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-- I just proved that the moon is falling.

I just proved that the moon is falling.

What follows is an interesting science thought that I came up with; one of those "what if..." moments. Comments and criticisms are encouraged. I found myself puzzled with the following physics question:

Tidal generating stations have recently become a popular renewable energy source... you generate power by using the gravitational potential energy of water at high tide to turn turbines. This gravitational energy comes from the moon's pull on the water on the surface of the Earth. Now the law of conservation of energy dictates that when we harnass the energy in this system, it's gotta be coming from somewhere. My question is this... are we in fact robbing the moon of it's gravitational potential energy? In other words, will using tidal energy cause the moon to fall to the Earth, and if not, where the hell do those extra Joules of energy come from?

I have examined this problem from a dynamics standpoint as well (instead of from a conservation of energy standpoint) and the result seems to be the same. The center of gravity of the Earth has to be moving closer to the moon when the water is falling (falling water pulls the Earth upward with as much force as the force with which the water is pulled downward.) Since the force that makes all this happen is external, the Earth is not equivalently being forced downward as the water is given gravitational potential energy again. Therefore, the Earth is moving upward in a non-balanced fashion whenever such water is falling, and has a net displacement in the direction that is toward the moon.

So the moon is falling!!! We're all going to die!!! Stop tidal generating stations immediately!!!!

(PS... I'm not sure if this has been posted or written up before, but it is nonetheless a rather interesting result. Of course, we'd have to generate a LOT of tidal energy before the moon ever fell noticibly)

Actually, the moon is getting farther away from the earth a few centimetres every year, and yes it's because of the tidal effect.
http://www.mikekemble.com/space/discovery2.html

noone has ever been on the moon, YET.

i'm from the internet

quote:

Originally posted by Slag Actually, the moon is getting farther away from the earth a few centimetres every year, and yes it's because of the tidal effect. http://www.mikekemble.com/space/discovery2.html

That's a different effect though due to the earth's rotation and the dragging force of the tidal waters. In this case, the moon gains gravitational potential energy and the Earth loses angular momentum.

New question: how much tidal energy would we have to generate to negate that effect and cause the moon to remain stationary? Then we'd only be stealing energy from our Earth's rotation!

NOONE HAS EVER BEEN ON THE MOON.

prove me wrong.

THERE IS NO SUCH COUNTRY AS MADEGASCAR.

prove me wrong.

It's called an orbit.

Let's hypothetically say that your "theory" were true - if that were the case, it would also be true for electrons orbiting atoms, and every atom in the universe would eventually collapse on itself. And considering their size, they'd collapse on themselves in an infinitessimal fraction of a second.

It should therefore be pretty easy to see why your hypothesis can't possibly be correct.

Tidal energy is based on a principle similar to the centrifugal/centripetal force from revolving motion in classic mechanics. That force does not slow down the revolutions or even affect the motion at all. It is in fact a "side-effect" of the motion itself - since the revolution requires a constant acceleration (and thus a force which is constant in magnitude), the aforementioned forces are in opposition to the accelerative force. Everything balances out - no energy is (under ideal conditions, neglecting air resistance and such) lost or converted in that process.

Of course, the moon's orbit is not perfectly circular; it's elliptical. That's why the moon is actually gradually getting further away from the Earth. But that has little if anything to do with your suppositions.

noone has ever been on the moon, the radiation between the moon and earth from the sun is so great it will fry the person in a spacerocket like a frenchfry at mcdonalds.

quote:

Originally posted by arek noone has ever been on the moon, the radiation between the moon and earth from the sun is so great it will fry the person in a spacerocket like a frenchfry at mcdonalds.

I knew about the moon getting further away from Earth every year ... my question is as follows:

is the Moon going to escape the Earth's gravitational pull sometime in the future, considering the pace it it moving away from our planet? If not, what will happen then?

quote:

Originally posted by Magnetonium is the Moon going to escape the Earth's gravitational pull sometime in the future, considering the pace it it moving away from our planet? If not, what will happen then?

Yes, eventually it will, but not in our lifetime, and not for a very long time. I guess what will happen then is that we have very long days? I don't really get the question - I don't imagine that the human race will even still be alive by then.

Eventually the sun is going to supernova too... but it's not really anything we need to worry about, considering how far in the future that is.

quote:

Originally posted by arek noone has ever been on the moon, the radiation between the moon and earth from the sun is so great it will fry the person in a spacerocket like a frenchfry at mcdonalds.

its not that great actualy

So the conclusion is: we should "rob" the moon of its energy even more

quote:

Originally posted by DigiNut It's called an orbit. Let's hypothetically say that your "theory" were true - if that were the case, it would also be true for electrons orbiting atoms, and every atom in the universe would eventually collapse on itself. And considering their size, they'd collapse on themselves in an infinitessimal fraction of a second. It should therefore be pretty easy to see why your hypothesis can't possibly be correct. Tidal energy is based on a principle similar to the centrifugal/centripetal force from revolving motion in classic mechanics. That force does not slow down the revolutions or even affect the motion at all. It is in fact a "side-effect" of the motion itself - since the revolution requires a constant acceleration (and thus a force which is constant in magnitude), the aforementioned forces are in opposition to the accelerative force. Everything balances out - no energy is (under ideal conditions, neglecting air resistance and such) lost or converted in that process.

Everything balances out under ideal circumstances only. When the moon (an external force in the Earth-water system) reorders the gravitational energy of the water through its gravity, it doesn't gain or lose any energy because the total gravitational energy in the water is constant. The force of the moon, as it revolves, tugs on the Earth, but because the moon is orbiting, and the Earth is spinning, all of these forces cancel and the net acceleration of the water is zero with respect to the Earth-moon system.

The problem is when you let the water fall at high tide (as in a tidal generating station), for a moment, the Earth is accelerated upward (in the direction of the water). Until the water lands, decellerating the Earth to its prior velocity. The system then loses energy. However, when the water rises back up, the system regains its energy. It's like a person jumping up and down. While he or she moving upwards, the Earth is moving downwards, and vice versa. The net displacement of both is zero at the end though.

The situation is different though when the rising force is external and the falling force is internal. In this case, the moon loses energy when the water rises, and the Earth loses energy when the water falls. Consider the following example:

A <-moon (in orbit)

B <-person
C <-planet

Suppose the person fires a grappling hook at the moon and pulls himself upwards a few stories onto a building. Then he jumps off and lands on the surface of the planet again. During the first part, he gets gravitational energy from the moon, and during the second part, he steps off the building and his gravitational energy is essentially converted into heating the planet up and making noise.

What you said is all correct... perhaps you didn't quite understand what I meant by tidal energy. I'm talking about tidal generating stations. They have a big empty pit that is above the low tide level but above the high tide level. Above that are some turbines... there are floodgates above and below the pit. During low tide, gate #2 is open so all the water in the pit is drained out. Then the gates are closed... when high tide comes, floodgate #1 is opened, the water flows in, turns the turbines, and makes power. When the reservoir is filled up, floodgate #1 is closed again and the process repeats itself.


--high tide--------------------
|===(floodgate 1)===|
|*******************|
|******turbines*****|
|*******************|
|...................|
|...................|
|===(floodgate 2)===|
---low tide------------------


If I'm wrong, could you please explain to me where this energy comes from?

quote:

Originally posted by DJ_Elyot If I'm wrong, could you please explain to me where this energy comes from?

The Sun.

The earth-moon dynamic isn't a closed system. They both have their own gravities generated by the entire solar system, including the sun and even the other planets and moons. Distant galaxies can even have some small effect, but it's obviously considered to be negligible.

So maybe the moon loses some of its gravity to the earth and the earth loses some of its gravity to the sun... either way, the moon is not falling.

quote:

Originally posted by DigiNut The Sun. The earth-moon dynamic isn't a closed system. They both have their own gravities generated by the entire solar system, including the sun and even the other planets and moons. Distant galaxies can even have some small effect, but it's obviously considered to be negligible. So maybe the moon loses some of its gravity to the earth and the earth loses some of its gravity to the sun... either way, the moon is not falling.

Can't be the sun. The same thing would happen even if there was no sun.

quote:

Originally posted by DJ_Elyot Can't be the sun. The same thing would happen even if there was no sun.

Actually, no, it wouldn't. Can you give us some kind of evidence to support that claim?

Without the sun, the Earth would be free-floating in space and there'd be no gravity to speak of.

I repeat, planetary dynamics are NOT a closed system. Energy can come from and go to many places.

If you had just the rotating Earth, the orbiting moon, and the water on the surface of the Earth in a closed system, the same thing would happen. You'd get bulges in the water from the moon's gravity. These bulges would appear to come and go because of the rotating Earth and orbiting moon. Using the same tidal generating station, You'd be able to generate energy in the same way!

quote:

Originally posted by DJ_Elyot If you had just the rotating Earth, the orbiting moon, and the water on the surface of the Earth in a closed system

Do you not realize that this "closed system" you speak of is physically impossible?

Just think of any chemical reaction that is classified as "exothermic" or "endothermic" - in order for chemistry to work at all, there has to be an environment. Physics and gravitational dynamics are the same way. NOTHING works in a "closed system". We can ignore the sun and try to model things with the earth and moon in the "black box" sense, but we still have to keep in mind that there IS this black-box environment and that it can be either an energy source or sink.

Look, I already explained why your theory was incorrect; now you're just being stubborn. I'm not going to argue - go ahead and mail your findings to a physics journal, I'm sure they'd love to publish this.

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