<blockquote>
  <p>And this seems to go on forever.</p>
</blockquote>

<p>Not strictly true.</p>

<blockquote>
  <p>Io seems to remain in orbit perpetually. Have we discovered magic?</p>
</blockquote>

<p>No and no.</p>

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

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

<p>Plugging the values for Io into it, its total kinetic energy is approximately $7 \cdot 10^{40}$ Joule according to <a href="http://www.wolframalpha.com/input/?i=17330+*+(8.9319+*+10%5E22)%5E2+%2F+2" rel="noreferrer">Wolfram Alpha</a>. 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.</p>

<p>But yeah, on a human time scale it does look like magic.</p>

CC BY-SA 3.0
2018-02-14T17:10:02.803Z
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
CC BY-SA 3.0
2018-02-14T21:32:13.943Z
There wouldn't be tidal forces if it wasn't in orbit, @zephyr. Energy is what keeps it there.
Beanluc
CC BY-SA 3.0
2018-02-14T21:32:42.263Z
Until it doesn't.
Beanluc
CC BY-SA 3.0
2018-02-16T15:53:27.793Z
@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
CC BY-SA 3.0
2018-02-14T09:43:54.903Z
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](https://en.wikipedia.org/wiki/Volcanology_of_Io). If the whole surface (42E12 m^2) was at that temperature (it's not), by the [Stefan-Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_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
CC BY-SA 3.0
2018-02-13T22:51:07.360Z
2018-02-14T11:41:27.807Z
2018-02-14T11:41:27.807Z
Florin Andrei
<p>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.</p>

<p>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.</p>

<p>(Note: the answer to <a href="https://astronomy.stackexchange.com/q/25061/7982">How can tidal heating lower Io's orbit</a> 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.)</p>

CC BY-SA 3.0
2018-02-14T14:48:17.123Z
More likely, it would (together with the other moons) leave Jupiter's orbit if space and time wouldn't collapse first, because it orbits prograde.
Peter - Reinstate Monica
CC BY-SA 3.0
2018-02-14T16:35:03.683Z
@zephyr ...awwww. Why does it always have to be *"no"* the answer to _"Is it magic?"_. Damn [Clarke](https://en.wikipedia.org/wiki/Clarke%27s_three_laws) always pulling the rug under our wishful feet... :(
xDaizu
CC BY-SA 3.0
2018-02-14T20:40:26.013Z
@xDaizu It just means the technology is insufficiently advanced ;-)
Devon_C_Miller
CC BY-SA 3.0
2018-02-15T15:38:21.373Z
-1 for lying about Io not being a magical energy machine just so you can try to steal all of the energy for yourself!!!!1
Nat
CC BY-SA 3.0
2018-02-13T20:28:46.833Z
So short answer: No.
zephyr
CC BY-SA 3.0
2018-02-13T22:34:45.970Z
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
CC BY-SA 3.0
2018-02-13T23:04:13.637Z
@RBarryYoung, resonant interactions with Europa and Ganymede are preventing it from settling in to tide-friendly orbit.
NeutronStar
CC BY-SA 3.0
2018-02-14T02:11:17.443Z
@RBarryYoung Io is mostly tidally locked now, but as Joshua points out, small fluctuations are enough to create the continuous volcanic activity.
userLTK
CC BY-SA 3.0
2018-02-14T05:12:35.817Z
Very nice! I've just asked [How can tidal heating lower Io's orbit?](https://astronomy.stackexchange.com/q/25061/7982)
uhoh
CC BY-SA 3.0
2018-02-13T19:49:50.357Z
2018-02-14T16:52:03.160Z
2018-02-14T16:52:03.160Z
antlersoft
<p>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.</p>

<p>That energy (which can be, and is, turned into electricity by <a href="https://en.wikipedia.org/wiki/Tidal_power" rel="noreferrer">tidal power stations</a>) 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)...</p>

CC BY-SA 3.0
2018-02-14T10:02:02.317Z
2018-02-14T20:55:25.623Z
2018-02-14T20:55:25.623Z
DevSolar
<blockquote>
  <p>Is Io a magic energy machine?</p>
</blockquote>

<p>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.</p>

<p>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.</p>

CC BY-SA 3.0
2018-02-14T12:01:12.727Z
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.  http://www.meldrethhistory.org.uk/images/uploaded/originals/overshot.jpg   Obviously "magic energy" doesn't exist, but long term energy source.
userLTK
CC BY-SA 3.0
2018-02-14T16:40:16.353Z
@userLTK: Yes - basically the same as harnessing wave power on Earth.
Lightness Races in Orbit
CC BY-SA 3.0
2018-02-14T17:12:17.750Z
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
CC BY-SA 3.0
2018-02-16T06:16:27.537Z
@zephyr I don't know, but there is some related discussion in comments below [this answer](https://astronomy.stackexchange.com/a/25083/7982).
uhoh
CC BY-SA 3.0
2018-02-14T11:55:47.300Z
2018-02-14T11:55:47.300Z
David Hammen
<p>A worldbuilding answer:</p>

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

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

CC BY-SA 3.0
2018-02-14T10:26:26.880Z
2018-02-14T21:59:34.277Z
2018-02-14T21:59:34.277Z
userLTK
<p>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?</p>

CC BY-SA 3.0
2018-02-14T13:56:58.743Z
@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
CC BY-SA 3.0
2018-02-14T14:27:43.497Z
@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
CC BY-SA 3.0
2018-02-14T10:43:03.963Z
This is more a physics question.
Peter - Reinstate Monica
<orbital-mechanics><io>
Is Io a magic energy machine?
FranklyT
# Is Io a magic energy machine?

(Asked by: username_0 on 2018-02-13)

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?

**Tags:** orbital-mechanics, io
> **Comments:**
> **username_2**: This is more a physics question.  
> **username_1**: @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.)  
> **username_2**: @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.)  

---

## 5 answers

### Answer by username_7 on 2018-02-13. Score: 41

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](https://astronomy.stackexchange.com/q/25061/7982) 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.)

> **Comments:**
> **username_4**: So short answer: No.  
> **username_11**: 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.  
> **username_12**: @RBarryYoung, resonant interactions with Europa and Ganymede are preventing it from settling in to tide-friendly orbit.  
> **username_13**: @RBarryYoung Io is mostly tidally locked now, but as Joshua points out, small fluctuations are enough to create the continuous volcanic activity.  
> **username_14**: Very nice! I've just asked [How can tidal heating lower Io's orbit?](https://astronomy.stackexchange.com/q/25061/7982)  
> **username_2**: More likely, it would (together with the other moons) leave Jupiter's orbit if space and time wouldn't collapse first, because it orbits prograde.  
> **username_8**: @zephyr ...awwww. Why does it always have to be *"no"* the answer to _"Is it magic?"_. Damn [Clarke](https://en.wikipedia.org/wiki/Clarke%27s_three_laws) always pulling the rug under our wishful feet... :(  
> **username_9**: @xDaizu It just means the technology is insufficiently advanced ;-)  
> **username_10**: -1 for lying about Io not being a magical energy machine just so you can try to steal all of the energy for yourself!!!!1  

---

### Answer by username_3 on 2018-02-13. Score: 23

> 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](http://www.wolframalpha.com/input/?i=17330+*+(8.9319+*+10%5E22)%5E2+%2F+2). 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.

> **Comments:**
> **username_6**: 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](https://en.wikipedia.org/wiki/Volcanology_of_Io). If the whole surface (42E12 m^2) was at that temperature (it's not), by the [Stefan-Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_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  
> **username_4**: 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.  
> **username_5**: There wouldn't be tidal forces if it wasn't in orbit, @zephyr. Energy is what keeps it there.  
> **username_5**: Until it doesn't.  
> **username_4**: @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.  

---

### Answer by username_15 on 2018-02-14. Score: 16

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](https://en.wikipedia.org/wiki/Tidal_power)) 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)...


---

### Answer by username_1 on 2018-02-14. Score: 3

> 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.

> **Comments:**
> **username_13**: 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.  http://www.meldrethhistory.org.uk/images/uploaded/originals/overshot.jpg   Obviously "magic energy" doesn't exist, but long term energy source.  
> **username_16**: @userLTK: Yes - basically the same as harnessing wave power on Earth.  
> **username_4**: 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.  
> **username_14**: @zephyr I don't know, but there is some related discussion in comments below [this answer](https://astronomy.stackexchange.com/a/25083/7982).  

---

### Answer by username_13 on 2018-02-14. Score: 3

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.


---

