So let's go observing!
Fire up the applet and start collecting data. Each time you click "Step" you'll get a new picture of Jupiter and its moons in the upper window, and a new set of datapoints in the lower. The time between steps is controlled by a little pulldown menu below the reset button.
Sometimes you'll see that it's cloudy out, and you won't get any data. And when it's daytime (from 6:00 - 18:00) you won't get any data either. Keep observing until you build up your dataset with lots of data.
Now use the slider bars to fit a sinusoidal curve to the points. The parameter "a" controls the fitted distance, while the parameter "P" controls the period of the orbit. "Shift" moves your fit from side to side so that you can best match it up to the data.
So try and fit four sinusoids to the data. It's tricky; start with the most distant moon and work your way inwards. You may have to do it using different sets of data taken at different intervals. When you have a good fit to all the moons, write down P and a for each of the four moons.
Now, for each moon calculate . Do the numbers come out to be pretty close to one another? (Don't worry if they are not exactly the same -- it's hard to make a perfect match when you fit the data.)
Now, from your P and a for each moon, calculate Jupiter's mass. If we measure P in days and a in kilometers, and we want Jupiter's mass in kilograms, then the gravitational constant G is given by
G = 5 × 10-10.For each moon, what do you get for Jupiter's mass? So what is your best estimate for Jupiter's mass? Why does it help having four moons?
Compare the value you've calculated to Jupiter's true mass. (Don't peek until you've done it yourself!)