OUTLINE OF  THE EXERCISE

This laboratory exercise purposes to determine Jupiter's mass using Kepler's Third Law, after a study of the movements of its four Galilean satellites. The moons' movements are calculated by the software using algorihtms developed by the Belgian astronomer Jean Meeus, and their position at a given time is superimposed on a middle-range photograph of Jupiter taken by the Pioneer 10 space probe. One only has to place the mouse pointer on a moon and then click, to display its abscissa x, expressed in Jupiter diameters, along the equatorial line perpendicular to the line of sight (Fig1.) The movement of the moons is assumed to be circular and thus uniform.

     Students set an observing time interval at the start and then, by clicking on the <Next>  button, they increment time by one set interval. Positions are plotted versus time on supplied rectangular grids suited to each satellite, a complete plot requiring from 15 to 20 measurements (for each satellite). Time is counted in Earth-days. They should obtain a sine curve showing x=f(t) shown on Fig. 2 for an imaginary moon named CLEA.

The period and amplitude of the sine curve give respectively the period T and the radius (or semi-major axis) a of the moon's orbit. These are then converted into Earth-years and astronomical units (AU) respectively. With these units, Kepler's third law is simply written: M_J =a³/T²(4 Pi²a³/GM in SI units).

Four values of Jupiter's mass are thus calculated, from which a mean value and an error interval can be inferred. A few supplementary questions on errors, on applying this method to the Earth-Moon system etc. complete the exercise.

SESSION PROTOCOL

The students should have read beforehand the leaflet (in English) written by the Project CLEA team. In order to reduce their workload, I have made a French translation of the written parts of the leaflet, which I hand out with the English original a week beforehand.

Though this preparation work is to be expected as a matter of course in 'classes préparatoires', it may not be exigible in other classes (lower or upper secondary), where a preparatory session dedicated to theoretical aspects may be required. Central force movements and thus Kepler's third law are on our syllabus; this lab exercise is a good illustration of lessons, which allows students to apply the mathematical tools seen in class and to discover their practical use in astronomy. However, since the study is limited to circular orbits, the exercise can be used to illustrate planetary movements in earlier classes where these are on the syllabus.

The software introduces a semblance of realism by generating random cloudy days in which observation is not possible. On the other hand, whenever the moon is behind or in front of Jupiter, its position is unavailable (at least in the old versions of the software: it is on the latest ones). Lastly, a given time interval is only suitable for one of the moons, so that  first, a trial curve has to be plotted for the four satellites, then a rough estimate of their period determined, and a new series of measurements taken for the two or three moons whose curve is not satisfactory.Measurements and plottings take a good two hours and some students have to complete the treatment of their data after class. A few clever students "cheat" and get a rough estimate of the time taken by each moon to go round the planet by fast-forwarding the display, clicking repeatedly on the <Next> button without reading the moons' positions. It is far less realist but saves time.

As a whole, my students seem to find this exercise entertaining, interesting and easy, as the maths level necessary is really basic, which for technicians who have small physics and less maths and struggle all year long to fill the gaps in the knowledge of these two subjects, is a very pleasant surprise.

APPRAISAL

For: This exercise is easy to use. The software runs perfectly on our ten-year-old computers and earlier versions can be stored on 1.44 MB diskettes.They are self-executable,  requiring no installation: all you have to do is copy the files on your computer's hard drive.The manuals supplied with the software are very clear.

The exercise is pleasant and instructive. If one takes care to draw the students' attention to the flaws and inaccuracies of the model used by the software, it is a good introduction to astronomy and, moreover, an opportunity to approach modelling issues.

Against: Despite trying hard to be realist, the software does not entirely succeed. Particularly the moons'details are not displayed and especially, Jupiter's rotation is not accounted for and neither are variations in lighting, projected shadows etc, which can give astronomical novice wrong ideas about Jupiter.
The supplied documents are in English. They must be translated for the students or a project can be set up with the English teacher, but it takes time.

CONTACTS

CLEA software can be downloaded fromthe Gettysburg University website http://public.gettysburg.edu/~marschal/clea/CLEAhome.html (use the link below).

You can also order a CD online (the latest versions are quite large, especially for people with dial-up connections to the internet) or by sending an e-mail to clea@gettysburg.edu. It is absolutely free for teachers and if need be, you can give the name and address of your institution. The software come with a student's manual, a user's guide for the teacher and in some cases, with exercises in .pdf or Word format. I have personally  used only two of the proposed lab exercises, the one I have reviewed here and 'The Classification of Solar Spectra', because they can fit without too much trouble in my syllabus. The other exercises, however, can also be interesting and only want assesment.