Earth's Rotation and Atmosphere

[PeterDonis]

Presumably you develop some sort of closed circulation

Yes. Which, as jim hardy's post points out, is exactly what happens in the Earth's atmosphere.

 

[OmCheeto]

In a fluid that was initially stationary, if that's what you mean.

I think Drakkith answered this in post #2

The atmosphere formed with the rest of the Earth and thus has been rotating with it from the very beginning.

I'm still not sure what we are discussing, so I'll reference back to some research I did back in March, and my commentary on why the atmosphere is so weird, that I can't begin to explain it.

I was diddling around with the http://earth.nullschool.net simulator yesterday, and things were no better.
From sea level to about 1500 meters, the atmosphere is consistently random, and very much traveling at the same speed as the Earth.
Above that elevation, things get very strange, and I suspect it is the tilt of the Earth which is causing it.
The northern and southern hemispheres, atmospherically, look like they are from two different worlds.

 

[olivermsun]

Yes. Which, as jim hardy's post points out, is exactly what happens in the Earth's atmosphere.

Keep in mind, though, as Jim Hardy's post also points out, the Earth system is being heated at the equator, so there's quite a different set of mechanisms causing the large-scale circulation that we actually observe.

 

[rootone]

It has to be said a well that the atmosphere always has been a part of the planet. just as the ocean is.
It' s overall angular momentum has been in synch with the rocky planetary body from the beggnning, it did not need to be accelerated to match the rocky stuff,
and there is nothing at the outer edge of the atmosphere which is applying a braking force to it.

 

[PeterDonis]

the Earth system is being heated at the equator, so there's quite a different set of mechanisms causing the large-scale circulation that we actually observe.

Yes, good point; what we should be doing is comparing the relative numbers for convection and the rotation effect.

 

[D H]

I started to think about that and I think that would be correct. However, that's assuming those equations would even apply to a rotating sphere. I found a paper about boundary layers of a rotating sphere in a still fluid, and I'll try to look into it more to see what it says when I get a chance. http://www2.leicester.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/sjg50/Garrett - Peake 2002 JFM.pdf

However, there was an interesting tidbit in the introduction:
"When a sphere rotates in still fluid a flow is induced in which the fluid moves over the outer surface from the poles to the equator and is ejected radially from the equator." That's what I was saying in the beginning.

That article is about flow of air around a small object in a large, uniform gas. It has nothing to do with the topic at hand. I suggest you read about general circulation models instead.

 

[Iseous]

That article is about flow of air around a small object in a large, uniform gas. It has nothing to do with the topic at hand. I suggest you read about general circulation models instead.

So a spherical Earth rotating with an initially still atmosphere is nothing like a sphere rotating in an initially still gas?

 

[rootone]

But it didn't have an initially still atmosphere, (and what exactly does 'still' mean here anyway?, still in relation to what?)
The whole planet including the atmosphere originally formed out of a condensing cloud of material including gases, and all of it had angular momentum.

 

[Iseous]

Still to an outside observer who is not rotating with Earth. Regardless, once the sphere in that experiment started rotating and getting the gas to rotate with it, then it is no longer "still" either. So whether it started off not rotating, or you looked at a point once the sphere and gas around it was already rotating (fast forward into the experiment), you would get the same steady state eventually unless there was an outside energy source influencing the gas. But if you're going to claim it all had angular momentum, then where did that come from? These clouds were the result of gravitational forces acting on one another. But how would gravity cause something to rotate on its own axis? It acts at the center of mass, which would not do that. That would require a force not acting on the center of mass (i.e. not gravity).

 

[PeterDonis]

But how would gravity cause something to rotate on its own axis? It acts at the center of mass, which would not do that.

You are taking an approximation (that the gravity of a spherically symmetric body can be viewed as being produced at its center of mass) and using it where it is not valid. The solar system formed from a diffuse cloud of gas and dust. That cloud was not exactly spherically symmetric; the forces between individual pieces of the cloud did not average out to a single "force of gravity" acting from the center of mass of the cloud.

The above is actually another way of saying that the cloud started out with angular momentum. Other clouds that formed other stars also started with angular momentum. In order to average everything out to get zero angular momentum and spherical symmetry (to a good approximation), you need to look at much larger distance scales, comparable to the entire observable universe. At that scale, the universe as a whole has (as far as we can tell) zero angular momentum. But much smaller regions of it, like stellar systems, do not.

 

[rootone]

The entire solar system formed with an initial angular momentum, so for that matter did the Milky way galaxy.
Smaller structures obtain their momentum from larger more massive structures.
There is no evidence to the contrary - (which would be that initially static objects form and later they somehow start to spin).

Edit:
As Peter said, on the very largest scales it looks as if the spin of galaxies is arbitrary and cancels out overall on the cosmic scale, although locally within the gravitationally bound systems, a very definite and coherant rotation exists from their beginning.
The same applies to Earth's atmosphere - It came into existence as a part of the early Earth and it always has been rotating along with the rest of the planet.

 

[Iseous]

Any object can be simplified to a center of mass for a gravitational force or sum of gravitational forces. That is why if you drop an object of any shape, it falls straight down (toward the center of mass of Earth) without any rotation about its own axis (because the gravity is acting at the center of mass of the object that dropped). Even though it is being pulled by many different masses, the net force acts essentially between their centers of mass. An object would only rotate if you apply another non-gravitational force to it away from its center of mass.

 

[rootone]

Yes correct, but in the case of the Earth's atmosphere it isn't needing to acquire any spin, it's a part of the planet and it always was.
It's not as if the revolving planet with no atmosphere ran into a huge motionless and very dense gas cloud which then stuck to it.

 

[Iseous]

If this was part of a giant gas cloud, then the gas would have just been pulled toward Earth from gravity just like all the other mass. So yes, the atmosphere did not necessarily have to have its own spin initially. But gravity would not explain the initial spin of the Earth or other bodies to then rotate the atmosphere in any way.

 

[rootone]

The initial spin of Earth, all of it including the atmosphere, arises because the initial cloud of material from which the Earth condensed was already rotating.
That cloud of material obtained it's rotation from the larger scale cloud of material which was the nebula which gave rise to the overall solar system.
This also was initially formed with some amount of spin, (which is why the planets have orbits and do not fall into the Sun)

 

[Iseous]

Okay, but that doesn't specify what forces actually caused that. You just keep going back further into the past and say that the thing before it had the spin already, but no explanation of the forces involved to actually do that. The big bang was basically an explosion outward, which would give an outward radial motion, not any spinning. So unless you just want to keep going back and say that everything already had a spin right from the start of the big bang...

 

[PeterDonis]

Any object can be simplified to a center of mass for a gravitational force or sum of gravitational forces.

This is not correct as you state it. Strictly speaking, only an object with zero angular momentum can be simplified in this way. In practice, objects that are small enough can be approximated this way even if they have angular momentum, for many purposes, but not for all. (For what "small enough" means, see below.)

That is why if you drop an object of any shape, if it isn't already spinning, it falls straight down (toward the center of mass of Earth) without any rotation about its own axis (because the gravity is acting at the center of mass of the object that dropped).

See my correction above. The object has zero angular momentum at the end because it has zero angular momentum at the start.

Also, suppose the object is a long ("long" meaning kilometers long), thin rod, oriented horizontally, with one end higher than the other. What will happen when you drop it? The Earth's gravity will pull the lower end a little more strongly than the upper end, so the lower end will fall faster. Which means...the object will start rotating (about a horizontal axis).

So your claim breaks down in two scenarios: one, objects that are already spinning; two, objects that are large enough for different parts to have different gravitational forces on them (i.e., large enough for tidal effects to be important), which can start them spinning.

 

[PeterDonis]

Yes correct

No, he's not correct. See my previous post.

 

[PeterDonis]

The big bang was basically an explosion outward, which would give an outward radial motion on average, not any spinning.

See my correction above. I've already posted about this here; the universe as a whole has zero angular momentum (as best we can tell), and has since the big bang, but that is just a large-scale average; it does not mean individual sub-regions of the universe cannot have angular momentum.

 

[rootone]

It's observationally true that objects on the scale of galaxies are spinning, and from that we can see why smaller systems within galaxies derive their rotations.
I agree with you that it isn't clear how the spinning on the largest scales got going, but it does seem that there is no preferred direction for spinning galaxies, it's apparently random.
So on the scale of the whole observable Universe the total spin is zero as far as we can tell.
However spin does exist at the scale of galaxies, as a matter of observation, it's not theory.

@Peter - OK. I'll check back the detail of that later, no time now,
What I was agreeing with, (forgetting spin for this purpose), was that if two massive objects exist within a cosmologically close distance they will be gravitationally bound and would attract each other.

 

[Iseous]

So your claim breaks down in two scenarios: one, objects that are already spinning; two, objects that are large enough for different parts to have different gravitational forces on them (i.e., large enough for tidal effects to be important), which can start them spinning.

Your initial scenario is trivial. If it's already spinning it will keep spinning, that doesn't mean the gravitational force made it spin. It just didn't apply any moment to stop it or make it spin faster.

Your second scenario is still relatively trivial unless you are talking about such a large distance that the force of gravity changes significantly over that distance. An object that is only a few km would not be nearly large enough for such an effect that is actually noticeable in any significant way. If you were talking about an extremely massive object like a a super-massive black hole, then approaching that would stretch the object or potentially cause rotation because of the strong variance in the gravitational field. Otherwise, even for a large object like Earth, an extremely long object would be needed. However, such a long object would not even be naturally created by gravitational forces because they would be tending toward spherical or at least somewhat round objects and definitely not a long rod.

 

[PeterDonis]

Your second scenario is still relatively trivial unless you are talking about such a large distance that the force of gravity changes significantly over that distance.

Okay, then we're talking about such a large distance. Are you claiming that such a scenario is impossible? Consider the huge cloud, a light-year or so across, from which the solar system formed. Are you claiming that the gravity of such a cloud is so perfectly spherical that there would be no tidal effects on any part of the cloud?

even for a large object like Earth, an extremely long object would be needed.

An object of more or less the same size as the Earth, yes, at least to make an easily observable effect--one km long might not be enough (but then again, it might; differences in gravity have been measured over tens of meters in laboratory experiments), but a few hundred km long would be enough. But we're not actually talking about the Earth here, but about the cloud of diffuse gas and dust from which the solar system formed--or, more generally, all such possible configurations during the history of the universe. To claim that no differential gravity ever acted anywhere to start things spinning (in various different directions across the universe, averaging to zero) is an extremely extravagant and improbable claim, but that appears to be the claim you are making. You might want to stop and think.

such a long object would not even be naturally created by gravitational forces because they would be tending toward spherical

Why? Why would a mass distribution that doesn't start out as spherically symmetric, become spherically symmetric because of gravity?

 

[PeterDonis]

If it's already spinning it will keep spinning, that doesn't mean the gravitational force made it spin.

But this shows, as you say, that if it's already spinning it will keep spinning. You might want to think about what that means, since you have been claiming (or apparently claiming) that gravity creates spherically symmetric mass distributions. A spinning mass is not spherically symmetric, and if gravity doesn't change its spin, gravity won't make it spherically symmetric.

 

[Drakkith]

Okay, but that doesn't specify what forces actually caused that. You just keep going back further into the past and say that the thing before it had the spin already, but no explanation of the forces involved to actually do that. The big bang was basically an explosion outward, which would give an outward radial motion, not any spinning.

This is completely wrong. The big bang was not an explosion and the expansion of the universe is not like normal radial motion. In any case, as Peter has already said, individual parcels of gas (or plasma in this case, see below) can have net angular momentum even though the whole universe has no net angular momentum.

So unless you just want to keep going back and say that everything already had a spin right from the start of the big bang...

That is indeed the case. The spin arises from variations in the density of the hot, dense plasma that filled the very early universe. The angular momentum of each particle in these slightly denser regions didn't quite cancel out, leaving a net angular momentum for each 'parcel' of plasma. The variations in the density allowed gravity to act on the denser regions, making those regions more and more dense, eventually forming galaxies and stars. The angular momentum of the initial regions of plasma was conserved during this process, which is where the spinning comes from.

 

[olivermsun]

Big bang aside, the Earth's surface is in fact constantly accelerating (and decelerating) the atmosphere wherever there's a velocity difference at the surface.

 

[Iseous]

Are you claiming that the gravity of such a cloud is so perfectly spherical that there would be no tidal effects on any part of the cloud?

I don't think it really has anything to do with the shape of the cloud. The force of gravity can be simplified to a single point mass acting at a certain distance, regardless of the size or shape of the mass. The main thing that would matter is the size/shape of the object being pulled by this gravity and how much the gravitational force changes over its mass. In most cases the center of gravity will be the same or very close to the center of mass, and thus no spinning would be induced. The only cases where this wouldn't be true is if the object is extremely long or it is in a very strong gravitational field such as near a black hole where the forces change enough to create a center of gravity far from the center of mass. However, even in a case like this, the object would essentially turn into a pendulum, not a spinning ball. The center of gravity of the smaller object being moved would try to align itself with a line intersecting the centers of mass of the interacting objects (because with that orientation there would be no moment formed). So if you had a long rod, it would essentially want to point toward the equivalent point mass where it felt the force of gravity. This would cause the rod to start rotating toward that orientation, but as soon as it passed that orientation, it would be pulled back, thus creating a pendulum motion; not a full spinning motion.

To claim that no differential gravity ever acted anywhere to start things spinning (in various different directions across the universe, averaging to zero) is an extremely extravagant and improbable claim, but that appears to be the claim you are making. You might want to stop and think.

As I just explained above, the spinning would most likely be a pendulum motion rather than the rotation of the planets we see. It would still be possible to get the full rotation if the masses moved in the perfect way to get something moving toward a specific orientation, and then moved far enough out of the way to be unable to reorient it. Regardless, a cloud of dust would not create the conditions for centers of gravity to be very far from the centers of mass of objects. The cloud is huge and not very dense, so obviously the forces of gravity would not change greatly with distance nor would the gas be large, continuous objects like a rod. So induced spinning would be very small, if any.

Why? Why would a mass distribution that doesn't start out as spherically symmetric, become spherically symmetric because of gravity?

Almost all the planets, stars, moons, and asteroids/meteors are spherical or round. They were created by gravitational forces, so it seems to be the natural formation. However, mathematically, since all points on the surface of a sphere would be at the same gravitational potential, there would be more of an equilibrium than other shapes, such as a rod (and since everything tends toward an equilibrium, the sphere would be the natural tendency). Objects would be attracted to the center of mass (to go toward the least gravitational potential), so on a sphere, there are no points that would have lower gravitational potential than another (except if there were different elevations such as a mountain, but that's why things will roll down). On a rod, things would want to roll toward the center, making it even itself out over time so that there was no specific point to which mass would "fall" toward, and hence create a sphere eventually.

This is completely wrong. The big bang was not an explosion and the expansion of the universe is not like normal radial motion. In any case, as Peter has already said, individual parcels of gas (or plasma in this case, see below) can have net angular momentum even though the whole universe has no net angular momentum.

Then what kind of motion is it? For one, big bang sounds like an explosion. For another, it started out as a singularity and expanded outward. If it started out as a point, there's not much else it can do besides radiate outward. And I'm not saying they can't have angular momentum. I am asking how they actually got it in the first place.

That is indeed the case. The spin arises from variations in the density of the hot, dense plasma that filled the very early universe.

I'm not sure how a spin would arise from these variations in density. I'll have to think about that.

 

[D H]

So a spherical Earth rotating with an initially still atmosphere is nothing like a sphere rotating in an initially still gas?

Why are you holding on to this completely incorrect concept?

The whole planet including the atmosphere originally formed out of a condensing cloud of material including gases, and all of it had angular momentum.

That, too, is incorrect.

I'm not sure how a spin would arise from these variations in density. I'll have to think about that.

That applies to the gas giants but not the terrestrial planets.

The dominant theory is that terrestrial planets formed by little clumps of dust colliding and joining to form bigger clumps of dust, which in turn collided to form little tiny rocks, which in turn collided to form bigger rocks. Eventually this resulted in planetesimals (objects about a kilometer in diameter), then planetary embryos (tens to hundreds of kilometers), then protoplanets (Moon to Mars-sized objects), and finally, planets. Whatever angular momentum the protoplanets had was wiped out by the last few collisions that resulted in the formation of the terrestrial planets.

Per the giant impact hypothesis, our Moon is a result of an oblique collision between the proto-Earth and a Mars-sized object. That collision would have wiped out whatever angular momentum the proto-Earth had prior to the impact, and it would also have wiped out whatever primordial atmosphere the proto-Earth had prior to the impact. The Earth's second atmosphere formed after that giant impact by outgassing from the early Earth. In other words, the atmosphere formed rotating with the Earth.

Note that the Earth was rotating much faster then than it is now, possibly as fast as one rotation every four to six hours. You have been asking the wrong question all along. Since the atmosphere formed from a rapidly rotating Earth, the right question asks why the Earth's atmosphere rotates so slowly. The answer is of course friction. The time scale between changes at the surface to the top of the planetary boundary layer is about an hour (that's pretty much the definition of the planetary boundary layer). The time scale to the top of the troposphere is a few days, to the top of the stratosphere, a weeks or months, and to the thermosphere, years to decades. That's tiny compared to the 4.5 billion years that have transpired since the formation of the Earth was complete.

 

[Drakkith]

Then what kind of motion is it? For one, big bang sounds like an explosion. For another, it started out as a singularity and expanded outward. If it started out as a point, there's not much else it can do besides radiate outward.

That's not an accurate description of what happened, but you'll have to make a thread in the cosmology forum or look up some of the existing threads there, as explaining it here would be off topic.

And I'm not saying they can't have angular momentum. I am asking how they actually got it in the first place.

Take a parcel of gas or plasma. Every particle in this parcel is moving about and will thus have some angular momentum about an axis passing through the parcel's center of mass. If we add up all the angular momentum vectors we will almost certainly not get zero. This is true even if our parcel of gas is within a larger parcel of gas that does have zero net angular momentum. If we were to look at a smaller parcel of gas within our original parcel, it too would have a different amount of angular momentum than the original parcel. This is because the random motion of the gas particles will give us different results when we add up the momentum of different particles.

I'm not sure how a spin would arise from these variations in density. I'll have to think about that.

Angular moment is spin. When the gas collapses under the force of gravity, the angular momentum the gas cloud already has is conserved. This means that, just like an ice skater pulling in their arms while spinning, the angular velocity of the gas cloud must increase in order to conserve angular momentum. The variations in density allow the gas to collapse under the force of gravity in the first place.

 

[D H]

The variations in density allow the gas to collapse under the force of gravity in the first place.

That is the (by far) dominant theory of how stars form. It is anything but the dominant theory of how planets form. Even if planetesimals did form by gravitational collapse, this still does not explain how those planetesimals combine to form planetary embryos and then planets. And it certainly doesn't explain how the Earth's atmosphere formed. The Earth's atmosphere, along with the atmospheres of Venus and Mars, formed after the planets formed. Instead of forming from gravitational collapse, the terrestrial planets' atmospheres formed from within via the huge amount of volcanic activity that marked the planets' early Hadean conditions.

 

[Drakkith]

That is the (by far) dominant theory of how stars form. It is anything but the dominant theory of how planets form.

I'm not addressing the question of how the Earth's atmosphere formed, but the one about where spin originally comes from.

 

[PeterDonis]

The force of gravity can be simplified to a single point mass acting at a certain distance, regardless of the size or shape of the mass.

You have repeated this incorrect claim several times. Either give a reference or show your work, or stop making it. You are skating close to a warning at this point.

Almost all the planets, stars, moons, and asteroids/meteors are spherical or round.

No, they're not. The ones that have negligible rotation are, to a good approximation. But the ones that have significant rotation, which means, at a minimum, the Earth, Jupiter, and Saturn, are not. They're oblate spheroids. In the case of Jupiter and Saturn, you can see the oblateness in pictures.

Once again, you have repeated incorrect claims several times now. Please take a step back and think.

 

[PeterDonis]

The OP's question has been sufficiently addressed. Thread closed.