New! I have a Javascript Jupiter's moons page -- prettier, more features, and no Java required. That said, if you still want the Java version:
The "Juplet" Java applet shows the positions of the four Galilean satellites of Jupiter, their shadows, and the great red spot.
To show the positions of the moons at a different time, edit the date in the text field then hit return to recalculate. If you see "Can't Parse Date" or the time appears to be off, or if you have any other problems and want to send a bug report, first see my bug report page.
Current GRS position: system II longitude 80. some years one can find its location at the ALPO Jupiter section.
This applet is also available as part of a Zaurus PDA package.
I have some sketches of what small telescopes will show on Jupiter and other astronomical objects.