# Does earth tidal friction use up or add to the moon's gravitational potential energy?

1. Jan 18, 2005

### Andrew Mason

I am a little puzzled by the following:

The moon in causing earth tides causes the earth to generate heat loss due to friction and slows down the earth rotation. This decreases the angular momentum of the earth. The angular momentum of the earth and moon system combined cannot change. So the moon and earth have to increase their angular momentum. It is said that they do this by increasing their radii of rotation about the earth-moon centre of mass: the earth and moon have to move farther apart.

I don't see how that can happen. Since the moon acquires greater potential energy, this compensation for loss of angular momentum takes energy. Where is the energy supposed to come from?

Would the earth not simply develop more of a wobble to provide the needed angular momentum?

AM

2. Jan 18, 2005

### Chronos

Due to tidal locking, some of the Earth's angular momentum is gradually being transfered to the Moon's orbital momentum, which causes a slowing of the Earth's rotation [days lengthen ~15 µs per year] and an increase in the Moon's distance from Earth [~38 mm per year]. Note: most of the slowing of the Earth's rotation is caused by tidal friction in the oceans, not tidal locking by the Moon.

3. Jan 18, 2005

### Andrew Mason

But the problem is: It has to do WORK to move farther away. Where does the energy come from?

AM

4. Jan 19, 2005

### Chronos

From the angular momentum of the Earth. Earth slows its rotation, Moon increases it's distance from Earth.

5. Jan 19, 2005

### Andrew Mason

Ok. That makes sense. But, in that case, the explanation for the earth slowing down cannot be that it is due only to the energy loss from tidal friction. Perhaps this is one of those interactions analogous to an inelastic collision: momentum is conserved, some energy is lost and some is transferred.

AM

6. Jan 19, 2005

### LURCH

It might be a more helpfull description to say that tidal friction is the mechanism by which energy (rotational energy) is transferred from the Earth to the Moon (in the form of gaining altitude).

7. Jan 21, 2005

### Chronos

Correct, tidal friction is not the only force in play. Tidal locking, a form of torque is also in play, but has a much smaller effect compared to tidal friction.

8. Apr 27, 2010

### shomas

Re: Does earth tidal friction use up or add to the moon's gravitational potential ene

Would tidal locking arise from gravitational anomalies such as a mountain range pulling on the moon, effectually slowing earths rotation while adding that angular momentum to the moon rotation around the earth?

I am wondering generally how much energy is lost from earths rotation daily, assuming 2 millisecond spin down over 100 years.

9. Apr 27, 2010

### sylas

Re: Does earth tidal friction use up or add to the moon's gravitational potential ene

It arises mostly from the ocean, with some also from "tides" in regular rock. I am not sure how significant gravitational anomalies might be... not as much as tides.

Earth's moment of inertia J is about 8 x 1037 kg m2.

The energy is 0.5 J ω2, where ω is the rotational velocity in radians/sec.

The rotational velocity is 2 pi / P, where P is the period (seconds in a day).

So energy is E = 2 pi2 J P-2 = 1.58 x 1039 P-2.

The CHANGE in energy with the length of the day is dE/dP = -3.16 x 1039 P-3. The minus sign means a longer day corresponds to less energy.

So, if the change in the length of the day is 0.002 (2 milliseconds), then the energy change is dE = -3.16 x 1039 P-3 dP = 1022 Joules, approximately. That's over 100 years, so the energy lost per day is about 2.7 x 1017 J. That works out to about 3.1 TeraWatts. Most of this energy goes into heat, with only a small fraction actually transferring to the Moon as it takes up the loss in angular momentum.

Cheers -- sylas

PS. Very old thread... but good question to revive it.

10. Apr 30, 2010

### Jon Richfield

Re: Does earth tidal friction use up or add to the moon's gravitational potential ene

Earth's mascons and mountains cannot have much to do with it. Consider: the reason that we can accelerate the moon is because the Earth is rotating at a higher frequency than the revolution of the moon: 1/24hours vs 1/28days. Now, the leading parts of the planet drag the moon forward, whereas the training parts retard it. However, a mountain or Petronas tower leads and trails roughly equally long each day, so their effects pretty nearly cancel out. Therefore the moon isn't really receding.
I blame it all on global warming.

Mind you, some other spin doctor seems to have the idea that tidal forces on our sloppy planet (not just the watery bits, lawyers and other slush, but the solid bits like politicians and statues of general Haig) form bulges under the attraction of Luna (Hah! and you thought that only money attracted them? Their schemes aren't called lunatic for nothing!) But says the spin doctor, the bulge stays a bit ahead of the moon because, once lifted, it cannot simply reside immediately, because of inertia and viscosity and stuff (not to mention global warming!) so its attraction is systematically forrard of the moon, speeding it up.

And a good job too, because if it were the other way round, we would by now be spinning like crazy and ducking every time the moon passed overhead a few times a day.

You reckon that couldn't happen? Hm? Think what would happen if either the earth or moon moved retrograde. But not both? Hm?

Couldn't both!

Global warming say I!

Jon