Where does the energy come from when a low moon's heating by shape change?

[Cesrate]

This thing is significant in low Jupiter moons. It is heated by shape change during orbiting. My question is how and where does these energy come from? As the total energy is conservative.

[Tex_NL]

... As the total energy is conservative.

Actually it isn't.

Our own moon is to blame for ocean tides, this obviously requires energy. This energy is taken from the moon as it ever so slowly drifts away from us. The same would be true for tidal forces between Jupiter and it's moons.

[Cesrate]

So when a moon is drifting away by tidal force its mechanical energy is reducing for other effect.

[Tex_NL]

As far as it was once explained to me yes. But now that I think of it, energy could also be taken way from rotational speed causing either or both bodies to slow down.

Please keep in mind I am doing this from memory, I have no links or solid data to back this up. There must be much more knowledgeable people out there.

[EatThePath]

My understanding is that in the case of the earth and luna, the energy is coming from earth's rotation. The tidal bulge is being carried forward by earth's rotation, and then pulls the moon 'forward' even as the moon pulls it 'backward'. Thus the moon gains orbital velocity and the earth's rotation slows. Estimates have the orbit of the moon much lower and the rotation of the earth much faster back when it was formed. It also seems plausible that the moon itself once had an unlocked rotation, and tidal forces have long since sapped all available energy out of that.

[Nuke]

isnt energy being added to the moon as it is spiraling out, and that takes adding energy not removing it. as i remember the energy is actually coming out of the angular momentum of the earth. earth slows down, moon accelerates (its orbital velocity is decreasing but its orbital energy is going the other way, since its storing that energy as potential energy). id go into more detail but i really dont have time to write a long post right now.

wait ninjad.

[WestAir]

Won't, in the case of Earth and Luna, the moons distance and the Earths spin one day reach an equilibrium where the Moon stops drifting away and the Earth stops slowing its spin?

[PakledHostage]

I don't think that's likely for the Earth-Moon system. The two bodies need to be in fairly close orbits around each other and their masses need to be fairly closely matched for the parent body to become tidally locked. There's a good introduction to the subject of tidal locking on Wikipedia.

And incidentally, I recall reading in a book called "The Life and Death of Planet Earth" that the Moon may have been instrumental in the development of life on the early Earth. The moon used to be in a closer orbit that caused tides hundreds of times larger than our current tides. The resulting vastly larger intertidal zones on that early Earth were rich environments in which life could flourish.

[softweir]

@westair: No. So long as the moon stays orbiting Earth then the process will continue. It is expected that the moon will eventually drift so far from Earth that solar gravitational effects will become significant, the moon's orbit will become irregular, and it will eventually leave Earth altogether. There will then be a somewhat dangerous time when it might collide with Earth (which would be truly spectacular - for those far enough away to view it dispassionately) but if not then successive close encounters with Earth will eventually separate them and it would become a planet in its own right.

In the case of moons being heated by tidal interactions, the energy comes from a combination of their own axial rotation and from their orbital momentum: as a moon on an even slightly elliptical orbit moves closer to and further from its parent body, so the degree of gravitational distortion increases and decreases, leading to a massive flexing of the moon's crust which generates heat. The other consequence is that the moon loses momentum, and ends up slightly closer to its parent body.

Edited June 2, 2013 by softweir
Ninja'ed

[PringleMan]

Actually the moon IS slowing the Earth's rotation indirectly via the tidal bulge. The bulge has a slight frictional affect on the Earth, slowing its rotation ever so slightly. In the short term this is pretty meaningless, but I think the existing geologic record shows some evidence of a current slowing of several hours already. The sun will burn out before we ever become tidally locked.

Anyways back to the OP, the energy is basically from internal friction due to the gravitational tidal forces acting on the moons of Jupiter. Io sees the worst of it because it is so close in, and gravity drops over distance squared. Even a few hundreds of kilometers (radius of the moon) can cause a pretty big difference in gravitational force (and thus gravitational potential energy).

Io is small enough that it SHOULD have been geologically dead if it were around another planet such as Earth (much like our own moon). However because it is so close to a massive body like Jupiter it gets squeezed and bulged and stressed constantly. It is not really right to think of the energy "coming" from somewhere. Thinking of energy that way is a little off to begin with, unless you want to get down to the quantum level where you describe mass as energy waves. Besides which, you mentioned that the energy is conservative, and this is not the case. In the whole universe energy is "conserved," but in an individual system it does not have to be.

[Brotoro]

Io, Europa, and Ganymede are maintaining a 4:2:1 orbital resonance with each other. They are also moving slowly outward from Jupiter due to tidal interactions (for the same reason Earth's moon is moving away). This tendency to move outward would be greater for Io (since it is in closer where tidal affects are stronger), and as it moves out, the interactions with Europa that maintain their 4:2 orbital resonance will tend to pump Europa's orbit higher at the expense of Io's orbital motion...and the slight changes in eccentricity that these interactions cause as they do their work result is Jupiter flexing the moons and heating their interiors (tidal forces by Jupiter work to circularize the orbits of the moons). So there are a lot of things going on simultaneously, but the ultimate source of the energy for this comes from Jupiter's kinetic energy of rotation, which decreases as tidal forces cause its moons to move outward into larger, higher energy orbits.

[Fuzzy Dunlop]

This is why my anti-tidal power campaign is called "Keep The Moon"

[Stochasty]

There is an easy way to visualize what's happening tidally in the Earth-Moon system. Imagine the Earth and the Moon from the perspective of a co-rotating coordinate system, so that the positions of the Earth and the Moon are fixed. In this system, there are two forces acting on each body: gravity, wanting to make the Earth and the Moon fall towards each other, and the centripetal force which holds them apart (this force is "fictional" - due only to the rotating coordinate frame - but it's real enough from this perspective). The centripetal force scales as 1/r, whereas gravity scales as 1/r^2, so there's a force gradient across both the Earth and the Moon which generates mechanical strain (this is the tidal force).

Because of this mechanical strain, the surface of the Earth wants to elongate along the axis between it and the Moon. If the Earth were tidally locked to the Moon then eventually this tidal force would completely deform the Earth until it was slightly egg-shaped so as to relieve this stress. However, because the Earth is spinning, the direction of that strain changes on timescales much too short for the strain to be relieved. On the other hand, the Earth's surface is not homogeneous, and the air, water, and rock all respond to the strain on different timescales; importantly for our consideration, water responds much more quickly than rock - this is why there is a tidal bulge in the ocean. If the respond were infinitely quick, that bulge would point straight to the Moon; however, it takes time for water to flow, which means the Earth has rotated slightly, so the bulge will always be slightly East of the Moon. Because the Moon orbits in the same direction as the Earth spins, that bulge constantly leads the Moon in it's orbit. Furthermore, the bulge itself gravitates, causing the Moon to want to fall "forwards" ever so slightly, picking up energy (which it steals from the Earth, causing the Earth's rotation to slow down), which (as anyone who's spent time playing KSP knows) means that the Moon is slowly drifting away from us as it orbits. Eventually, if not for solar effects, the Moon would drift out and the Earth would slow down until the Earth became tidally locked.

A second interesting case of tidal effects is Neptune's Moon Triton, which has a retrograde orbit. Because of this, the tidal bulge actually trails Triton's orbit, causing it to lose orbit and spiral inwards. Eventually, Triton will reach Neptune's Roche limit and will be torn apart by the tidal stress (forming a new and rather spectacular ring around Neptune in the process).

What's happening with Jupiter is more complicated, because Jupiter has multiple large moons including the heavy weight champ Ganymede. Because of inter-moon interactions, both Io and Europa have slightly eccentric orbits, which produces non-constant gravitational strain in a similar way that rotation does for the Earth. However, because Jupiter is a bully, the forces involved are much, much larger than they are for the Earth-Moon system, leading to substantial internal heating from frictional forces as Io and Europa try to reshape themselves to relieve the strains.

Edit:

This is why my anti-tidal power campaign is called "Keep The Moon"

This is exactly backwards. If you wanted to try to keep the Moon, you should be in favor of utilizing the tidal power (preferably before it has a chance to distort the surface of the Earth). By opposing tidal power, you are ensuring that all of the energy is dissipated through friction, doing maximum work towards slowing the rotation of the Earth. You are also ensuring maximum bulge height, maximizing lunar drift.

Edited June 2, 2013 by Stochasty

[Fuzzy Dunlop]

This is exactly backwards. If you wanted to try to keep the Moon, you should be in favor of utilizing the tidal power (preferably before it has a chance to distort the surface of the Earth). By opposing tidal power, you are ensuring that all of the energy is dissipated through friction, doing maximum work towards slowing the rotation of the Earth. You are also ensuring maximum bulge height, maximizing lunar drift.

I thought it worked like this

By using tidal power you increase the friction on the ocean, effectively dragging the tidal bulge east of where it should be. That mean rotation slows down more and the moon drifts out faster.

Interestingly it appears that the moon has receded at very different speeds over the earth history (it can't have always been receding at the present rate because that would mean 4 billion years ago it would be too close the earth to even form). Basically when all the continents are jammed together in one supercontinent (i.e. pangea) there's not much to stop the ocean just running around the planet without losing any energy, so the earth doesn't slow down much and the moon recedes slowley. When all the land is spread out with lots of little nooks and cranies, like today, you have a high friction system and the moon recedes relativly rapidly.

[Stochasty]

By using tidal power you increase the friction on the ocean, effectively dragging the tidal bulge east of where it should be.

Yes, but you also shrink it (if I recall correctly). Remember that it's the tidal bulge that's doing work on the Moon, so any work that you extract from the tidal bulge can't be used by the Moon. You're probably right that you increase friction (which means you're effectively extracting work from the Earth's rotation, too), but that process doesn't directly affect the Moon.

That said, this is a weird non-linear next-to-next-to-leading order process which I haven't studied in great detail; I'm just going by what my intuition tells me about the system, which means there's a good chance I'm wrong. If you happen to have a reference regarding tidal power systems and their effect on the Moon you should probably trust that over me.

[Cryocasm]

It's fairly simple..actually...

Water is not solid, that's the answer. Because it is not solid, it is very easily "dragged" into the tidal bulge, but this is not about hydrodynamics tied in with astrophysics, the question was interior heating.

The Jupiter-Io system is a prime example for forces on the interior, and this comes from Jupiter's gravity pulling Io at different strengths at different points of the planet. During Io's travel of the perihelion of its orbit (which occurs every 1.77/2 or .885 days), Io is compressed by Jupiter's gravity, conversely, during the aphelion, Io is allowed to expand. These forces which occur on a daily basis introduce lots of friction to the interior of the moon, which in turn creates a molten core, resulting in Io's torus of particles around Jupiter as well as (most likely, if we use our Earth) tectonic regions due to a mostly solid mantle. This all comes from its parent world, Jupiter.

[Fuzzy Dunlop]

Yes, but you also shrink it (if I recall correctly). Remember that it's the tidal bulge that's doing work on the Moon, so any work that you extract from the tidal bulge can't be used by the Moon. You're probably right that you increase friction (which means you're effectively extracting work from the Earth's rotation, too), but that process doesn't directly affect the Moon.

If you take energy out of the earth's rotation (slow it down) the moon has to gain some, because you have to conserve angular momentum.

Edit: you're not acctually extracting energy from the tidal bulge, the earth rotates faster than the bulge, so by increasing the friction between the two, you're adding energy to the bulge, which ends up in the moon.

Edited June 3, 2013 by Fuzzy Dunlop

[Nuke]

it doesn't matter because the sun will vaporize it before it has a chance to get away.

[softweir]

^ ^ ^ Exactly - these processes are so slow that nothing we do will make more difference than a spit in the ocean.