The Orbits of The Galilean Satellites

The Galilean Satellites and Kepler's Laws


Download this Web Start Simulation and use it in answering the questions below.

Email all of your answers to the questions below to

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What you should be observing in the smaller window is a top view of the 4 Galilean Satellites. These satellites were initially discovered by Galileo and if you click on the image above, you will see a version of his observing log book where he noted the change of positions of the moons in each nights observations. If you click the switch view button, the view will switch to what is observed from the earth. Go ahead and do this.

At the right of the applet display you can see the days ticking away and the "phases" of the satellites as seen if you lived on Jupiter.

Exercises:

DO NOT CLICK ON THE IMAGE OF ANY OF THE SATELLITES INITIALLY, THIS COMES LATER

1. Now check the box which says "Pause Every 24 hours". The motion should pause. Click the Pause/Resume button to advance the view in 24 hour increments. Now you are essentially being Galileo. Make sure your are in the view mode where you are *not* looking at jupiter from the top. In this mode, which simulates the view from the Earth, you should observe the galaxies moving from side-to-side of the planet. Observing the system for a few "days" and then answer the following questions:

  1. What is your estimate of the orbital time period for the innermost satellite, Io?

  2. What is your estimate of the orbital time period for the outermost satellite, Callisto?

Later on we will deal with more accurate measurments but for now, determine your best estimates just using this naked eye method. Report these estimates to the instructor.

2. Now uncheck the "Pause Every 24 hours" button and switch back to the top view and just let the applet run. By observing Io and Callisto, estimate how many times Io goes around in its orbit for each time that Callisto goes around. Compare this ratio to the ratio of the periods that you found above and report that comparison to the instructor.

3. Continue to observe the system and estimate the rough period for the alignment of all the 4 satellites. That is, approximately how many days does it take for the phases of all 4 satellites to be full at exactly the same time. Make sure you hit the pause button close to the moment it occurs (this configuration only lasts for 0.2 days!) Report on what you think the sketch in Galileo's log book would look like during such an alignment configuration? Hit the switch view button to confirm your report. What does the system look like, that is, can you see any of the moons?

4. Now click the switch view button again so you have the top view of the system. Click on the actual image of Callisto - the motion should stop and a red circle should appear around the image of Callisto. Click again in the red circle. The orbit will resume and you will see a straight (green) line being traced out until one-half of orbital period has occurred. A readout will then tell you the diameter of the orbit and the orbital period (which you can now compare to your eyeball estimates). Record these values (you will graph them in a bit) and do the same procedure for the the 3 satellites. Report these values to the instructor.

Now use this graphing applet to plot your data. The X-values should be the radius of the orbit in units of thousands of kilometers (e.g. for Callisto it should be 3768) and the Y-value should be the orbital period in units of days. From the appearance of your graph do you think there is a correlation between distance from Jupiter and orbital period.? Why do you think Galileo failed to discover this relation.