Tidal Locking

[TheBlackCat]

I understand that tidal forces between two objects orbiting each other causes tidal stresses between the two objects, which results in a loss of energy, a change in the orbital distance, and a slowing of the objects' rotation. This is what makes sure the moon always has the same side facing Earth, and has slowed Earth's day significantly over the eons. It also has put Mercury in a metastable orbital resonance with the sun. My question is, what about the Earth's orbit around the Sun? I understand that the Earth would have next to no impact on the Sun, but has tidal forces with the Sun altered the length of Earth's year over the eons? I mean the absolute length of the year (I guess in Iternational Atomic Time), not the number of days (since the length of the day has changed itself this is a poor measure).

[hhEb09'1]

I understand that tidal forces between two objects orbiting each other causes tidal stresses between the two objects, which results in a loss of energy, a change in the orbital distance, and a slowing of the objects' rotation.

But it's not the tidal stress per se. It's the internal friction of the body that causes the effect. By delaying the response of the tidal bulge, the friction causes the tidal bulges to be off the center line between the two bodies. Unequal graviational forces on the two bulges then result in a torque that changes the rotation of the body.

There is a tiny change in the length of the year over centuries--and I happened to read it in an old almanac last night!--but I cannot remember the value. I'll look it up.

[adiffer]

For the tidal friction mechanism to increase the length of Earth's year, you would have to see a corresponding reduction in the spin rate of the Sun. It's an angular momentum transfer problem.

As far as I know, this does not happen in a measurable manner. Measuring the spin rate of the Sun isn't that simple, though. There are also a lot of other influences on the Earth's orbit that may swamp the piece you are looking for. Think of the torque on our orbit due to Jupiter and you'll see what I mean.

[crosscountry]

My question is, what about the Earth's orbit around the Sun? I understand that the Earth would have next to no impact on the Sun, but has tidal forces with the Sun altered the length of Earth's year over the eons? I mean the absolute length of the year (I guess in Iternational Atomic Time), not the number of days (since the length of the day has changed itself this is a poor measure).

YES!!! just as the moon has taken some of our angular momentum so has the sun.


See, even though the sun is much further away than the moon it still has effects on our tides. Actually they are substantial. If we had no moon we would still have tides. They'd be about 1/2 as high because the sun's gravitational force is about 1/2 of the moons (because of distance).



SO, Just as the internal friction of the earth slows it (giving the moon our angular momentum) the sun does the same thing.



I cannot say how significant this effect is, but it happens.

[Ken G]

Actually, the Sun does not cause a tidal bulge on the Earth, it only weakens (or strengthens) the bulge due to the Moon. Thus on balance, I'd expect it to have not much additional effect on the internal friction! There are times when the Sun increases the Earth's deformation, and times when it decreases it. So on the whole I would not expect it to have much effect on the Earth's rotation rate. Although then there's the Earth's tilt, and other issues, so this is such a hard problem I wouldn't want to be quoted on any of it! For example, there are places that really only get one high tide per day, despite what I tell students.
However, the original question was on the effect on the Earth's orbit, not the Earth's rotation. I'll bet the coupling is between the Earth's orbit and the Sun's rotation, as pointed out by adiffer, so the issue is what kind of deformation of the Sun does the Earth cause. Obviously very small, but I'll await hh's data. Even with that, adiffer makes the point that it might not be due to the Sun at all.

[hhEb09'1]

Actually, the Sun does not cause a tidal bulge on the Earth, it only weakens (or strengthens) the bulge due to the Moon.

It's the moon that weakens or strengthens the bulge due to the Sun--the Sun was here first

Obviously very small, but I'll await hh's data.

I can't remember which almanac! I'll just look in them all...

[publiusr]

Jupiter might be big enough to cause a hydrogen tide on the sun. I wonder how/if that factors in solar weather...

[Ken G]

It's the moon that weakens or strengthens the bulge due to the Sun--the Sun was here first .

Cute! But what I mean is, the bulge that the Sun originally made pointed at the Sun, but when the Moon appeared, the whole bulge got wheeled around toward the Moon. This means, to lowest order, the Sun lost its ability to rob the Earth of angular momentum in the net, even though it still alters the strength of the tides, just not in the net. Kind of a minor issue, I suppose!

[hhEb09'1]

Cute! But what I mean is, the bulge that the Sun originally made pointed at the Sun, but when the Moon appeared, the whole bulge got wheeled around toward the Moon. This means, to lowest order, the Sun lost its ability to rob the Earth of angular momentum in the net, even though it still alters the strength of the tides, just not in the net. Kind of a minor issue, I suppose!

I'm not sure that is even true. The tidal braking depends upon a lag in the reaction of the earth to the sun's field, just as well as the moon's. The asymmetry needed for braking shouldn't be modified that much. Just as the moon's bulges aren't braked by the sun, because it pushes as well as pulls on them, I'd think the same thing would be true for the sun's. I'll look around and see if I can find a cite.

[crosscountry]

Cute! But what I mean is, the bulge that the Sun originally made pointed at the Sun, but when the Moon appeared, the whole bulge got wheeled around toward the Moon. This means, to lowest order, the Sun lost its ability to rob the Earth of angular momentum in the net, even though it still alters the strength of the tides, just not in the net. Kind of a minor issue, I suppose!

I disagree. The sun works on both the sun and the moon. It applies torque when the E-M system is perpendicular to the radial direction of the sun and no torque when we are aligned with the sun.



Just like the earth as tides, we cause tides on the sun (although much less dramatic). Those solar tides rob the sun of angular momentum and give it to the earth.

Thus our orbit is increasing.


The analogy of the E-M system is pretty accurate.

[adiffer]

It's been a while since I've looked at this problem in detail, but this is what I remember.

Any pair of fluid rotating bodies in orbit around each other will distort due to tides and their angular momenta will couple. If the spin axes are aligned, they will trade with each other until they tidally lock and present the same side to each other. The orbital angular momenta will also couple to the rotational version for each body because a tidal distortion torques an orbit. Again, if the spin axes are aligned, the semi-major axes tend to increase.

Both the Sun and Moon cause a tidal distortion on the Earth. The Moon causes a larger one, so the coupling of the Earths angular momentum is strongest with the Moon. The Moon can't effectively couple to the Earth's orbital angular momentum, but it can act as a handle on the Earth/Moon system exactly as crosscountry describes. Other bodies like the Sun and Jupiter can couple to our system through the Moon's orbit and make a realistic simulation quite messy. The relatively large mass of the Moon compared to Earth makes this even more interesting.

Remember also that the Earth is quite fluid. Even without external torques, we can change our inertia tensor in an appreciable way and have a radical impact on the angular velocity. Our coupling to the Moon means an alteration like that can have an impact on many other bodies in the inner solar system. We already know the Earth is one of the more important 'stirrers' when it comes to asteroid orbits, so we have a potentially chaotic effect on all bodies around us.

Anyone wanting to really get into this should try similating it all. By the time you track down all the things that can have a significant impact, you will truly realize that the solar system isn't finished yet. It only seems that way because of our relatively short lives. 8)

[Ken G]

Sounds like a complicated issue indeed. My point was simply that the combined tidal effect of Sun+Moon should look a lot like the Moon's by itself, only sometimes bigger (spring) and sometimes smaller (neap). On average, then, the coupling of the Earth's rotational angular momentum to the Moon's orbit should not be greatly affected by the Sun, it should mostly average out. If this is true (simulation needed, I agree), the Sun would not rob the Earth of much rotational angular momentum, though the Earth may rob the Sun of a tiny bit (I rather doubt it is significant compared to all the other factors that adiffer is talking about, but I really have no idea). I guess I was just being picky, no offense intended.

[crosscountry]

Sounds like a complicated issue indeed. My point was simply that the combined tidal effect of Sun+Moon should look a lot like the Moon's by itself, only sometimes bigger (spring) and sometimes smaller (neap). On average, then, the coupling of the Earth's rotational angular momentum to the Moon's orbit should not be greatly affected by the Sun, it should mostly average out. If this is true (simulation needed, I agree), the Sun would not rob the Earth of much rotational angular momentum, though the Earth may rob the Sun of a tiny bit (I rather doubt it is significant compared to all the other factors that adiffer is talking about, but I really have no idea). I guess I was just being picky, no offense intended.

you're kinda right. remember that the moon "robs" angular momentum from the earth. Due to tidal friction, the earth slows down. To compensate the moon takes that angular momentum (to keep it conserved).



Since you agree the earth causes tides on the sun (however small) you'll also agree that the earth similarly gains angular momentum.

[hhEb09'1]

If this is true (simulation needed, I agree), the Sun would not rob the Earth of much rotational angular momentum, though the Earth may rob the Sun of a tiny bit (I rather doubt it is significant compared to all the other factors that adiffer is talking about, but I really have no idea).

Since you agree the earth causes tides on the sun (however small) you'll also agree that the earth similarly gains angular momentum.

Yes, the relationship should be symmetrical--angular momentum lost should be equal to angular momentum gained. But really, the Sun is rotating slower than the moon, and it is the Earth that is probably losing angular momentum in the exchange.

Part of the problem with a simulation is that the source of tidal friction in the Earth has not been clearly identified--but a coefficient can be inferred from the lunar data.

[Ken G]

Since you agree the earth causes tides on the sun (however small) you'll also agree that the earth similarly gains angular momentum.

You're talking about orbital angular momentum, which must be distinguished from rotation. But I think we are in agreement! Interesting point hh, that the actual sources of friction cannot be modeled without using the very data we would be trying to explain. Glad I don't do such simulations!

[crosscountry]

Yes, the relationship should be symmetrical--angular momentum lost should be equal to angular momentum gained. But really, the Sun is rotating slower than the moon, and it is the Earth that is probably losing angular momentum in the exchange.

break it into two parts. first the E-M system. we've already talked about it, but to refresh:

the moon causes tides. those tides don't rotate with the earth, thus they slow the earth's spin down (due to friction). Angular momentum is conserved, so as the earth slows its rotation, the moon gains orbital momentum.


now the S-E system. Think of the sun as the earth in the previous example. think of the earth as the moon. Now, as we already know, the sun causes its own tides on the earth. this again slow the earth's rotation. But momentum is conserved, so the net effect is a greater radial distance from the sun. greater orbital momentum.

BUT, the sun also has tides due to the earth. Thus the sun's internal friction causes it to lose rotational momentum and it gives us that momentum in the form of orbital so for another reason the earth-sun distance is growing.

[hhEb09'1]

That sounds right

[crosscountry]

it took a lot of thought. now I need to grade some homework

[Duane]

it took a lot of thought. now I need to grade some homework

And I need an aspirin! interesting discussion

[Kaptain K]

Thus our orbit is increasing.

While it is true that our orbit is increasing, and I would agree that tidal forces have some effect, I would think that they are totally swamped by the fact that the Sun is losing mass at the rate of 4 million tons per second! And that's just from fusion, it doesn't include mass loss from the solar wind.

[crosscountry]

While it is true that our orbit is increasing, and I would agree that tidal forces have some effect, I would think that they are totally swamped by the fact that the Sun is losing mass at the rate of 4 million tons per second! And that's just from fusion, it doesn't include mass loss from the solar wind.

very true. I was just answering a question and think I did so effectively.

[hhEb09'1]

OK, I have a couple more then

now the S-E system. Think of the sun as the earth in the previous example. think of the earth as the moon. Now, as we already know, the sun causes its own tides on the earth. this again slow the earth's rotation. But momentum is conserved, so the net effect is a greater radial distance from the sun. greater orbital momentum.

BUT, the sun also has tides due to the earth. Thus the sun's internal friction causes it to lose rotational momentum and it gives us that momentum in the form of orbital so for another reason the earth-sun distance is growing.

1) Why is there no net gain/loss for the Earth in the first exchange, but there is in the second?
2) What is the internal friction in the Sun that causes that?

[crosscountry]

the earth does lose angular momentum in the first one. We are actually slowing down the period of an earth rotation. The effect is very small, but over eons eventually the earth will rotate once every full moon (it will always show the same face to the moon)


2) the sun is not a solid. nor is it uniformly dense. as like the moon causes the earth to be an "oblate spheroid" the earth does the same to the sun (although very slightly). AND the sun rotates at its own rate. It rotates much faster than the 1x per year orbit of the earth.

so, we are pulling it one way, but it rotates on its own. thus tidal forces and friction.


does that make sense?

[DALeffler]

What's the sequence of events: Would the earth first get slowed in its rotation around its axis and then get its orbit increased; or does the earth get its rotation slowed and its orbit increased at the same time?

[crosscountry]

it is all about conservation of momentum.


as the sun's rotation slows the radius of the earth's orbit increases.


similarly, as the earth's rotation decreases, the moon's distance increases.


but actually, the moon will always have a larger effect than the sun, due to proximity.

[scorpionman_53]

Maybe my question has relation with BLACK CAT member's question. Why orbital destance of moon is altering during its orbiting??.Infact which forces/force effect on its rotation??

[Count Zero]

Tidal force are causing the Earth to transfer momentum to the Moon. The Earth's rotation rate slows, and the energy is added to the Moon's orbital velocity, causing it to move further away from the Earth. Of course, as the E-M distance increases, the tidal forces decrease. The Moon will probably enter a solar orbit before the Earth slows down to a tidal-lock.

[Count Zero]

FYI, Tidal forces vary in direct proportion to the mass, and as the inverse cube of the distance. The Sun (IIRC) is ~26.4 million times more massive than the Moon, but is 400 times further away.

26,400,000/(400^3) = 26,400,000/64,000,000 = .4125

So the tidal forces from the Sun are ~4/10 of those from the Moon.

[Kaptain K]

The Moon will probably enter a solar orbit before the Earth slows down to a tidal-lock.

1) Technically, it already is in a solar orbit. Although, from an Earth-centric point of view it orbits the Earth, it's orbit is always concave to the Sun.
2) The Moon will never escape from the Earth - unless it gets outside help!
3) I remember reading that the Earth-Moon system will reach tidal lock in about 3-5 billion years, at which time, the "day" and "month" will be 55 of our current days long and the distance to the Moon will be around 350-400 million miles (560-640 million Km). This assumes that the Sun doesn't become a red giant first, in which case, all bets are off!

[crosscountry]

3) I remember reading that the Earth-Moon system will reach tidal lock in about 3-5 billion years, at which time, the "day" and "month" will be 55 of our current days long and the distance to the Moon will be around 350-400 million miles (560-640 million Km). This assumes that the Sun doesn't become a red giant first, in which case, all bets are off!

My memory fails me sometimes too. the sun is only 93 million miles away on average. A moon at that distance would in fact be orbiting the sun past Jupiter.

I've heard 55 days or so