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.