What causes angular momentum in rotating bodies

John15

Starting at BB everything moves outwards with linear momentum so unless the BB event was rotating where does the angular momentum come from, the earth rotates, it orbits the sun, the galaxy is rotating and the sun orbiting within it. So it seems that angular momentum is the norm for bodies within the universe yet apparently the universe itself does not spin.
If the earths orbit is due to spacetime curvature where does its spin come from and that of all rotating bodies.
Linear momentum is a conserved quantity unless acted upon by an external force.
What outside forces acted upon the origional linear momentum?

Mark M

Well, that's simply incorrect. The big bang wasn't a point in space, it occurred everywhere at once. It was the moment in time at which the universe was extremely hot, and extremely dense.

Drakkith

The Big Bang was not an explosion in space. It was the expansion of the Universe leading from a very hot, very dense state to the cooler much less dense state it is in now. This happened everywhere at the same time. (The expansion is actually still going on in the present) The spin of the Sun and planets, along wither their revolutions in their orbits is a result of the collapse of the gas cloud that formed the solar system. During the collapse the cloud had angular momentum that had to be conserved, just like an ice skater accelerates when she pulls her arms in during a spin.

I have heard of theories about the universe having spin, but I don't believe any of them are considered to be true yet.

The Earth's orbit is a result of the effect of gravity, which is a result of the curvature of spacetime by energy and mass. This has nothing to do with spin. That is simply an effect of rotating an object about an axis.

Whatever force you apply to an object.

D H

Nice, simple, but not right. Conservation of angular momentum explains the collapse of the cloud into a disk, but it does not explain the spin of the Sun and the planets. Almost all of the solar system's mass is in the Sun, almost all of the solar system's angular momentum is in the orbits of the planets (and most of that, Jupiter). Planetary rotation arises from largely from torques that occur during the planets' formation rather than conservation of that initial angular momentum. Planetary formation is still an open problem, as is the rotation of the Sun (or the lack of it). All of those exoplanets and their weird orbits have thrown a monkey wrench into our nice pretty picture.

This explanation begs the question, where did that initial angular momentum come from? The standard explanation for that is gravity gradient torque. That standard explanation isn't quite standing up to scrutiny, however. The numbers apparently aren't quite right.

This is an exciting time for those who study solar system and galaxy formation. There are lots of open questions, and that means lots of opportunities for a thesis and continued research.

Antiphon

The total angular momentum of the universe could be zero, that doesn't rule out any local variations.

What about the numbers doesn't add up?

And the observed clumping and large-scale structure isn't consistent with a homogeneous uniform outward expansion; or is it?

D H

That's correct. That the universe has zero net angular momentum is to me the easiest solution. There's no reason to conjecture that the universe is spinning as a whole. Local variations in density obviously exist; just look at the night sky, or at the CMBR. These local variations create local gravitational fields. A mass such as a gas cloud subject to a non-uniform gravity field will experience a change in angular momentum. The mechanism is gravity gradient torque. The gas cloud starts spinning. Note that conservation of angular momentum means the gas cloud must in turn exert a torque on the source of the gravity field.

Gravity gradient torque appears to not quite fit what scientists see/simulate. It's still the preferred explanation as the cause of angular momentum because the mechanism is well understood and is known to exist. We see it right here on the Earth in the lunisolar precession and on satellites orbiting the Earth such as the Space Station. (The preferred attitude for the Space Station balances gravity gradient torque against torque from aerodynamic drag, minimizing the work the Station has to do to maintain it's attitude.)

Conservation of angular momentum is critical for the formation of the disk, but it also presents some problems. If angular momentum was conserved during star formation it would put the brakes on the formation of the star. Forming stars need some mechanism to put the brakes on angular momentum. There are a number of proposed mechanisms by which forming stars shed excess angular momentum, but as far as I know there isn't a consensus explanation yet.

Antiphon

Maybe it does put the brakes on star formation. Could it be that you must form stars from only very slowly spinning gas clouds? I don't see a problem with that.

John15

I realise the BB was not an explosion in space but as everything is apparently moving away from everything else presumably in a linear direction then something must have started things spinning from the beginning, pure linear motion would not allow anything to form in the universe.
I posted the question because I read somewhere that there is a problem in accounting for all angular momentum seen.
There is also the problem with Venus as it spins in the opposite direction to other planets.
I can see how the origional gas/dust cloud of the solar system can orbit the sun but I dont see how the coming together of the same causing planetary spin unless all particles were already spinning in the same direction otherwise spin of one would tend to cancel spin of another.
I have also read that the ignition of the sun would cause a shockwave through the dust cloud which would cause linear motion away from the sun which would also have to be countered.

D H

There are many things wrong with your notions.


One problem is that the Hubble expansion is a very large scale phenomenon. The attractive nature of gravitation dominates over the expansion at shorter distances, where "shorter distances" means the size of a cluster of galaxies. Gravitation dominates over the expansion at the scale of the formation of a single galaxy, and complete dominates at the scale of the formation of a star.

In short, you are ignoring gravity. The expansion has little, if any, effect on small scale structures such as galaxies. A star system is a tiny, tiny structure compared to the scale at which expansion dominates over gravitation.

Another problem is that just because the net angular momentum of a collection of objects is zero does not mean that the angular momentum of each object is zero. So where does this angular momentum come from? One answer is gravitation. Because gravitation is an inverse square force, two bodies interacting gravitationally can exert torques on one another. We see this right here on the Earth in the oceanic tides and in the 26,000 year lunisolar precession of the Earth's rotation. Both phenomena are caused by tidal torques. These tidal torques, aka gravity gradient torques, also act on larger scale objects in space such as clouds of gas. Tidal torques spin up clouds of gas of all sizes, from the huge primordial clouds that eventually became our galaxies down to the smaller clouds from which stars form.

Yes, there's a problem, and I've alluded to this problem in my earlier posts. This just means that there are opportunities galore for future PhD candidates to write a neat thesis. It's a devil in the details kind of problem. The basic mechanisms such as tidal torques are well-understood and are well-observed. There are various conjectured mechanisms to address the angular momentum problem, but these remain conjectural at this point. We need better telescopes and better computer models to fully resolve these open questions.


The nice, wrapped up in a pretty box with a ribbon and and bow picture you get in high school and even undergraduate science classes is never quite right. There would be no point in getting a PhD if a science was fully understood and comprehensible at the undergraduate level. Fortunately, there is not one branch of science that is fully understood. There are lots and lots of opportunities for PhD candidates of all sorts to extend their selected field.


One answer is a collision. A collision is not needed, however. All that is needed are tidal torques from the Sun and Jupiter, plus a good dose of chaos theory. This is a separate issue, however. Let's keep this thread on one subject.


That isn't needed. The rotation of the first three gas giants most likely resulted from planetary migration. Once the protoplanet has formed, it orbits at a slightly greater speed than does the surrounding gas. This is a simple consequence of orbital mechanics. The protoplanet races through the cloud, gathering material and losing linear momentum as it goes. This clears a path through the cloud along the protoplanets orbit and also causes the protoplanet to migrate sunward into a new source of yet-ungobbled (and hence more dense) material. That gradient in density creates a torque on the protoplanet as it gobbles up new material. Think of a snowball rolling downhill, gathering material and angular momentum as it goes.

The same applies to the inner planets to a less extent. Whether it fully explains the rotation rates of the inner planets is an open question.


When the Sun ignited it blew the left over gas out of the solar system. The stuff that had already accumulated into clumps, not so much. Radiation pressure is proportional to area (length squared), mass is proportional to volume (length cubed). There's a cube-square law relation going on here that makes small objects much more susceptible to radiation pressure than are larger objects.

Drakkith

The expansion of space is not a linear movement through space. It is a rate of expansion, where things further away from each other recede faster and accelerate quicker than they do for things closer to each other. Simple linear movement does not address this.

As for the angular momentum, it is possible for a gas cloud to have a non zero angular momentum that must be conserved during collapse. This is responsible for the rotation of the sun and the orbital direction of the planets. However the issue with Venus is much more of a question of how the planets formed and the early history of the solar system. Perhaps a large planetary body impacted it, forcing its spin in the opposite direction? What little spin it has at least. If I remember correctly Venus has a very very slow rate of spin.

John15

Coming back to Venus, you are right about its spin apparently its spin is slower than its orbit i.e its day is longer than its year. The strange thing as far as I have read is thats its lower atmosphere spins the same way as the planet but its upper atmos. spins the same way as the other planets. This obviously comes to the question is there an outside as yet unknown force acting on it, I would guess that the planets spin, being so slow now, may be slowing down and could possibly change direction to fit in with the rest of the solar system. Just guessing that at some point in the past the rate of venus's spin would have been closer to that of the other planets. I will admit that I only know the rate of the earths spin. Would I be right in thinking the sun being the center should have the fastest rotation rate and has it?

D H

Venus' upper atmosphere is weird. Venus' upper atmospheric winds are retrograge, and since Venus' rotation is retrograde, Venus' upper atmosphere rotates the same way that six of the other seven planets do. (Uranus is also an oddball).


Explaining the rotation of Venus' upper atmosphere (explaining it well, that is) is one of those open issues in science. Explaining it in a hand-wavy fashion is a bit easier to do. It's almost certainly caused by Venus' diurnal bulge. Consistent with this are observations of huge upwellings on Venus' dawn side, huge downwellings on its evening side. This is pretty much what one would expect with such a thick atmosphere. How these upwellings/downwellings create the huge zonal winds is an open question. Note that a similar mechanism occurs in the Earth's upper atmosphere. It too is also rotating faster than is the planet itself, but in the case of the Earth, it's only 10-20% faster than the Earth's rotation, and it's prograde.


Nope. The Sun rotates at a ridiculously low rate, one revolution per 24.47 days at the equator. Even though the Sun accounts for 99.9% of the total mass of the solar system, it only accounts for 4% of the total angular momentum of the solar system. The orbital angular momentum of Jupiter alone represents 60% of the total. The Sun loses angular momentum to the solar wind, so it did rotate faster long ago than it does now. Even accounting for this loss, there's still a mismatch between distribution of mass and distribution of angular momentum in the solar system.

Lino

D H, Could I ask if you can give me some pointers on "gravity gradient torque" please? I've done the standard searches, but the results discuss the relevance of "gravity gradient torque" to particular situations but assume that I / the reader understands "gravity gradient torque" - and I'm afraid that I don't!

Any and all pointers / help greatly appreciated.

Regards,

Noel.

Naty1

I watched a TV program last night that mentioned galaxy formation is not entirely understood nor is the relationship between supermassive black holes and galaxy formation. It appears the while the outer planets and stars of galaxies are not in our era coupled to supermassive black holes at galactic centers, they were coupled in the past. There is a mathematical relationship of that coupling that remains today.

Also, dark matter filaments are, I believe, still thought to figure in galaxy formation but that process is apparently not entirely understodd yet either. So as DH noted, lots more to learn.

D H

Hmm. You're right. Web pages are very spare, and journal articles assume the reader understands the basics. You need a book. Here's one, http://books.google.com/books?id=uTw...torque&f=false. It's typical in saying

After much mathematical manipulation, one arrives at
[tex]\vec N = \frac{3 \mu}{r^3} \hat r \times (\mathbf I \,\hat r)[/tex]

And that's for the torque exerted by a point mass on some other object. And yes, it takes a lot of mathematical manipulation just to get that simple result. It's a real mess if the attractor is also lumpy.

Here, [itex]\vec N[/itex] is the torque on the object, [itex]\mu[/itex] is the product G*M, where M is the mass of the central (point) mass, [itex]r[/itex] is the distance between the point mass and the center of mass of the object, [itex]\hat r[/itex] is the unit vector from the point mass to the object's CoM (or reverse; it doesn't matter), and I is the object's moment of inertia tensor.

Note that the torque is zero if the object has a spherical mass distribution because [itex]\mathbf I \,\hat r[/itex] is parallel to [itex]\hat r[/itex]. But that's only valid if the central mass is a point mass (or equivalently, it has a spherical mass distribution). If an object with a spherical mass distribution exerts a torque on some other object with non-spherical mass distribution, that other object must exert a torque back on the first object spherical mass distribution to conserve angular momentum.

Lino

Thanks D H. Very much appreciated.

Regards,

Noel.

John15

DH thanks for the honest answers, its nice to find someone willing to admit there are holes in our knowledge even with something as close to home as the solar system.
Orbits are obviously caused by gravitation but I still fail to see how planetary spin can be caused by gravity, at least spin much greater than 1 per orbit, say similar to the moon.
Is it known whether any of the plantets are losing/gaining spin.