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

uohomework@gmail.com

The simulation should be open now and you should be observing 4 white dots changing position with respect to Jupiter. This will simulate what Galileo first saw when he pointed his telescope at Jupiter.

In addition to this simulation, you need to click on the image of Galileo at the top of this page - that will open up a new window in which a view of his original log book is shown. If you go down to the bottom of that image, you will see a sketch of Jupiter and the positions of the 4 moons.

To simplify this virtual observing make sure you check the box that says stop at the beginning of a new day . This will allow you to record the configuration every 24 hours.

You will also need to make use of the reset button to reset the clock back to day zero.

Exercises/questions:

1. If you look at Galileo's log book you will notice that most of the sketches shown 4 moons on one side of Jupiter. Using the simulation determine

    a) the time it takes (in days) for you to do from day zero to the first occurence of 4 moons on one side of Jupiter.

    b) how many days (or fractional days) does this configuration maintain itself (for instance, could Galileo observe this two nights in a row)

    b) Determine approximately how long it is between successive configurations of 4 moons on one side.

2. Galileo's log book also shows instances where only 3 moons are recorded. This can happen when one of the 4 moons is either obscured behind Jupiter or is directly in front of Jupiter so it can't be seen as an individual white dot:

    a) again determine, from day zero, how long it takes to a 3 moon configuration to first appear

    b) how long does this configuration maintain itself?

    c) approximately how log is it between successive configurations of only 3 moons being visible.

3. Which of these two configurations is the more common (e.g. 4 moons on one side, or 3 moons only visible).

4. Determine if its possible that Galileo could have observed Jupiter and seen no moons at all.

5. Now you need to make some real measurements with this simulation. These measurements are the orbital periods (in units of fractional days) and orbital diameters (i.e distance from Jupiter which corresponds to the physical radius of these circular orbits). You will have to invent your own units of measuring orbital distances from the simulation (i.e. you could put a ruler on the screen and measure distances in millimeters or whatever).

Report your measurements for the inner most and outer most satellites.

    What is ratio of orbital times between the innermost and outermost satellites?

    What is the ratio of orbital distances between the innermost and outermost satellites?

6. Later on we will learn about Kepler's laws which represent a relation between orbital period and orbital distance. In principle, Galileo could have deduced this relation from his observations of the Jupiter moon system. He failed to do this. Speculate on a reason he was unable to find this correlation between orbital period and orbital distance.