The Orbits of The Galilean Satellites

Astronomy 121 Group Homework Assignment #1

Due 1/26/11 in class

The Galilean Satellites and Kepler's Laws


Click here for the simulation. First I'll walk you through the simulation and then you can start over and use it in answering the questions below. All assignments need to be typed, (no handwriting!), neat and with names of all group members listed.

Introduction

You are all going to be Galileo and make observations (albeit simulated and indoors) of Jupiter and it's moons. This simulation tries to replicate the available dark times of observation. As you will see the moons around Jupiter move significantly during one night of observation, therefore there are different configurations of the four predominate moons. Galileo observed these objects more or less at the same time each night for 15 nights and recorded the changing positions, inferring many orbital properties.

How the Simulation Works - Do this first!

  • The simulation should be open now. Click on the button called Observe the spyglass

  • Click on this button and you see a tiny image of Jupiter and its moons through a simulation of Galileo's telescope. This is the first observation of the night, just after twilight.

  • Now click on the "Continue" button and the moons move to a new position, simulating some hours passing and an observation made later in the in the evening.

  • Clicking on the button again will advance the moons further at sometime before dawn.

  • Now click the button one more time and you get a little cartoon of Galileo and one of his inventions. Note that it says Day#2. This is daytime and Galileo is not observing stars!

  • Clicking on the button will show the positions of the moons that evening after sunset. Note they are in different positions than when you last saw them. And then you can click on the continue button for the moons to advance just as you did for day one.

  • For convenience, the first configuration you see after the cartoon will be referred to as "twilight", the configuration after that is "midnight" and the third is "dawn". The Galileo cartoon is considered "daylight". Okay, now reload the page to start over (you can do this anytime to reset the simulation).

    Note there isn't a more accurate clock because Galileo also did not have an accurate clock. As a result, you will have to estimate, from the simulation, fractional days. To make things easy, assume that each time step is equal to 1/4th of a day (daylight = 1/4th of day, 3 night observations = 3/4ths of day)

    Exercises/questions:

    1. If you haven't done so, reload the page and start at day 1. You will start with three moons on the left side.
      a) Now click through the observations and determine the time it takes (in days or fractional days) for four satellites to appear all on the left or right side.

      b) How many days (or fractional days) does this configuration (4 satellites all on one side) maintain itself? If Galileo observed once a night at roughly the same time (twilight, midnight or dawn) would 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) Determine how long it takes to a 3 moon configuration to appear after the first 3 moon configuration. Which specific configuration is it?

      b) How long does this configuration maintain itself in days or fractional days?



    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

      Keep each observing time (twilight, midnight, dawn) separate.

        a) What is the frequency of occurence of each of these possible configurations over this 16 day period for (i) twilight, (ii) midnight and (iii) dawn observations?

        b) Now assume you only observe at one time (twilight, midnight or dawn) per night, which configurations (if any) would you be able to see at least two nights in a row? Specify configuration, observing time and length time of configuration in days.

        c) If you could observe at all times (minus daylight) which (if any) configurations would you see in a row? Specify configuration andlength time of configuration in days or fractional days.

        d) !!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, again keeping twilight, midnight and dawn observing times separate.

        e) Now inspect Galileo's actual log book. Are there any end state configurations that you observed but not represented in his sketches if you observed only at (i) twilight times (ii) midnight times or just (iii) dawn times? Do this for the 32 days of observation.

    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 distances (i.e., distance from Jupiter which corresponds to the physical radius of these circular orbits). Orbital periods are simply the time it takes for the moon to return to the same spot. Do your best at estimating it since you can't observe at all times. For the orbital distances, you will have to invent your own measuring units from the simulation (i.e., you could put a ruler on the screen and measure distances in millimeters or whatever). The orbits of the moons are nearly circles for our purposes. If we could take a space ship to Jupiter and "hover" over Jupiter and it's moons, we would see a big planet with 4 major moons circling at 4 different but constant radii. But from Galileo's (and the Earth's) perspective, we have a much different view of Jupiter and it's moons where the moons appear to approach and move away from Jupiter. They all appear to move in straight line. Obviously, this is because we are viewing circular motion from the side or 90 degrees. Therefore, you will need to think about where in the orbit of a moon from Earth's perspective you need to make the measurement to get the true moon-Jupiter distance.

        a) Report your measurements of orbital times and orbital distances (e.g., the radius of the orbit) for the innermost and outermost satellites in days/fractional days and whichever distance unit system (inches, mm, cm) you used.

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

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

    5. Recall from class Kepler's 3rd law 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.