jup_sm
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The Revolution of the Moons
of Jupiter
Student Manual to Accompany the CLEA computer exercise
Name_____________________
OFFICIAL USE ONLY
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Historical Background
We can deduce some properties of celestial bodies from their motions despite the fact that we
cannot directly measure them. In 1543 Nicolaus Copernicus hypothesized that the planets
evolve in circular o
its around the sun. Tycho Brahe XXXXXXXXXXcarefully observed the
locations of the planets and 777 stars over a period of 20 years using a sextant and compass.
These observations were used by Johannes Kepler, an assistant of Brahe’s, to deduce three
empirical mathematical laws governing the o
it of one object around another. The addition of
Isaac Newton’s law of gravity allows us to determine the mass of an object that is being o
ited.
Newton’s version of Kepler’s third law for a moon o
iting a much more massive parent body is:
where M is the mass of the primary body, in units of the solar mass.
d is the length of the semi-major axis of the elliptical o
it in units of the mean
Earth-Sun distance, 1 A.U. (astronomical unit). If the o
it is circular (as will
e assumed in this lab) the semi-major axis is the same as the radius of the
o
it.
p is the period of the o
it in Earth years. The period is the amount of time
equired for the moon to o
it the parent body once.
In 1608 the telescope was invented, allowing the observation of objects not visible to the naked
eye. Galileo used a telescope to discover that Jupiter had four moons o
iting it and made
exhaustive studies of this system. The Jupiter system was especially important because it is a
miniature version of the solar system which could be studied in order to understand the motions
of the solar system. The Jupiter system provided clear evidence that Copernicus’ heliocentric
model of the solar system was physically possible. Unfortunately for Galileo, the inquisition took
issue with his findings; he was tried and forced to recant.
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3
p
dM =
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Introduction
We will observe the four moons of Jupiter that Galileo saw through his telescope. They are
named Io (pronounced “eye-oh”), Europa, Ganymede and Callisto (in order of distance from
Jupiter). The moons appear to be lined up because we are looking edge-on to the o
ital plane
of the moons of Jupiter (see Figure 1).
As time goes by, the moons will move
about Jupiter. Although the moons move
in roughly circular o
its, you can only
see the perpendicular distance of each
moon to the line of sight between Jupiter
and Earth.
Therefore, the perpendicular distance of
the moon should be a sinusoidal curve if you plot it versus time (see Figure 2). By taking enough
measurements of the position of a moon, you can fit a sine curve to the data and determine the
adius of the o
it (the amplitude of the sine curve) and the period of the o
it (the period of the
sine curve). Once you know the radius and period of the o
it of that moon and convert them
into appropriate units, you can determine the mass of Jupiter by using Kepler’s Third law. You
will determine Jupiter’s mass for each of the four moons; there will be e
ors of measurement
associated with each moon, therefore your Jupiter masses may not be exactly the same.
The Jupiter program simulates the operation of an automatically controlled telescope with a
charge-coupled device (CCD) camera that provides a video image to a computer screen. It is a
sophisticated computer program that allows convenient measurements to be made at a
computer console, as well as adjusting the telescope’s magnification. The computer simulation
is realistic in all important ways, and using it will give you a good feel for how astronomers
collect data and control their telescopes. Instead of using a telescope and actually observing
the moons for many days, the computer simulation shows the moons to you as they would
appear if you were to look through a telescope at the specified time.
APPARENT POSITION OF A
MOON
The apparent position of a moon
varies sinusoidally with the changing
angle form the line of sight as it o
its
Jupiter. Here the apparent position is
measured in units of the radius of the
moon’s o
it and the angle measured
in degrees.
Figure 1
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Overall Strategy
This is the overall plan of action for this laboratory exercise:
• Use the CLEA Jupiter program to observe and measure the apparent positions of the moons
of Jupiter.
• Plot your observations for each moon on the appropriate graph paper supplied with this write-
up.
• Carefully sketch in the curve (sine curve) best representing the data on each graph.
• Determine the period and semi-major axis for the o
it of each moon form its graph, then
convert the values to years and AUs, respectively.
• Calculate the mass of Jupiter from your observations of each moon, then determine the
average value for Jupiter’s mass form your individual values.
Installing and Running the CLEA Jupiter Software
1. Once you have downloaded the software package for the CLEA Jupiter program, it will
appear as a file called “JupLab”.
2. Double click on this icon or file name and a self-extracting program will run. This
program will install the software on your computer. Follow the instructions that are shown
to you.
3. Once the program is finished installing, there will be an icon located on your desktop that
looks like this:
4. Double click this icon. This should
ing up a starting screen with a list of menu items
across the top.
Using the Jupiter Program
1. Open the Jupiter program by
double-clicking on it with the
mouse. The first screen should
look like this:
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You must first select “File” then “Log In” from the menu before taking data. A popup window
will appear that looks like this:
DO NOT ENTER ANYTHING IN THIS WINDOW!
2. Click “OK” to continue. The program will show you a warning box that looks like this:
simply click “OK” and continue.
3. The next screen will look like this:
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4. Select “File” then “Run”. The next dialog box to appear is Set Date/Time.
There is nothing to change for this box.
5. Click “OK” to continue.
6. Select “File” then “Timing” to set up the time interval. The next dialog box to appear is
Timing Intervals.
The observational time interval will need to be changed to 12 hours.
7. Click “OK” to continue.
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8. The next screen should look like this:
9. You can display the screen at four scales of magnification by clicking on the 100X, 200X,
300X and 400X buttons at the bottom of the screen. In order to improve the accuracy of
your measurement of a moon, you should use the largest possible magnification that
still leaves the moon on the screen.
10. In order to measure the perpendicular distance of each moon from Jupiter, move the
pointer until the tip of the a
ow is centered on each moon and click the mouse.
Information about the moon will appear at the lower right corner of the screen. This
includes the name of the selected moon, the x and y pixel location on the screen, and the
perpendicular distance (in units of Jupiter’s diameter) from the Earth-Jupiter line of sight
for the selected moon as well as an E or W to signify whether it is east or west of Jupiter.
If the moon’s name does not appear, you did not center the a
ow exactly on the moon;
try again.
Jupiter is in the center of the screen, while the small point-like moons are to either side.
Sometimes a moon is behind Jupiter, so it cannot be seen. Even at high magnifications,
they are very small compared to Jupiter. The cu
ent telescope magnification is
displayed at the upper left hand corner of the screen. The date, UT (the time in Green-
wich, England) and J.D. (Jupiter’s diameter in A.U.) are displayed at the lower left hand
corner of the screen.
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Click on each of the moons to find the number of J.D. (Jupiter diameters) the moon is
away from the center of Jupiter. Notice the edge on Jupiter is 0.5 J.D. To measure each
moon accurately, switch to the highest magnification setting that leaves that moon on the
screen. If the moon is behind Jupiter, record the distance for that moon as zero. Below is
an example of how to record your data:
Example:
(1) Date (2) Time (3) Day (4) Io (5) Europa (6) Ganymede (7) Calisto
7/ XXXXXXXXXX XXXXXXXXXX15
7/ XXXXXXXXXX XXXXXXXXXX
Column 1: Local Date
Column 2: Universal Time
Column 3:
Day - number of day (e.g. 1.0, 1.5, 2.0, ...) NOT counting cloudy days.
Enter cloudy days in the space provided at the bottom of the data
sheet.
Columns 4-7: Record each moon’s position under the column for that moon. Use + for west and - for east.
For example: If Europa were selected and had an X = 2.75W, you would enter that in
column 5 as +2.75.
11. When you have recorded the Universal Time and the perpendicular distances for every
moon, you may make the next set of observations by clicking on the Next button.
12. When a new screen appears, be sure to return to 100X zoom and repeat steps 9 – 11.
13. When you have finished taking all of the necessary readings, you may quit the program
y selecting “Quit”.
Cloudy Days
In reality, astronomers often have to deal with