# Could the Galilean moons tidally lock Jupiter?

From my understanding, given enough time, the gravity of the Moon is gradually increasing the time it takes for Earth to rotate around its axis, and that, as a result, in the distant future, Earth will be tidally locked to the Moon (ignoring the fact that the Earth and Moon system will probably be swallowed by the sun before this could happen as the Sun dies in five or so billion years).

Thinking about this fact, I started wondering if, given a preposterous amount of time, Jupiter could become tidally locked as a result of the gravitational force exerted on it by its Moons? Or would the fact that its Moons are fairly similar in Mass and that their positions differ, mean that Jupiter wouldn't get tidally locked, as it would be getting pulled on from more than one direction? If Jupiter only had one Moon, Ganymede, would they become tidally locked if given enough time? If so, why not? However slowly, surely Ganymede must exert tides on Jupiter, and in doing so slow down its rotation?

• I think that the scale is on the order of the Earth becoming tidally locked to the ISS. – ShadoCat Jul 25 '18 at 19:46
• Jupiter isn't solid, it doesn't even rotate at a constant angular rate (rotation rate depends on latitude). – barrycarter Jul 25 '18 at 19:51

Every action is accompanied by equal and opposite reaction.

Specifically, the braking of spin of a planet due to tidal forces exerted by a moon is accompanied by the planet's tidal bulging accelerating the moon's orbital speed (which promptly converts into increase of orbital radius and corresponding reduction of orbital speed).

If the moon is massive comparing to the planet, in relatively low orbit, and the orbital period not very different from the planet spin period, eventually the planet will lock tidally. But if there is a huge mass difference and significant difference in periods, the moons will either get ejected from the system or travel to orbit so high the tidal forces will be too weak to eject them. And considering both mass of Jupiter and its rather brisk spin rate (1 Jupiter day is 10 hours long) the latter scenarios are more plausible.

Note, for moons below the synchronous orbit altitude the same influence is braking; lowering the moon orbit and eventually deorbiting the moon; this might be the eventual fate of Metis, the innermost moon of Jupiter; orbital radius of 129,000km vs 160,000km of synchronous orbit radius. Similar fate may meet the retrograde moons.

• Interesting! I guess that's why Triton will eventually collide with Neptune? – Happy Koala Jul 25 '18 at 20:04
• Came to think of another example; Phobos will collide with Mars, while Deimos will eventually gain enough speed to escape from Mars. – Happy Koala Jul 25 '18 at 20:08
• @HappyKoala: Yes; Triton is well above the stationary orbit, but it's retrograde; for these tidal forces are braking regardless of period. BTW, with deorbiting it's not that simple; Phobos may fall apart into a ring of rubble any time now; it's already below Roche fluid limit, nearly equatorial nearly circular orbit (just 1deg inclination); that would mean as the rubble is distributed around the orbit there won't be a single traveling tidal bulge (or traveling ridge, if it was an inclined ring); just a rather static equatorial ridge that doesn't exert all that much braking force. – SF. Jul 25 '18 at 20:43

Could the Galilean moons tidally lock Jupiter?

No.

I think we can just look at the angular momentum for a quick answer.

The rotational angular momentum of Jupiter is estimated here to be about 7E+38 kg m^2/s based on uniform density. Surprisingly, it's given as 6.9E+38 kg m^2/s here and here as well.

The same link lists the four largest moons and the sum of their angular momentum is about 4.5E+36

With a factor of over 150 more angular momentum in Jupiter's rotation than in the orbits of its four largest moons combined, I don't think they can possibly put much of a dent it Jupiter's rotation rate at all.

I'll be editing this answer as soon as I can find some better information about Jupiter. So I've asked Total rotational angular momentum estimates for Jupiter?.

For a Jovian satellite, the vis-viva equation gives us (for a circular orbit)

$$v = \sqrt{GM_J/a}$$

So the orbital angular momentum will be

$$mvr = mr\sqrt{GM_J/r} = m\sqrt{rGM_J}.$$

This shows that if a satellite's orbit around a central body is raised, there isn't an immediately obvious fundamental limit to the amount of angular momentum it can take from the planet.

Castillo is currently at 1.9 million km, and Ganymede is about 1.1 million. To increase their orbital angular momentum by a factor of 100 however would require a factor of 10,000 increase in their orbits' sizes, and that would put them way way beyond the Jupiter's Hill sphere with respect to the Sun, so no dice!.