Physics question: Conservation of energy and orbits

[Alex Franke]

I unfortunately got to thinking about physics again... Fortunately there seems to always be a lot of smart people here to help me through these troubling times.

Say you build a dam across an estuary somewhere that happens to experience a reasonably significant change in tide, and you use the energy of the water flowing in and out twice a day to turn some turbines to power your local wood shop.

Where does the energy come from?

It seems to me that the energy powering your BT3K in this case is coming from a system "powered" by the moon and its orbit around Earth (admittedly an infinitesimal amount). So if that's true (and I don't know if it is), taken ad absurdum, how is the moon's orbit affected?

[cgallery]

If you are asking whether the gravitational pull on the moon is changed by the resistance of the water over the turbines, the answer (I think) is no. That is, adding the turbines to the water would not change the moon's orbit. That is because mass (matter) is the critical factor here. What the mass is doing is immaterial.

[Kristofor]

Our moon is already exerting it's influence on the Earth slowing our spin. The dam holding a tiny little bit of extra water would act to add to that effect but not by very much (tiny fraction of the mass of the earth).

The energy is coming from the whole planet slowing down. But again, take the mass of the earth relative to your reservoir and it's not going to have a very significant impact...

Kristofor.

[Alex Franke]

Wow. Thanks for the quick responses!

That is, adding the turbines to the water would not change the moon's orbit. That is because mass (matter) is the critical factor here. What the mass is doing is immaterial.

I guess my thought was that it would (again taken to the absolutely absurd) offset the center of mass because you're slowing the effect of the tide by taking energy out of it. And that if the center of mass is offset, there would be a slightly larger tug backward on the moon, which would slow it down.

The question is really, "where does the energy come from?"

The energy is coming from the whole planet slowing down. But again, take the mass of the earth relative to your reservoir and it's not going to have a very significant impact...

I'm not sure I understand this -- doesn't it imply that that the slowing of the planet is causing the tides? Isn't it also the Earth/moon system that's slowing Earth's rotation?

(Yeah, I get that energy taken from the system wouldn't be significant in even a billion years -- I tend to take thoughts like these to the extreme in an effort to figure out what's going on... But I recognize that installing a turbine won't bring the moon crashing down )

Edit: BTW, where's the kinetic energy of Earth's slowing rotation going?

[cgallery]

Oh, then the energy is derived from gravitational potential energy, and converted into kinetic energy?

[LCHIEN]

You're slowing the world down a bit, but don't worry, the relative masses are so gigantic that the effect is essential unmeasurable.

[jackellis]

I agree with Loring. Of course I can foresee the situation a million (or perhaps several million) years from now scientists start raising an alarm about the impact of tidal energy on the earth's climate, which would not be unreasonable as the rate of the earth's rotation slows.

I'm all for renewable energy but people are fooling themselves if they think electricity from renewable energy is perfect in any way. It has environmental impacts and it is very difficult to match electricity production from renewable resources with electric demand without spending lots of money on backup fossil-fired generating plants or horribly expensive and inefficient storage devices.

You can have electricity that's reliable, cheap and clean. Pick any two.

[Mr__Bill]

Just in case you want to read more about it... Bay of Fundy NS

[Kristofor]

Wow. Thanks for the quick responses!

I guess my thought was that it would (again taken to the absolutely absurd) offset the center of mass because you're slowing the effect of the tide by taking energy out of it. And that if the center of mass is offset, there would be a slightly larger tug backward on the moon, which would slow it down.

With gravity the important factors are mass and distance, but distance is the higher order component. Let's ignore any relativistic effects of spinning mass.

With tides we need to remember that there are about two tides per day.

On the high tide with the moon overhead, by holding some quanitity of water in your resivoir after the moon passes you would be effectively moving the center of mass of the Earth back a (tiny) little bit relative to the moon.

On the high tide with the moon on the opposite side of the Earth by holding some quanitity of water in your resivoir as the moon approaches you would be effectively moving the center of mass of the earth closer a (tiny) little bit relative to the moon.

On average you can't be changing the balance unless you're perpetually pumping the water uphill and storing it there.

In both cases by holding the water on the "sides" of the Earth you create tiny little "ears" of mass that add additional torque to slow the rotation of the Earth.

The question is really, "where does the energy come from?"

I'm not sure I understand this -- doesn't it imply that that the slowing of the planet is causing the tides? Isn't it also the Earth/moon system that's slowing Earth's rotation?

Other way around, it's the tidal effect that is causing the Earth to slow down. And yes, those are mostly from the moon (the sun has ~1/3 of the tidal pull that the moon does, and the other planets, asteroids, etc. all have some tiny impact of their own)

Edit: BTW, where's the kinetic energy of Earth's slowing rotation going?

I'm not sure but I'd guess mostly to heat. The tidal forces make liquid water form the tides, but they have the same type of impact to a lesser degree on the surface of the Earth. That much earth/water being pulled likely creates a lot of friction/heat.

[Alex Franke]

On the high tide with the moon on the opposite side of the Earth by holding some quanitity of water in your resivoir as the moon approaches you would be effectively moving the center of mass of the earth closer a (tiny) little bit relative to the moon
. . . .
In both cases by holding the water on the "sides" of the Earth you create tiny little "ears" of mass that add additional torque to slow the rotation of the Earth.

Ah yes -- I forgot about the other side.

So is it more of an angular momentum issue? If we all lift our glasses at the same time (away from the axis or rotation), then Earth's rotation has to slow down a bit in order to conserve its angular momentum?

I'm not sure but I'd guess mostly to heat. The tidal forces make liquid water form the tides, but they have the same type of impact to a lesser degree on the surface of the Earth. That much earth/water being pulled likely creates a lot of friction/heat.

Yeah, that makes sense.

Just in case you want to read more about it... Bay of Fundy NS

Cool. Thanks for the link!

I also found more Bay of Fundy info here: http://en.wikipedia.org/wiki/Bay_of_Fundy, and even an article on "the only tidal generating station in North America" here: http://en.wikipedia.org/wiki/Annapol...rating_Station

I will immediately start blaming these guys when ever my days start to feel really, really long!

[JimD]

This is only a restatement of what I think has been said but the way I look at it, the energy for the generator comes from gravity. The gravity effect is altered by a neglible amount by the repositioning (or constrained position) of the water. That altered gravity effect may change the overall gravity effect on the earth and its rotation by some even more negligible amount.

Jim

[gsmittle]

You guys make my brain hurt..

g.

[Habe]

Time for another adult beverage.

[Alex Franke]

Time for another adult beverage.

That's how I got into this mess in the first place! For some reason Glenfiddich makes me think of physics. Weird, I know.