Predicting the Configuration of the Satellites of Jupiter.

CARA Yerkes Summer Institute, August 1995

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This is meant to be handed out to the students.*

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.

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 21.6The 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 ________ greenUse 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?

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?

- Sometimes we can see only 3, not 4, moons. Where is the missing moon, and how do we know where it is?
- How can we tell whether the moons are moving clockwise or counter-clockwise around Jupiter?
- 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?
- 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? - Why are the satellites always strung out in a line?
- Why is the line of satellites not perfectly straight?