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[Maximum Spin]

Space, actually, as it boils off.

It has no significant effect on the momentum of the planet, for the reasons of mass differential that Culise outlined, but insofar as it technically happens, that's where the momentum goes.

Technically, that's not losing its angular momentum. You can't lose angular momentum to space, because space isn't a thing. It's just... particles fucking off with some of the angular momentum. Like assholes. Really, those particles are such jerks.

[Reelya]

Reelya: Okay. Here's the thing. If the atmosphere was exerting drag on the planet, we'd all be able to feel it. There would indeed be 1000mph winds around the equator. This is not the case. Therefore you can probably guess your analysis is wrong. And also the rotating atmosphere does have angular momentum.

There wouldn't be 1000mph winds, because the air is in fact moving as well. But without a constant force, you can plot the gravitational trajectory of any air particle and work out where it should go. You could then work out the force needed to keep the air moving at the right speed, and get a good estimate of the required energy for that at each altitude based on air density.

The point is that locally, any particle only knows about it's own straight-line trajectory and forces acting on it. The particle doesn't have "rotate around the Earth" imprinted on it, because that's a constrained motion. That's what I meant by saying that no energy was needed because of "angular momentum" was misleading. It does require energy, because it's forcing the particles into a motion that's not their unconstrained motion - they're constantly being accelerated (change in velocity).

And sure, air has angular momentum, however, in air, at any time, you have particles traveling in every possible direction. This is what makes spinning gas different to a spinning rock. The spinning rock can be treated with a simplifying approximation because the motion of particles within the rock is small compared to the spinning velocity. Air is more complex than that and can't be treated exactly like an arbitrary spinning solid object.

Also as to where the energy goes if the planet is pushing air particles around ... it's also emitted into space as heat energy. Friction creates heat, that comes from somewhere. Same deal.

[Culise]

However, it's notable that Venus has an extremely slow rotational period, along with a really dense atmosphere. that took billions of years however. But not 10^18 years.

Major issue with that: Venus is *extremely* weird.  Not only does it have a rotational period of 243 days, its rotation is also retrograde.  Drag might be a decelerative force, but it wouldn't increase Venus's rotation in a retrograde direction.  By the same token, its axial tilt is rather unusual at a mere 2.6° absolute off vertical.  It is highly improbable that atmospheric drag is the fundamental reason for its unusual rotational behaviour.  To add on with something you didn't mention yet, while Venus' rotational period has actually slowed down over the scant few decades that sum up the total history of human observation of Venus' surface, it's also not clear that this is being caused by its atmosphere and not, say, transfer of angular momentum between Earth and Venus for another hypothesized cause.  It may also be possible that Magellan's instruments were off by a few minutes. 

Bear in mind also that angular momentum is conserved: if the solid structure of the Earth loses angular momentum to its atmosphere, the atmosphere is gaining that angular momentum.  Where then is that angular momentum then being lost?  I mean, we have observed that drag aside, simple changes in wind appear to lead to effects on the Earth's rotation: El Niño seems to be capable of increasing the length of Earth's day by less than a millisecond, which seems to be regained as the phenomenon concludes.  In this, the aforementioned question about the change in Venus' rotational period takes on another factor: even if it's the atmosphere, is it atmospheric drag, or is it a solar-driven wind that's causing a transfer of angular momentum from the planet to the atmosphere like a ballerina stretching out their arms? 

EDIT:
Also, I said the Earth's atmosphere is on the order of 10¹⁸ kg of mass (specifically around 5*10¹⁸, give or take).  Nothing about it taking 10¹⁸ years.

[Maximum Spin]

The force keeping the atmospheric particles from crashing into the ground due to gravity is provided by the Sun. Specifically, the thermal energy of the air causes it to push back against collapsing. This is what keeps the air in its faux-stable orbit.

And sure, air has angular momentum, however, in air, at any time, you have particles traveling in every possible direction. This is what makes spinning gas different to a spinning rock. The spinning rock can be treated with a simplifying approximation because the motion of particles within the rock is small compared to the spinning velocity. Air is more complex than that and can't be treated exactly like an arbitrary spinning solid object.

It totally can be and we do.

The outer envelope of the atmosphere, modulo ingress and egress, still behaves like a single body, and its angular momentum is conserved.

Your whole "newtonian physics straight lines" thing neglects the fact that newtonian physics is in fact not actually true; the atmosphere has a rotating frame of reference and therefore it has angular momentum.

[Reelya]

the atmosphere has a rotating frame of reference and therefore it has angular momentum.

That's just an approximation. How does any one particle know to rotate it's frame of reference around an arbitrary point? There's clearly no basic force of physics that does that. It's only an outcome of systems.

Rotating the frame of reference for a particle around some arbitrarily chosen point is just a human convenience. Particles exist in their own local frame of reference only. If one molecule of air is happening to be traveling east or west, then it's current frame of reference for that one molecule isn't actually "rotating" around the Earth in a direction that the particle doesn't happening to be traveling. So it's just an approximation for a bunch of molecules, and it won't actually be 100% accurate for any of them, only on average.

Well, a spinning fluid might stop spinning by friction. If angular momentum is conserved, then something carried that off. The only candidate is that the heat energy generated by the friction actually has the angular momentum.

[Maximum Spin]

Particles exist in their own local frame of reference only.

Every particle is at rest in its own local frame of reference.

Honestly I think you need to pick up a book on general relativity, okay?

Well, a spinning fluid might stop spinning by friction. If angular momentum is conserved, then something carried that off. The only candidate is that the heat energy generated by the friction actually has the angular momentum.

A) please stop editing more wrongness into your posts after the fact
B) the angular momentum is transferred to the thing it experienced friction against. 3rd law of motion.

[Reelya]

My point was that each particle responds only to local force strengths in it's own frame of reference. It can't "know" that it's supposed to spin around another point. That's not what it's unconstrained motion would be. A solid object lets you ignore that, because the bonds between atoms are so strong relative to the rotational speed.

Also, angular momentum is only conserved in closed systems, unless acted on by a torque. That's part of the definition. It has to be a closed system without any other forces acting on it. It's equivalent to the Newtonian mechanics statement that a particle will always travel in a straight line unless a force acts on it.

Application of force can in fact change the angular momentum of a system. e.g. friction force changing the kinetic energy to heat energy. This would happen with or without the sun being there.

[smjjames]

Except that without the sun, all you'd have is a frozen atmosphere, or at least whatever hydrogen is still under Earths gravity.

You can't have an atmosphere without some form of heat, be it internal or external.

Edit: okay, yeah, I contradicted myself, a rogue gas giant floating in the depths of space would still have an atmosphere through its internal heat, as would a brown dwarf.

[Maximum Spin]

The particles are actually constrained by gravity, which means that their local straight lines "curve" toward the planet. However, you also seem not to understand that all frames of reference are equivalent. That's the point of general relativity.

Also, angular momentum is only conserved in closed systems, unless acted on by a torque. That's part of the definition. It has to be a closed system without any other forces acting on it. It's equivalent to the Newtonian mechanics statement that a particle will always travel in a straight line unless a force acts on it.

Angular momentum is conserved in general - in an open system, it may seem to disappear from the system because it moves elsewhere. Which takes us back to my original question, where do you think the angular momentum goes?

Application of force can in fact change the angular momentum of a system. e.g. friction force changing the kinetic energy to heat energy. This would happen with or without the sun being there.

The friction force is not an outside force, it doesn't carry away any angular momentum. Radiative heat transfer could, but that's a separate issue not involved here.
ETA: Also, it occurs to me that it may help to point out something else.

As of right now, it is not friction with the Earth that keeps the atmosphere rotating.
The atmosphere is rotating because it was previously rotating and has no reason to stop.

Remember that the atmosphere-Earth system is nearly closed in terms of matter - the matter in the atmosphere either came from the Earth or came from the same condensing mass of cosmic dust as the Earth. If the Theia impact hypothesis is true, that event essentially set the atmosphere spinning at the same time it set the Earth spinning — if not (unlikely), the atmosphere and Earth likely retain their primordial angular momentum from the aforementioned mass of cosmic dust. Since (nearly) every "change" in the atmosphere since has been an exchange between the atmosphere and the surface, nothing would have caused the atmosphere to lose speed relative to the Earth, so there isn't any drag between the two to begin with.

[Reelya]

It's turning into heat however. Citations:

https://physics.info/rotational-momentum/

However, ignoring energy lost to heat generated by the tides, the angular momentum of the Earth-Moon system must remain constant.

In other words, conservation of momentum in a closed system is only true if you ignore any resultant energy lost through friction. In this case the moon/Earth is a closed system. Yet it still loses momentum via friction. So the friction still counts as a torque, even if both the things rubbing together are part of the closed system. Whether there's one planet or two, they're both closed systems as far as conservation laws go, so the same rules apply. Friction generates heat, which is a transfer of energy.

http://physics.bu.edu/~duffy/py105/Momentum.html

The total energy is always conserved, but the kinetic energy does not have to be; kinetic energy is often transformed to heat or sound during a collision.

Friction is basically a lot of little collisions. In those situations, kinetic energy becomes heat energy.

https://courses.lumenlearning.com/boundless-physics/chapter/conservation-of-energy/

    Rotating objects have rotational kinetic energy.
    Rotational kinetic energy can change form if work is done on the object.
    Energy is never destroyed, if rotational energy is gained or lost, something must have done work on it to change the form of the energy.

I mean, it's not really high tech stuff here. If friction causes heat, and heat is energy then conservation of energy requires that it came from somewhere, which was the kinetic energy of particles involved in the friction collision. Some of that energy came from the sun, but not all of it. In this case, it's not a given that a system which undergoes friction keeps spinning at the same rate, because it's losing energy to anotherform.

As for the sun warming things up yeah. But the sun doesn't make planets spin. In this case, the sun gives the atmosphere more pressure, which increases friction between the air and the planet. And that, on average, causes kinetic energy to be converted into heat energy at a faster rate.

One last thing and them I'm done I think:

https://news.nationalgeographic.com/news/2012/02/120214-venus-planets-slower-spin-esa-space-science/

According to the new data, Venus is rotating 6.5 minutes slower than it was 16 years ago, a result that's been found to correlate with long-term radar observations taken from Earth.
...
One possible cause for the slowed spin is friction caused by Venus' thick atmosphere and high-speed winds. The motion of the atmosphere on Earth, for example, has been observed to affect the planet's rotation rate, albeit to a much smaller degree.

So ... Venus's rotation period is losing 24 seconds per Earth-year, otherwise completely unexplained. Compare that to Earth losing 1.7 milli-seconds per century. At that scale it's looking more feasible that drag could be a big factor. Also if Venus had once been spinning much faster and atmospheric friction was proportional to speed, then there would have been a rapid slowdown at some point. e.g. if Venus spun once per day, but with the same 90 pascals pressure atmosphere, would it lose 24 * 240 seconds per Earth year at the start? (obviously you'd integrate the loss-function over time to get it more accurate than that).

Hmm, might be interesting to calculate the atm pressure on Earth vs Venus, multiply that by surface area, rotation speed, and see how close the numbers line up.

[Maximum Spin]

Heat energy is kinetic energy.

You're probably thinking of heat radiated as infrared photons, which can carry angular momentum, but in this case should also be symmetric; the tiny difference they would make (not enough to have the effect you claim) balances out anyway.

BTW, angular momentum really is always conserved. In the case of loss from heat, it's because the radiation actually carries angular momentum away and deposits it somewhere else. The angular momentum still exists.

ETA: Let me further be absolutely clear: radiated heat from any self-interaction (whether between the earth and the atmosphere or just within the atmosphere, or within the ocean, or whatever), if it were asymmetrical, would reduce the angular momentum of the whole earth-atmosphere system, causing the Earth to move into a different orbit in compensation. It would not cause the atmosphere to drag against the Earth, except briefly as the momentum change propagates through the system.

[Starver]

However, it's notable that Venus has an extremely slow rotational period, along with a really dense atmosphere. that took billions of years however. But not 10^18 years.

Major issue with that: Venus is *extremely* weird.  Not only does it have a rotational period of 243 days, its rotation is also retrograde.

Is its rotation truly retrograde? I would class it as 'insufficiently prograde', given its orbit.

Sidereally, does it not still spin as expected of most significant bodies in the system? (Uranus being the notable exception.) Just slower than the apparent observable back-rotation of the Sun around it? And Mercury seemingly has a stretch in its orbit where the slow 'absolute' rotation (3:2 ratio) is outpaced by the 'sun falling behind it'.

Or maybe I'm wrong, I have a spinning head trying to visualise the various levels of relative spinning from the various observers one might involve.

[Reelya]

Heat energy is kinetic energy.

You're probably thinking of heat radiated as infrared photons, which can carry angular momentum, but in this case should also be symmetric; the tiny difference they would make (not enough to have the effect you claim) balances out anyway.

Well, look at the data on Venus, it's not even rotating fast yet it's slowing by an additional 24 seconds of day-length every Earth-year. Other than atmospheric drag there's really no plausible explanation for the change, since Venus lacks a moon as well.

Also, why should emitted infrared photons be "symmetric"? Space is a huge heat-sink. And hot things constantly emit in the infra-red. And it doesn't matter if you also get heat from the sun. Heat generated by friction from motion is radiated as heat energy. It isn't going to magically turn back into the same motion you had before just because you added more heat from the sun. That's not how entropy works. Entropy isn't symmetric.

[wierd]

Infra-red photons are not, defacto, heat energy. It is EM energy, emitted in the blackbody emission curve. It can be absorbed by other, cooler, objects and that absorption will increase the velocity of the atom that absorbs it, which increases its kinetic energy-- but that is a conversion process-- the IR photon is not itself a form of kinetic energy.

[Maximum Spin]

Also, why should emitted infrared photons be "symmetric"?

Because they are being emitted in all directions equally because internal interactions are happening everywhere at the same rate.

Space is a huge heat-sink.

Actually no, you can't conduct or even convect into it, so it's really hard to lose heat to space.

And it doesn't matter if you also get heat from the sun. Heat generated by friction from motion is radiated as heat energy. It isn't going to magically turn back into the same motion you had before just because you added more heat from the sun.

Who said anything about the sun? Where are you even getting this? And again, there's no such thing as "heat energy". Heat is just kinetic energy. It's always the same motion because it is motion.