Moon Io orbits Jupiter 4 times as fast as Ganymede. Set moon pairs to 1 for just Ganymede to Io. Set to 2 to see the pattern for the Ganymede-Europa pair also. Europa orbits 2 times as fast as Ganymede. These ratios 4:2:1, are a kind of orbital resonance. With a dot placed at the X of one moon and the Y position of the other, a pattern is revealed. Spacebar hides variables. We make pairs of musical notes play when pairs of moons align (when they have the same angle). The notes are octaves apart. The highest note is for Io and has twice the frequency of the note for Europa and so sounds one octave higher. Europa's note has twice the frequency of Ganymede. This is to bring out the analogy between the doubling of orbital frequencies and musical frequencies (once called the music of the spheres). You can adjust "speed" but the ratios of the angular frequencies of the moons will remain 1:2:4. Moons sizes are not to scale. Distance to Jupiter is not to scale. "p" key for polar view of Jupiter, "s" for side view.
Io goes around Jupiter twice for every time Europa does. Europa circles Jupiter twice for every time Ganymede does. The ratio of their frequencies is 1 to 2 to 4. Setting pen to X of one moon and the Y of the other yields Lissajous patterns that look like infinity symbols. Moons and their orbital radius not to scale. For every one orbit Ganymede makes, Europa makes two and Io completes four. Io’s volcanoes are a direct result of this relationship because the gravity tugs of Europa and Ganymede, combined with the tidal force of Jupiter, produce a continuous source of heat for Io’s interior. We give each moon a note. When pairs of moons align we hear pairs of notes. You can hear a musical rhythm (easier to hear at higher speeds). The angular frequency for the moons is not affected by the radius or circumference of the orbits. So the frequencies are not affected by the fact that the moons and their distances from Jupiter are not to scale. Ganymede's angular frequency (in arbitrary units) is set to "speed." Europa's angular velocity is "speed" X 2. Io's angular velocity is "speed" X 4.
