4
$\begingroup$

According to Wikipedia, re Europa's tidal flexing:

the tidal flexing kneads Europa's interior and gives it a source of heat, possibly allowing its ocean to stay liquid while driving subsurface geological processes.The ultimate source of this energy is Jupiter's rotation, which is tapped by Io through the tides it raises on Jupiter and is transferred to Europa and Ganymede by the orbital resonance.

https://en.wikipedia.org/wiki/Europa_(moon)

Does this imply that Jupiter's rotation is slowing over time, since it is losing energy due to raising tides on Io? (Or just generally, does raising tides cause rotation to slow?)

$\endgroup$
  • 1
    $\begingroup$ Just to clarify, you have one of your statements backwards. Jupiter's rotation is slowing over time, since it is losing energy due to Io raising tides on Jupiter. It is not due to Jupiter's tides on Io. $\endgroup$ – zephyr Apr 27 '17 at 19:59
6
$\begingroup$

Yes

Tidal locking is a mutual process, and both the satellite and the parent body will eventually permanently face each other. However, while tidal locking of a satellite can happen relatively quickly (that is, within the life span of the solar system), tidal locking of the parent body is extremely slow and will in a practical sense never happen (the current age of the universe is not enough in most cases).

The relative mass of the satellite and the parent body is one of the most important factors:

  • Charon and Pluto with a mass ratio of just 8.1 are already mutually locked.
  • The Moon and Earth has a relatively high mass ratio of 81. This causes a measurable effect on the Earth.

Compare that to the mass ratio of Juptier and Europa of 39,600 (or Io: 21300, Ganymede 12,800, Callisto: 17,600). While the time required for a locking of Jupiter itself is difficult to measure due to the fact that we don't have the necessary data about the moons, this is not a noticeable effect before the Sun dies.

Tidal locking of the parent body can most likely be justified by conservation of energy, but conservation of momentum gives a more intuitive view: As the satellite slows down and moves away from the parent body, its angular momentum increases (angular momentum is proportional to distance times velocity, and the orbital velocity is proportional to the square root of distance). This angular momentum must be supplied from somewhere. The only source for that is the rotation of the parent body. Even if all the moons of Jupiter were to completely escape, the angular momentum drain is not enough to stop the rotation of Jupiter.

$\endgroup$
  • 1
    $\begingroup$ Re Tidal locking of the parent body can most likely be justified by conservation of energy ... -- No, it can't. Tidal locking is inherently a dissipative process, meaning that mechanical energy is not conserved. Tidal locking of the parent body can most likely by justified by the fact that mechanical energy is not conserved. Some of that mechanical energy is converted to heat and radiated into space. How conservative the process is is measured by the body's tidal quality factor Q. A bigger Q means a longer time to lock, all other things being equal. Nonetheless, plus one. $\endgroup$ – David Hammen Apr 28 '17 at 1:14
4
$\begingroup$

Nope.

(Sorry, the other answer beginning with yes, I wanted to begin one with no), but both answers are correct from a certain point of view.

Jupiter's rotation is speeding up because it's contracting. See here. Jupiter does slow down due to it's tidal bulge and tugging from it's moons, but the bigger factor is that Jupiter loses more heat than it gets from the sun. As Jupiter loses heat and as it gravitationally coalesces, it gets smaller, which speeds up it's rotation. That's the larger of the two factors, though running the numbers makes me cringe a little, but I'm fairly certain.

The rate of rotation of a gas giant is somewhat difficult to measure with accuracy, I'm fairly confident that overall the shrinking is the larger of the two factors and Jupiter's rotation is slowly increasing.

For your 2nd question, a tidal bulge can slow down or speed up a planet, it depends on whether the moon moves ahead of or behind the tidal bulge. If Venus, which rotates very slowly, had a moon, the moon would likely slowly increase Venus' rate of rotation and the Moon would move towards Venus, not away from Venus. For moons around more rapidly rotating planets, the planet slows down by the tidal interaction and the Moons move away. In Jupiter's case, it's dense ionosphere may create some resistance that counteracts any tidal force moving it's moons away.

Io, Jupiter's innermost moon, by one article, loses about a ton a second to volcanic activity and tidal flexing and some of that material spirals into Jupiter creating it's permanent Auroras. It's difficult to say what the net effect on rotation from that would be, but it could have an effect.

There's a few different factors too look at beyond just the tidal interaction. Io, if it was alone with Jupiter, it could well slowly drift closer, but the 4 moon resonance might stabilize it's orbit somewhat. The entire picture of the motions of Jupiter's moons is above my pay-grade, but Jupiter's shrinking is still likely the single biggest factor, which means it's rotation rate is probably slowly increasing not decreasing.

$\endgroup$
  • $\begingroup$ I think I've missed something: "Io [...] loses about a ton a second..." A ton of what? $\endgroup$ – Asher Apr 30 '17 at 1:47
  • $\begingroup$ It's hard to see, but the Io is blue. Click on it, you'll see the source. "As Jupiter rotates, the magnetic forces strip away about a ton (1,000 kg) of Io’s material every second." If it's a bad source, I'll gladly delete that sentence. I took them at their word. I've also expanded the hyperlink. $\endgroup$ – userLTK Apr 30 '17 at 3:07
  • $\begingroup$ I see now, thank you. I don't consider myself qualified to verify a source, but you might edit the answer further to include the mechanism by which Io is losing the material. $\endgroup$ – Asher Apr 30 '17 at 3:21
  • $\begingroup$ @Asher I'd prefer not to go into it too much detail, other than to say tidally induced volcanoes, because it's complicated and discussed in some detail here: astronomy.stackexchange.com/questions/18567/… The ton a second might be way off, but Io does feed Jupiter's magnetosphere and it likely loses some gas to volcanic assisted jeans escape. Going into specifics is leaps and bounds over my head. I wanted to keep my answer to rotation rate and even then, I left some open questions. $\endgroup$ – userLTK Apr 30 '17 at 4:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.