# Is Io a magic energy machine?

Io gets its volcanic heat from being flexed by Jupiter's gravity, and this seems to go on forever. That sounds like a magic energy source, since Jovian gravity is perpetual and Io seems to remain in orbit perpetually. Have we discovered magic?

• This is more a physics question. – Peter - Reinstate Monica Feb 14 '18 at 10:43
• @PeterA.Schneider - There's nothing wrong with astronomy questions that involve physics. Astronomy is in a sense a branch of physics nowadays, and has been since Newton. (This very much was not the case prior to Newton's time.) – David Hammen Feb 14 '18 at 13:56
• @DavidHammen true, of course -- I was just piqued by "have we discovered magic?" because the answer is purely physics, can be given with zero knowledge of the specific bodies and orbits involved and is very short. By contrast, the (hypothetical) question "Where does the energy which sustains Io's vulcanism come from, and how is the energy transferred to it?" concerns the specific bodies and hence is on the astronomy side of this intersection. It is also quite long if answered correctly and exhaustively. (I admit that he question can also be meant as a rethorical starting point.) – Peter - Reinstate Monica Feb 14 '18 at 14:27

## 5 Answers

The energy driving Io's volcanism is derived from its orbital energy and (to a lesser extent by the orbital energy of the other moons and the energy of Jupiter's rotation). Similar mechanisms power the cryo-volcanism on Enceladus and the other icy moons. The available orbital energy reservoir is huge compared to that required to drive the volcanic activity.

This does imply that the gravitational interactions on all the moons in the system are changing their orbits and rotations, albeit slowly. Given unlimited time, the orbit of Io might decay to a point where it falls within Jupiter's Roche limit and is torn apart.

(Note: the answer to How can tidal heating lower Io's orbit describes this more precisely, and points out that tidal forces are transferring energy from Jupiter's rotation to the orbits of its moons, so Io's orbit in the long term gets larger (to the point of it leaving Jupiter orbit) rather than decaying.)

• So short answer: No. – zephyr Feb 13 '18 at 20:28
• I think that the more likely end point may be that Io becomes tidally-locked with Jupiter. Like our own Moon, with the same side always facing Jupiter, there would be no more (changes in the) tidal flexing. – RBarryYoung Feb 13 '18 at 22:34
• @RBarryYoung, resonant interactions with Europa and Ganymede are preventing it from settling in to tide-friendly orbit. – NeutronStar Feb 13 '18 at 23:04
• @RBarryYoung Io is mostly tidally locked now, but as Joshua points out, small fluctuations are enough to create the continuous volcanic activity. – userLTK Feb 14 '18 at 2:11
• @zephyr ...awwww. Why does it always have to be "no" the answer to "Is it magic?". Damn Clarke always pulling the rug under our wishful feet... :( – xDaizu Feb 14 '18 at 16:35

And this seems to go on forever.

Not strictly true.

Io seems to remain in orbit perpetually. Have we discovered magic?

No and no.

Io's orbital speed is $v = 17.33 \mathrm{km/s}$. Its mass is $m = 8.9319 \cdot 10^{22} \mathrm{kg}$

The formula for the kinetic energy is: $E = m \cdot v^2 / 2$

Plugging the values for Io into it, its total kinetic energy is approximately $7 \cdot 10^{40}$ Joule according to Wolfram Alpha. That's a very, VERY large amount of energy. Io can afford to spend a small fraction of it to keep itself warm for a very long time without significant apparent changes.

But yeah, on a human time scale it does look like magic.

• It feels like you need to take into account the heat loss to determine whether you're actually spending a "small fraction". The surface temperature near the volcanoes reaches 1600K. If the whole surface (42E12 m^2) was at that temperature (it's not), by the Stefan-Boltzmann law it would emit 370kW/m^2, for 1.6E19 W total. That's 5E26 J/year, so in a billion years you'd radiate 0.1% of the orbital energy, or << a tiny fraction.. Obviously you're right from the fact it's still there – Chris H Feb 14 '18 at 9:43
• What does Io's orbital energy have to do with it's volcanism? The volcanism is powered by tidal forces from Jupiter, not Io's orbital energy. – zephyr Feb 14 '18 at 17:10
• There wouldn't be tidal forces if it wasn't in orbit, @zephyr. Energy is what keeps it there. – Beanluc Feb 14 '18 at 21:32
• Until it doesn't. – Beanluc Feb 14 '18 at 21:32
• @Beanluc There also wouldn't be tidal forces if Io didn't have mass. Does that mean an equation calculating the total mass-energy of Io is relevant to it's volcanism? My point is that Florin is somehow equating Io's orbital energy to its volcanism which is just patently wrong. – zephyr Feb 16 '18 at 15:53

You don't have to look that far, actually. The tides here on Earth -- ebb and flow -- are "powered" by our Moon's gravity. It's not expressed as heat and volcanic activity, but the mechanisms are the same as on Io.

That energy (which can be, and is, turned into electricity by tidal power stations) is not "free", though. Earth used to rotate faster (making days shorter than today's 24 hours), and the moon used to be closer (it's still drifting away at ~4 cm per year)...

Is Io a magic energy machine?

No, it's not. The source of Io's energy is Jupiter's rotation. Think of the our Moon. It is slowly spiraling outward away from the Earth. The Moon is not a magic energy machine. It steals angular momentum and orbital energy from the Earth's rotation. While the transfer of angular momentum from the Earth to the Moon is very close to even, the transfer of energy is not. The Earth-Moon system is dissipative.

The same goes for Io and its volcanos. Io is very slowly stealing angular momentum and energy from Jupiter's rotation, and in the process, vents some of that stolen energy into space.

• But if we put something like a water wheel above those volcanoes, we'd be supplied with energy, like we get from mountain streams flowing downhill. meldrethhistory.org.uk/images/uploaded/originals/overshot.jpg Obviously "magic energy" doesn't exist, but long term energy source. – userLTK Feb 14 '18 at 12:01
• @userLTK: Yes - basically the same as harnessing wave power on Earth. – Lightness Races in Orbit Feb 14 '18 at 16:40
• Io may be stealing angular momentum and energy for Jupiter's rotation, but it would have no means of transfering that into volcanic energy. It would instead change its orbital distance much like our own Moon does. The volcanism is due to tidal forces from Jupiter. I'm not sure I see how most of your answer is relevant to the question. – zephyr Feb 14 '18 at 17:12
• @zephyr I don't know, but there is some related discussion in comments below this answer. – uhoh Feb 16 '18 at 6:16

A worldbuilding answer:

In terms of "Magic Energy" (I hate the word magic, lets say free energy)

Lets say we have a colony far from the Sun. Jupiter works, or, an outer planet, maybe even the theoretical Planet 9, where solar-energy panels would be pretty pointless, Uranium fuel might be scarce and 3He takes time to collect for fusion, so they need a power source.

In theory, a devise could be built using material and mass asteroids and carbon fiber cables, and some kind of structure where there was a spherical outside that stretches and squishes in an orbit, ideally, like Io, between the planet and it's large moon where some eccentricity and variation would be maintained.

The stretching back and forth and the mass of the outer shell of this object could pull pistons and make electricity. The amount of electricity would depend on the mass and size and flexibility of the spherical construct and the energy would come from a nearly limitless source - the planet's rotational energy.

Whether such a thing is practical is another question. I have no idea if it would be practical at all, but it's theoretically possible.

You'd also need a large moon, otherwise the orbit would circularize and energy would diminish. But a Planet-Large Moon system, maybe it could work. The downside is that so much energy would go into building the thing in the first place, I'm not sure it would be worth it.