The true resonance of Jupiter's moons

M.T. Cranium

Many of you probably know that Jupiter has four "main" or Galilean moons, known either as J-I, II, III and IV or as Io, Europa, Ganymede and Callisto.

And some of you may have read that the first three of these are locked into a resonance of 1:2:4 (that is, Ganymede makes one orbit while Europa makes two, and Io makes four).

But as I studied the actual data, I found that the true resonance of the three Galilean moons is not quite 1:2:4 but is very close to 61:123:247. Notice this means that during a period of about 437.15 days, Europa makes one extra orbit from what the simpler resonance would predict (123 instead of 122) and that Io makes three more.

The actual data reveal that the resonance is precise at an extra .0011 orbits making the "fundamental period" of the three-moon system 437.1575 days.

To clarify, that means that in that period, Io makes 247.0011 orbits, Europa makes 123.0011 orbits and Ganymede 61.0011 orbits. Once again, this makes the 61:123:247 ratio slightly approximate, although much closer than the 1:2:4 ratio.

If you wonder where J-IV (Callisto) fits into this picture, first of all, in the "fundamental period" (437.1575 days) it makes 28.24 orbits. This means that 4 times the fundamental period, or 1,748.63 days, brings Callisto back to almost its original orientation to the other three Galilean moons. The return is even more precise after 29 fundamental periods, which works out to 12,677.56 days, about 34.7 earth years (or almost three Jovian years).

From these calculations, and some observations, I noted that throughout many centuries and possibly millennia (probably not ever since the system came into being) J-I, II and III have been locked into this resonance which never sees them at the same alignment. Each pair reaches "mutual" alignments, or times when an observer on Jupiter would see them together, but all three of them never reach a triple alignment. For example (adjusted to the slight parallax induced by earth's orbital position) we see one set of mutual transits of Jupiter by Io and Europa each 437.1575 days, one set of Europa-Ganymede transits, and three sets of Io-Ganymede transits. Because the inner moons are moving slightly faster than the ratio 4:2:1 would imply, their alignments move back around the orbital paths between these occasions when they pass at what a Jovian observer would call "new moon." In other words, from that perspective, each alignment would come a few minutes earlier in the lunation, while from ours, they occur increasingly before transit of Jupiter.

I find the exclusion of the triple alignment interesting and wonder if anyone with a stronger background in orbital dynamics could speculate as to why a triple alignment is excluded? I am pretty certain that any three moons including Callisto can reach a mutual alignment.

Rubecula

I don't know the answer but if I may make a guess?

Mutual gravity fields cause acceleration and deceleration and the more aligned the moons are the more this effect occurs. Which means that although two may come into synchronicity (is that a word?) Three can not as the added gravitational effect causes the third (or fourth) moon to either speed up or slow down slightly for a short time.

Just a wild out there sideways guess I am afraid I have no idea if it has any truth, or even if it is plausible.

Calibos

We're simple Astronomical folk here on boards astronomy forum MT. The Irish astronomical boffins post over on www.irishastronomy.org and the international ones over on www.cloudynights.com. The most scientific answer you'll get from us here is, "Dunno, how dey work but dey shure is purty!"