In our edition of Sidereus Nuncius Galileo provides us with what seem to be enough observations to determine the periods of the moons of Jupiter, yet he says he's still working on it. Why? I have copied all the moons of Jupiter observations for you (see our PROWL site). Your job is to lay out Galileo's observations on a vertical line centered on Jupiter and spaced according to the dates and times of the observations (much depends on your doing this carefully!).
Each moon travels in a circle about Jupiter, and we see these circles edge on. Therefore we should see each moon swing from side to side as time marches on. If we plot the position of a moon (apparent distance away from Jupiter) versus time, it should trace out a regular (unchanging period, unchanging amplitude) sinusoidal curve. Click here to watch this happen. Your job is to connect the dots of Galileo's observations with regular sinusoidal curves. If you can draw four smooth sinusoidal curves through the correct points on your plot of the observations, you will be able to identify which dot is which moon and estimate the periods of each of the moons. This is hard to do for the innermost moons, but not so tough for the outermost, Callisto.
Work in groups of 4. Each group will put up a poster in the course room. Each poster should present the group's diagram of the observations (get the data from the "Galileo's data" pdf on PROWL) with the sinusoidal curve drawn through the outermost moon, and giving your best estimate of the period of that moon (with some measure of the uncertainty in your estimate). Write up your group's results in the Research Paper Format.
This page last modified 12:01, August 28, 2012.