The Orbits of The Galilean Satellites

Astronomy 121 First Homework Assignment

The Galilean Satellites and Kepler's Laws


Download this Flash Simulation (you might be prompted to get an update for of your Flash player) 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. There is a button that is called Observe Another Day

Do not yet hit the observe button. Record/measure/observe the starting positions of the individual white dots.

Each subequent time you hit the button advances the system by 24 hours. However, just like in real life, you don't have 24 direct hours of nighttime observations, so the sun will rise and set and get in your way. Each time the simulation now ends, represents the end of a 24 hour period and that's when you make your measurement/observations of where the moons are in comparison to where they were 24 hours earlier. You will have to devise your own system of measurement.

Hence, this simulation allows you to reproduce what Galileo did observe the Jupiter moon system once each night at the same time. As you hit the observe button you will observe the four white dots (which are the four large moons discovered by Galileo) changing position. Galileo recorded the changing positions and inferred many orbital properties and the purpose of this exercise is for you to repeat these steps.

Note that I have not provided you with a more accurate clock (other than the 24 hour clock encoded in the step button) because Galileo also did not have an accurate clock. As a result, you will have to estimate, from the simulation, fractional days.

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 reset the simulation at any given time, just reload the web page.

Exercises/questions:

  1. If you look at Galileo's log book (the one shown in the galileo lecture in class), you will notice that most of the sketches show 4 moons on one side of Jupiter. The simulation will start off with this configuration, with all moons on the left side.
    a) Determine the time it takes (in days) for the 4 satellites to now appear all on either the right side or the left side again.

    b) How many days (or fractional days) does this configuration (4 satellites all on one side) maintain itself? (For instance, could Galileo observe this two nights in a row?)

  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 long is it between successive configurations of only 3 moons being visible?


  3. Now reset the system and observe it for 16 days. There are 9 possible descriptive end configurations for this system:

    1. 4 moons on left side
    2. 4 moons on right side
    3. 3 moons right 1 moon left
    4. 3 moons left 1 moon right
    5. 2 moons on each side
    6. 3 moons left side
    7. 3 moons right side
    8. 2 moons left side 1 moon right
    9. 2 moons right side 1 moon left

      a) What is the frequency of occurence of each of these possible configurations over this 16 day period.?

      b) What configurations are able to maintain themselves for at least two nights in a row?

      c) DO NOT RELOAD - observe the system for the next 16 days and compare the configuration frequencies with those you just observed for the first 16 days

      d) Now again inspect Galileo's actual log book - which qualitative end state configuration doesn't seem to be represented in his sketches?

  4. 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). Now I realize that most of you will simply want to look up the answers to these questions and retro fit the answers to this exercise, but please refrain from doing that. The whole point of this exercise is to get you to use the only tool Galileo had available to him, namely his eyes and a 24 hour clock, to make these measurements).

    Report your measurements of orbital times and orbital distances (e.g., the radius of the orbit) for the innermost and outermost 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?

  5. 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. However, he failed to do this. Speculate on the possible reasons that he was unable to find this correlation between orbital period and orbital distance.