What fuels Io's volcanic activity?

[shelanachium]

Io is the most volcanically active body in the Solar System. This is because the outer satellites, especially the nearest, slightly distort its orbit from perfect circularity. So the distance of Io from Jupiter is not quite constant, and as tidal forces vary as 1/r^3, the distortion of Io in Jupiter's powerful gravitational field varies notably, creating considerable internal heat, just as does kneading a lump of dough.

All very well, but what part of the Jovian system is losing the energy that Io is gaining?

 

[robertm]

If the majority of Io's thermal activity is caused by the interaction of tidal forces from Jupiter and its moons then the energy is being generated internally by the deformation of its geology due to this gravity. The number of satalites surrounding a planet has no effect on the Fg that that planet applies to its satalites. Only the mass and dis. of the planet and its satalite has any bearing on the Fg. So no energy is being lost or "transfered". The energy is all created from internal deformation of Io's atoms (on a huge scale).

 

[cesiumfrog]

energy is .. created

I think not. This situation is similar to how our moon looses energy because the ocean tides lag (due to friction) behind it constantly.

 

[shelanachium]

'So no energy is being lost or "transfered". The energy is all created from internal deformation of Io's atoms (on a huge scale)'

Sorry, that won't do. The energy to do this must come from SOMEWHERE! Otherwise we could build a perpetual motion machine based on what is happening on Io. Were it convenient, a geothermal plant set up there would solve all our energy problems for a long time indeed.

A Wikipedia article suggested it was coming from Jupiter's rotational energy, but no explanation of why or how was given. Seems reasonable to me, and Jupiter has plenty of rotational energy to give away!

 

[Shooting Star]

QUOTE=shelanachium;1683408]All very well, but what part of the Jovian system is losing the energy that Io is gaining?[/QUOTE]

The tidal forces of Jupiter deform Io, which gives rise to the volcanic activity. The energy of that comes at the expense of Io's rotational kinetic energy (and possibly the orbital KE, too.) The rotation of Io slows down as a result. (I think this is the point robertm had tried to make.)

Jupiter does not lose any significant energy because of this. Just consider the hypothetical case if Jupiter had been a rigid hard sphere. The same tidal forces would have acted on Io, but not on Jupiter, and there would not have been any mechanism to make Jupiter lose any energy. In reality, tidal forces due to Io and the other moons of Jupiter must be there, but are probably insignificant.

 

[LURCH]

I think the orbital energy (of Io's orbit) is the key source, since this same effect would take place on a planet and moon that were tidally locked. Tidally locked bodies cannot give up rotational energy, as there potential difference is zero, yet, if the sattelite's orbit were as eliptical as Io's the core-heating would still take place. It is the difference between the major and semi-major axes that is generating the heat. Therefore, I must conclude that Io's orbit continues to get less eliptical as energy is used to make core heat.

 

[shelanachium]

But the ellipticity is maintained by the tidal effects of the satellites further out, especially the nearest, Europa.

 

[LURCH]

True. So, those orbits must be sharing in the effect, having their orbits elongated and their cores heated. But overall, the eccentricity of all these orbits must get rounded off, and the energy converted to heating of their cores, then radiating off into space.

 

[Shooting Star]

I think the orbital energy (of Io's orbit) is the key source, since this same effect would take place on a planet and moon that were tidally locked. Tidally locked bodies cannot give up rotational energy,...

Do you know for sure that Io is tide-locked to Jupiter?

I had mentioned that both the rotational energy and the orbital energy of Io contributes to Io's volcanic energy. Upon reading your post, I wanted to know more. Unfortunately, there are some contradicting information in the net.

http://www.planetaryexploration.net/jupiter/io/tidal_heating.html" corroborates what has been said in the last two posts.

http://csep10.phys.utk.edu/astr161/lect/jovian_moons/io.html" is really worth looking at.

http://en.wikipedia.org/wiki/Io_%28moon%29" gives only the tidal effect of Jupiter as the reason in the first few lines.

 

[LURCH]

Do you know for sure that Io is tide-locked to Jupiter?

Not at all. I only said that this effect would still take place if they were, and therefore rotational energy is not the key to answering this question.

However, Io is as tidally locked as it can be, under the present circumstances. What I mean is, because Io's orbit is elliptical, it can't really be synchronous. Elliptical orbits do not carry a constant speed, they must speed up through the lower portion and slow down at higher altitudes. So, in order to be perfectly synchronous, the moon would have to revolve on its axis at ever-varying speeds, which is pretty much impossible.

However, even if Io could somehow be in perfect tidal-lock, with one point always facing Jupiter, it would still be heated by tidal forces. The eccentricity of its orbit ensures that it will cotninue to be stretched out oblong, then returned to a more spherical shape, and this flexing is what causes the majority of the heating.

 

[shelanachium]

Our own moon rotates synchronously, but has an elliptical orbit. It therefore doesn't EXACTLY keep the same face to the Earth all the time - it appears to 'rock' a little from side to side. (look up 'lunar librations'). This indeed causes stress within the Moon and is thought to be one of the causes of moonquakes.

But the tidal effect of Earth on our moon is much less than that of Jupiter on Io, so our moon no longer has anything like Io's internal heat and volcanic activity.

 

[kamerling]

When a moon stretches, because of the tidal effect, it's gravitational attraction to the planet will become bigger by

$$\frac {m_m m_p G d r } {R^4}$$ where d is the height of the bulge, r is the radius of the moon and R the distance to the planet.

(this is actually a simplification, assuming that the mass of the moon is divided in two halves, at a distance R+r+d and R-r-d from the planet. The real effect will be smaller, but proportional to this).

If there was no friction, Io would be the most elongated when it was the closest to Jupiter.
Because the stretching and compression lag , Io will be slightly more spherical when it is moving towards Jupiter, and slightly more stretched when it is moving away from it, so the gravity is slightly less when Io is accelerated as it is moving towards Jupiter, and slightly more when Io decelerates as it moves away from jupiter. This will produce a breaking effect.

If Io was 10 meters more stretched on average when it was moving away from Jupiter, this would produce an extra gravitational force of 6.5*10^12N. This force acts over the 3400 km difference between perihelion and apihelion and would leech 2*10^19J/rotation from the planet, or about 1.3*10^14W.
The surface area of IO is 4*10^13 m^2 so that means about 3.2 W/m^2 of heat is produced. This compares to less than 0.1 W/m^2 of heat produced in the interior of the Earth by radioactivity.

 

[LURCH]

Thank you Kamerling. I knew it had to be happeneing but I did not know the mechanism by which it happened. So this breaking effect is constantly trying to "round out" Io's orbit, yes? And the pull of other moons keeps that orbit elliptical, by pulling on Io. Io must, in turn, the pulling on them. So, the orbits of Europa and Callisto are being made elliptical by their interaction with Io. Does this not mean that the eccentricity of the three moons could be added up and divided amongst them, to come up with an overall "average eccentricity," for the group? And this eccentricity (of the three moons combined) must also be decreasing over time, correct?

 

[kamerling]

And this eccentricity (of the three moons combined) must also be decreasing over time, correct?

I don't believe there is something like conservation of eccentricity. According to wikipedia, Io is in 4:2:1 orbital resonance with Europa and Ganymede. Jupiter is rotating faster than Io rotates around it, and the tides that Io raises on Jupiter would cause Io to move outward, if it weren't for the other two satellites. So it seems likely that the energy source of all this is Jupiters rotation. The angular momentum that Jupiter loses must eventually go to it's satellites.

 

[shelanachium]

Thanks! That's what Wikipedia said - but gave no explanation. I thought it had to be Jupiter's rotation; were the energy coming from the orbits of the satellites continuously changing in one direction, they would alter radically over geological time. Jupiter's rotation is a much larger source of energy.

 

[LURCH]

I don't believe that is correct:

It is the eccentricity that is causing the tidal heating (as I mentioned in response #6). If the orbit gets higher and Jupiter's rotation slows until the two are tidally locked, but Io's orbit retains its eccentricity, the heating will continue (and we have our perpetual motion machine). If Io's orbit were more rounded and as low as its current perihelion, Jupiter's rotation would continue to push the moon outward, but no heating will occur. Therefore, the planet's rotation is not the source of the heat energy.

Only by rounding off the satellite's orbit can we eliminate the heating. So, orbital eccentricity must be the source of the energy that is heating Io's interior. Although you are quite correct in saying that there is no such thing as "conservation of eccentricity," there is conservation of energy, and the energy is coming from the eccentricity. As energy is expended, the eccentricity must be decreasing.

 

[CDCraig123]

Has anyone given any thought to the idea that gravity is being turned into energy here. And before you say no energy is finite it can not be created. Is your answer based in the assumption that gravity is infinite or that gravity is nothing more then a force carrier. Think about this there is a force that can be measured that keeps the Earth from losing its orbit and flying into space. How do we measure gravity on this planet. If you jump out of a plane you will get pulled down at 9.8 meters per sec. Is that not the same as kinetic energy. In Ios case it seems to be locked into a orbit that heats its core if any of that heat energy was being transferred from the gravity of Jupiter at no lose of orbit or velocity if even 0.01% it would mean one of two things. Energy is Infinite or gravity is finite. One final thought as we speed around the sun on planet Earth doesn't our orbit create centrifugal force and gravity from our sun counter acts this centrifugal force keeping us locked into a stable orbit centrifugal force is kinetic energy there for doesn't gravity have to at least absorb energy.

 

[Nabeshin]

In Ios case it seems to be locked into a orbit that heats its core if any of that heat energy was being transferred from the gravity of Jupiter at no lose of orbit or velocity if even 0.01% it would mean one of two things. Energy is Infinite or gravity is finite.

But it does lose energy. Precisely the same with the moon, which is receeding from the Earth due to tidal interactions. The process is exactly analogous, so yes the energy does come from somewhere and no it is not an infinite reserve.

Edit: Wait what? I didn't even notice that this was a response to a three year old thread! CDCraig123: Please don't post in threads that are this old, if you really have a question/topic, please start a separate thread.