Tidal flexing and conservation of energy

[Bert 2]

This is a question which I have been been tossing around for some time. By looking at gravitationally induced deformation of celectial bodies, I wonder one thing; where is the conservation of energy? Here's the deal: tides, in the oceans of Earth or the siliciclastic crust of Io, are a manifestation of matters' affinity to itself. The moons gravity pulls water toward it's centre of mass, thus tides on earth. No big problem there. My question here is probably better illustrated by looking at tidal heating on Io (the Gallilean sattelite). It is known that Saturn's imense gravitational effects, coupled with gravitational pull from moons further from Saturn than Io generates extreme "push-pull" effects on Io, generating large quantities of heat due to friction within the sattelite. This heat is known to cause active volcanism on the moon. Following me? Good. This heat generated will then be lost to space as long wave rediation (infrared). Energy is lost from the Io system. The heat dissipates, the energy is gone. The energy of the system is A)Kinetic energy due to the angular momentum of Io and the other bodies and B) Gravitational potential energy. So if we are loosing heat out one end, we must also be gobbling up energy at the other. So does Io orbit closer and closer around Saturn with time, thus converting gravitational P.E. to heat? Or does Io's angular velocity decrease (Io looses K.E.)? I realize that in either case the stability of the orbit is affected.

 

[Janitor]

You've got Io going around Saturn, but I thought it was a moon of Jupiter.

The explanation I have heard is that the moons of Jupiter perturb each others' orbits such that any given moon's orbit deviates from a circle. And that deviation, since it causes the moon to alternately dip down lower and then rise higher in the central-force gravity well of Jupiter, leads to changes in Jupiter's field acting across the moon so as to flex the moon.

I would think that collectively the moons must be gradually getting closer to Jupiter as the millions of years go by. I suppose that as they get close to the Roche limit they will break up and become rings.

 

[Bert 2]

Oops!

Sorry, I meant Jupiter! Thanks for the reply. But I still can't see that energy path. Maybe the ocean tide is simpler. Let's say one was so harness some tidal energy (by whatever device). Let's it was used to do some work. Ok so now we've just used up some energy right? But we all know that there's no such thing as free energy. So to conserve, either the Earth gets closer to the sun, or the Earth slows in orbit?

 

[LURCH]

Originally posted by Bert 2
Sorry, I meant Jupiter! Thanks for the reply. But I still can't see that energy path. Maybe the ocean tide is simpler. Let's say one was so harness some tidal energy (by whatever device). Let's it was used to do some work. Ok so now we've just used up some energy right? But we all know that there's no such thing as free energy. So to conserve, either the Earth gets closer to the sun, or the Earth slows in orbit?

With tidal energy on Earth, you're dealing mostly with the Moon. There is a tremendous wealth of information about the Moon and tides at this great site I found. The energy that the Moon exrts on the tides is actively driving the Moon away from the Earth, and slowing the Earth's rotation. Eventually, the Earth will become tidally locked to the Moon as it is to us, and they will show only one side to each other.

This is not too dissimilar from what's happenning to Io. The force of gravity between the sattelite and the host planetr is acting as a break to brung them into synck with each other. The heating of the sattelite is the heat that results from that breaking action.

 

[Janitor]

Years/decades ago, I read an article in Scientific American on just the topic you bring up. In the case of the Earth, tides are basically caused by the moon and the sun, and I think the moon is more important.

The analogy that the article used (going by a very old memory here) is of a tire flexing as it rolls down the road. The flexing causes a conversion to heat. The more flexible a tire is (for a given speed and a given vehicle weight), the faster the rate of heating.

The moon's field (I will ignore the sun, to keep it simple) causes a bulge in the Earth and especially in the oceans on the earth. If the Earth were locked one face toward the moon (like the moon is in fact locked one face toward the earth), then there would be no heating taking place in the interaction between those particular two bodies.

Since Earth is rotating with respect to the moon, the bulge isn't able to move along the Earth's surface so as to stay exactly on the imaginary line joining Earth and Moon. Instead, it lags behind (about two hours behind, if I am remembering right).

The effect of this lag in bulge is that the moon doesn't quite see the Earth as a gravitational monopole. It sees a gravitational dipole. Again, if I am remembering right, two things of consequence are happening over very long time periods: Earth's rotation is slowing, and the moon is actually being raised into a higher orbit around the earth. You can think of the bulge as pulling the moon forward in its orbit, i.e. adding energy to its orbit.

Someone let me know if I am remembering this all wrong.

 

[krab]

Originally posted by Bert 2
So if we are loosing heat out one end, we must also be gobbling up energy at the other. So does Io orbit closer and closer around Saturn with time, thus converting gravitational P.E. to heat? Or does Io's angular velocity decrease (Io looses K.E.)?

The second: Io's rate of rotation slows.

 

[hermitme]

I have a question. Einstein's theory of Gravity says there is no force of gravity, it's just a space/time curvature. So if the planets cause a dimpling, per se, of space, can tidal pull be also considered a warping of the wall of the well thus causing matter not so much as being attracted by the other but sort of matter falling into the other body because of the flattening of the well's wall? I'm not sure I'm making sense. But tidal pull affects more than just water, it affects land also, right? Only it's too miniscule for us to notice? So can it be that matter is falling into the heavier body as the body is passing by? Is this making any sense to anyone? LOL