Labs from YSI 95 :
Predicting the Configuration of the Satellites of Jupiter.

Rich Kron and Richard Dreiser
CARA Yerkes Summer Institute, August 1995

This is meant to be handed out to the students.

Introduction

In this lab, we will plot the current positions of JupiterÕs four largest moons - the Galilean satellites - using a scale model of the system. We will look at this model edge-on to be able to predict what the system looks like when seen from Earth (in fact, we will view the model through the 10-inch reflecting telescope). Then, we will observe Jupiter itself, in order to check our prediction. A 35 mm camera will then be attached to the 10-inch reflector, and we will photograph Jupiter and its moons to chronicle the motions of the four satellites throughout the week.

The Model of Jupiter + Satellites

An upper window in the Yerkes main building is visible with the 10-inch telescope in the South building. (To do this, point the telescope at 3h17m, +38deg.) The distance is about 325 feet. The model appears to be the same angular size as the actual Jupiter system as seen from that distance.

We'll use a board that fits inside the window frame. On this, we mark a pattern that looks like a dart board, with radial lines every 15 degrees and four circles with radii of 2.3 inches, 3.6 inches, 5.8 inches, and 10.2 inches. Jupiter is a ball 3/4 inch in diameter. The computed positions of the satellites for 9:30 pm each evening are marked with push-pins.

Predicting the Configuration

Suppose that the line towards the Earth is called azimuth = 0 degrees, and we count degrees from this reference line counter-clockwise. The azimuths of the satellites on August 5 at 9:30 pm were as follows:

          A5

Io        59 deg
Europa    77 deg
Ganymede 174 deg
Callisto 217 deg.
The orbital data you need are:
            a       P            D
          (RJ) (days/360 deg) (deg/day)

Io        5.91     1.77         203	
Europa    9.40     3.55         101
Ganymede 15.0      7.16          50.3
Callisto 26.4     16.7           21.6
The first column gives the orbital radius in terms of the radius of Jupiter. The diameter of Jupiter is 40.1 seconds of arc. We were able to draw the circles on the "dart board" with this information.

Here's how to compute the azimuth for a satellite. Let the number of 24-hour intervals between 9:30 pm on August 5 and the present time be T. Let the azimuth of that satellite on August 5 be A5. Let the number of degrees per day that the satellite goes be D. Then,

azimuth = A = D * T + A5

If your answer for A is larger than 360, subtract 360 from it. If it is still larger than 360, keep subtracting 360 until you have a remainder that is less than 360.

Record here the azimuths so computed:

date for computation of azimuth: _________________

             A

Io        ________  red
Europa    ________  yellow
Ganymede  ________  blue
Callisto  ________  green
Use a pin to indicate the position of each satellite on the board for 9:30 pm tonight with the color code indicated above. Put the board in the window with azimuth = 0 degrees pointed directly at the 10-inch telescope. Finally, we'll look at it with the 10-inch telescope to see if your prediction is correct.

Sketch the configuration of the satellites that you observed tonight. For example, on August 5 the satellite configuration looked like:

*                         J   *    *       *
Is East to the left or to the right in your plot?

Estimating the Distance to Jupiter

Distances can be estimated by using the apparent sizes (also called the angular diameters) of things. For example, if you wanted to estimate the distance to the buildings in the Loop from a viewing point in Hyde Park, you could argue as follows. You observe that a building in the Loop appears to be 15 times smaller than an apparently similar building 3 blocks away. Then you could say that the Loop is about 15 x 3 = 45 blocks away from Hyde Park.

We'll do the same for Jupiter. We'll assume that the sizes of its moons are similar to the size of the Earth's Moon (that is, their actual sizes in miles, not their apparent sizes). Jupiter's moons appear to be dots only because they are so far away. So, we need to estimate how many times smaller than the Moon the dots appear to be, and this will tell how far away Jupiter is with respect to the distance to the Moon.

It is difficult to do this in one step, so will do it in two steps. The first step is to estimate how many "satellites" would be able to fit across Jupiter's diameter. (This may seem to be quite difficult to measure, but remember we're just estimating - is the number closer to 4, 40, or 400?)

Next we'll look at the Moon with the 10-inch, but before we do that, record how big the disk of Jupiter appears to be.

Now we need to estimate how many Jupiters could fit across the Moon's diameter.

OK: what is the number of Jupiter's satellites that can fit across the Moon's apparent diameter? What, then, is the estimated distance to Jupiter?

QUESTIONS

  1. Sometimes we can see only 3, not 4, moons. Where is the missing moon, and how do we know where it is?
  2. How can we tell whether the moons are moving clockwise or counter-clockwise around Jupiter?
  3. As Jupiter and its moons appear to move with respect to the much more distant stars, sometimes a star will happen to be seen nearby, and we see 5 points of light, not 4. How can we tell which is the interloping star, and which 4 are the real moons?
  4. Suppose at some later time you look at Jupiter through a telescope, and you see the following configuration:
    *                                * J              * *
    
    Which one is Callisto, and why? Which one is Io, and why?
  5. Why are the satellites always strung out in a line?
  6. Why is the line of satellites not perfectly straight?


Important Disclaimers and Caveats: