences observed in the motions of the satellites between the years 1986 and 2007. Consider changes in orbit shape, size, speed, and direction when discussing these variations. The variations could be due to the nature of the orbits, which are known to be complex, and with a variety of gravitational forces acting on the satellites.

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