How did gravity build astronomical objects that rotate?

[Paulibus]

How did gravity build astronomical objects that rotate?

It seems to me a safe bet, supported in part by observation, that the heterogeneous assembly of known astronomical objects comprising the observed universe, whose contents range from minor planets (one named for my mother) to the recently imaged remote galaxies observed by the Hubble telescope, and are all busily revolving or rotating. I’d like to understand, in broad terms, how this conglomerate, believed to have started out as a hot, dense, nearly homogeneous fluid some 13.7 billion years ago, became so heterogeneous and accumulated so much locally stored angular momentum.

The short answer that “Gravitational condensation did it” doesn’t quite satisfy me, although it is of course correct.

In struggling to gain a better understanding for myself of the fundamentals of structure formation, without relying on computer modelling done by others, I’ve had the thought
that fluid shear must have been an important aspect of the process. The elastic or plastic shear of solids is reasonably well understood, but involves descriptions of shear appropriate only for uniform deformation, like pure shear (described by a symmetric second-rank tensor) and engineering or simple shear (described as the sum of a pure shear and a rotation). In an astronomical context the dynamic behaviour of fluids within larger host structures involves more complicated shearing deformations and motions, as in gravitating gases and gravitating particulate fluids; like the rings of Saturn, interstellar dust clouds (Orion Nebula) or, on a larger scale, the star clouds in the central Milky Way. I suppose that even galaxies in
clusters (e.g. Fornax) are likely to be collectively sheared by gravity.

The conclusion I’ve come to is that: “Gravitational condensation was aided in creating a heterogeneous universe of rotating and revolving structures, which on different scales store angular momentum, by its central-force character that generates Keplerian shear, which can causes matter to rotate and revolve.” Is this oversimplified guess anywhere near correct?

And, finally, since tonight (30 September) is Full Moon, let me ask: does the Moon always
present the same appearance to us because Keplerian shear stresses the Earth produces, acting on the Moon, partly compensate for the centripetal stresses generated by the Moon’s 28-day periods of axial rotation and Earth-orbit revolving?

 

[rbj]

I’d like to understand, in broad terms, how this conglomerate, believed to have started out as a hot, dense, nearly homogeneous fluid some 13.7 billion years ago, became so heterogeneous and accumulated so much locally stored angular momentum.

i think the key word is nearly homogeneous. because gravity attracts matter and more mass means more gravity, then gravity has a tendency to amplify any non-homogeneties. dense areas become denser. that's what gravity does. it's why we have planets and comets and asteroids in the solar system instead of a big cloud of material.

also i believe the current thinking is that there were pockets of turbulence in the primordial universe. big swirls of turbulence eventually became galaxies, smaller swirls of turbulence became solar systems, and even smaller swirls became planets. all with a little spin.

 

[SHISHKABOB]

I think part of the reason is because when the "stuff" back then was falling together, it probably always hit at an angle. So that it would bounce off. If it's all random, it probably wouldn't be always hitting each other head-on.

So then also if the stuff is attracted to each other, then it would hit at an angle, and then come back after a while in a big sort of figure eight, I guess?

It's like... if you have two pieces of sticky stuff, and they hit each other off-center, they're going to stick together, but the whole glob at the end is going to be rotating.

So then imagine A LOT of sticky stuff falling into one spot. Eventually, the different rotations sort of average out into one rotation.

 

[Chronos]

Collisions are an important part of structure formation. During gravitational collapse, molecules shed kinetic energy via collisions with one another, creating turbulence in the cloud. A preferential direction of spin eventually emerges through this process which is further amplified by the increasing strength of the gravity well as particles spiral into the center of gravity. As more particles are drawn in, they basically go with the flow. Here is a computer simulation of this phenomenon - http://blogs.discovermagazine.com/8...imulation-of-spiral-galaxy-formation-to-date/.

 

[SHISHKABOB]

okay, so the preferential direction of spin arises from the fact that the distribution of both the actual particles *and* their initial velocities are not isotropic, right?

 

[Chronos]

It really does not matter. A preferred direction of rotation will emerge randomly from the chaos of all the collisions - even if the initial distribution and velocities are totally random. Of course, that kind of natural randomness is not all that natural. In most cases the initial distributions are not isotropic and that, of course, favors a particular outcome for the final direction of rotation, but, not the probability of rotation itself. The odds of no rotation emerging are worse than those of a coin flip coming up 'edges'.

 

[Vorde]

The rotation comes from the fact that there is only one angle you can hit an object and not make it rotate: straight in the direction of the center of mass. But an infinite amount of angles that will make it rotate: anywhere else.

Rotation results.

 

[Paulibus]

Thanks for these replies, all. I was a bit surprised at the near-unanimity and simplicity of your views along the lines of "Collisions between infalling lumps did it".

Perhaps I confused the issue by mentioning Saturn's rings as exemplifying Keplerian shear. They do so because the rings are particulate rather than solid, not because lumps rotate due to collisions, as discussed in your replies. (Only rbj differed, suggesting "pockets of turbulence" in the early universe as the origin of circular motions.)

An explanatory aside, about inhomogeneous Keplerian shear, which is a consequence of Newtons law of gravity:

Circular orbital speeds about the sun, for example, are inversely proportional to the square root of the orbit radius. Wheras in a rotating rigid body the tangential speed at any point is proportional to the point's distance from the rotation centre. Hence shear, probably labelled Keplerian more than a hundred years ago by Maxwell, who first analysed the nature of Saturn's rings, or Keeler who spectroscopically verified his analysis. Another aside: the Roche limit is also a consequence of Keplarian shear. Or tidal stresses, if one wants to put it more generally.

If "Collisions between infalling lumps did it" , why then does the sun rotate? Or spiral galaxies, for that matter? Not much of the universe is solid and fluid dynamics is a more appropriate tool in this context.

 

[Chronos]

The primordial cloud that gravitationally condensed to ultimately form the sun and planets acquired spin via molecular collisions. See the video I referenced on computer simulation of galaxy formation. It is the cliff notes version of a lengthy supercomputer numerical analysis. Rest assured the laws of fluid dynamics are strongly considered. Gas/dust clouds in interstellar/intergalactic space are diffuse and, for all practical purposes, behave like a perfect fluid during gravitational collapse.

 

[Paulibus]

Thanks for the reply, Chronos. Sadly, I'm unable to view the video you recommended. Bandwidth! Thanks also for reassuring me about a supercomputer analysis. But I would still like to know specifically if Keplerian shear is among the factors that promote the storing of angular momentum and if not, why not.

The colliding of molecules and bigger lumps must also be important, as other replies make clear. I don't disagree. But: does that program reveal the relative importance of such easily understood factors? Or does it churn away at, say, the Navier-Stokes equations seasoned with a pinch of Newtonian gravity , so that in the end one just concludes: "The formation of observed structures can be successfully modeled with classical physics?" Period? Or does one just have to watch and believe a movie of it happening? Perhaps there's a voice-over that highlights such simplicities as shear and collisions. Is there, and what does it say?

 

[ImaLooser]

My view is that if an energetic system can move in a certain way then it will. This is sometimes summed up as "everything that is not forbidden is required."

 

[rbj]

Thanks for these replies, all. I was a bit surprised at the near-unanimity and simplicity of your views along the lines of "Collisions between infalling lumps did it".

Perhaps I confused the issue by mentioning Saturn's rings as exemplifying Keplerian shear. They do so because the rings are particulate rather than solid, not because lumps rotate due to collisions, as discussed in your replies. (Only rbj differed, suggesting "pockets of turbulence" in the early universe as the origin of circular motions.)

...

If "Collisions between infalling lumps did it" , why then does the sun rotate? Or spiral galaxies, for that matter? Not much of the universe is solid and fluid dynamics is a more appropriate tool in this context.

well, as best as i can understand this is that if there were no swirls of turbulence in the primordial universe, i can see how spin can happen if two bodies fall toward each other, but because of the gravitational influence of other bodies, these two bodies do not fall directly toward their common center of mass. and if they hit each other slightly off center, then spin will result from that collision. but if angular momentum is conserved, there has to be some other bodies or groups of bodies that spin the other way in order for the spin-less initial conditions to be preserved in the overall universe. i don't know if that is the case or not. are there any studies that indicate if the universe as a whole has spin or not?

how soon in the early universe that swirls of ostensible turbulence appear, i also do not know, but it seems to me that it would be very early. but WMAP tells us it wasn't isotropic, and it's not hard for me to believe that the curl of velocity vectors of "stuff" was also not isotropic. and if so, i would call these "swirls of turbulence".

 

[ImaLooser]

well, as best as i can understand this is that if there were no swirls of turbulence in the primordial universe, i can see how spin can happen if two bodies fall toward each other, but because of the gravitational influence of other bodies, these two bodies do not fall directly toward their common center of mass. and if they hit each other slightly off center, then spin will result from that collision. but if angular momentum is conserved, there has to be some other bodies or groups of bodies that spin the other way in order for the spin-less initial conditions to be preserved in the overall universe. i don't know if that is the case or not. are there any studies that indicate if the universe as a whole has spin or not?

how soon in the early universe that swirls of ostensible turbulence appear, i also do not know, but it seems to me that it would be very early. but WMAP tells us it wasn't isotropic, and it's not hard for me to believe that the curl of velocity vectors of "stuff" was also not isotropic. and if so, i would call these "swirls of turbulence".

Maybe the universe had spin, maybe it didn't, but local effects dominate so it doesn't really matter. Let's say that you have a collapsing ball of gas. That ball is never going to be perfectly symmetrical and the center of mass is never going to be in the center. There is always going to be some asymmetry, and that's where the spin comes from.

The vortices come from Rossby waves and the Rossby instability. It is a very general property of rotating liquids and gasses. That's just what they do, form vortices.

 

[Paulibus]

Let's say that you have a collapsing ball of gas. That ball is never going to be perfectly symmetrical and the center of mass is never going to be in the center. There is always going to be some asymmetry, and that's where the spin comes from.

You sound very sure, Imalooser, about the origin of spin. Do you then include with spin all other circular motions --- of galaxies, stars, planets etc?

About Rossby waves; they are fascinating example of fluid motion in the atmospheres of rotating planets; waves driven by Coriolis forces, which are in turn are caused by thermally-driven motions of fluids away from or towards the poles, in rotating planets that are heated by stars. Do they occur in other places?

Interesting but not fundamental in the context of this thread; Rossby waves may well be a specific consequence of shear in a fluid, under special circumstances, but I don’t see how they can be the fundamental reason for the storage of angular momentum in the universe, which is what I’m trying to understand.

In fact it seems to me that none of the kindly folk who have so far contributed to this thread fundamentally understand shear, particularly Keplerian shear; let alone its general consequences in gravitating fluids. Come on, folk, this is not even real gravity stuff like General Relativity!
It’s simply gravitating matter ruled by Newton’s old law of gravity, and shear as in a greasy old pack of cards.

 

[Paulibus]

how soon in the early universe that swirls of ostensible turbulence appear, i also do not know, but it seems to me that it would be very early. but WMAP tells us it wasn't isotropic, and it's not hard for me to believe that the curl of velocity vectors of "stuff" was also not isotropic. and if so, i would call these "swirls of turbulence".

Yes, as you say, the early universe was not quite homogeneous, and the observed Cosmic Microwave Background reveals it. At the 1 part in 10,000 level it's patchy hot and cold compared to its mean,very low Black Body spectrum temperature of a few degrees Kelvin. The angular spectrum of patches matches very well what is expected from primordial quantum fluctuations manifesting themselves as "sound" waves in the then-plasma universe. I don't think there is any evidence one way or the other that would justify describing this as turbulence with vortices, although common sense suggests that fluid flow in the early universe can't have been laminar at the ruling extreme temperatures. Computer models of structure formation use the observed inhomogeneities to account pretty satisfactorily for the present day structures we observe with telescopes. But these models don't illuminate for me the fundamental physics -- they just tell us that "Gravity did it" which for a lot of physicists may be satisfactory, but it's not so far from the possibly equally unhelpful "God did it" approach. That's why I started this thread. I'm curious.

 

[ImaLooser]

You sound very sure, Imalooser, about the origin of spin. Do you then include with spin all other circular motions --- of galaxies, stars, planets etc?

About Rossby waves; they are fascinating example of fluid motion in the atmospheres of rotating planets; waves driven by Coriolis forces, which are in turn are caused by thermally-driven motions of fluids away from or towards the poles, in rotating planets that are heated by stars. Do they occur in other places?

Interesting but not fundamental in the context of this thread; Rossby waves may well be a specific consequence of shear in a fluid, under special circumstances, but I don’t see how they can be the fundamental reason for the storage of angular momentum in the universe, which is what I’m trying to understand.

In fact it seems to me that none of the kindly folk who have so far contributed to this thread fundamentally understand shear, particularly Keplerian shear; let alone its general consequences in gravitating fluids. Come on, folk, this is not even real gravity stuff like General Relativity!
It’s simply gravitating matter ruled by Newton’s old law of gravity, and shear as in a greasy old pack of cards.

Yes, spiinning planets, suns, galaxies, black holes. I'm not at all an expert on this stuff though. It is a simple fact that just about everything in space rotates, and I think the basic reason is "because it can."

Rossby waves occur in the oceans of Earth. They are believed to be crucial in stellar magnetospheres during the formation of planets. They are easy to create in experimental setups. I've read about them in superfluid helium. I'd like to know what the requirements are. I think all you need is a rotating gas or liquid and some sort of change in density.
As far as I know they don't have anything to do with "storage of angular momentum" other than that conservation of angular momentum is fundamental. Rossby waves are unstable and spawn vortices that usually dissipate angular momentum.

I know zero about Keplerian shear and a cursory search didn't help much. Have any references?

 

[Paulibus]

Try Wikipedia and Google. Or search for info about Saturn's rings. and why they are particulate and not solid If you can access it, Van Nostrand's Scientific Encyclopedia will explain it. Or, if all else fails, try reading post #8 in this thread.

I still don't think your Rossby waves are appropriate.

 

[rbj]

I don't think there is any evidence one way or the other that would justify describing this as turbulence with vortices, although common sense suggests that fluid flow in the early universe can't have been laminar at the ruling extreme temperatures. Computer models of structure formation use the observed inhomogeneities to account pretty satisfactorily for the present day structures we observe with telescopes. But these models don't illuminate for me the fundamental physics -- they just tell us that "Gravity did it" which for a lot of physicists may be satisfactory, but it's not so far from the possibly equally unhelpful "God did it" approach. That's why I started this thread. I'm curious.

well, if there is turbulence in some fluid, there is some scale, where you can zoom to, in which some region of turbulence is spinning, like eddy currents. if there is spin, there is an axis of rotation. along that axis, gravity will just pull the pancake flat. but in the two dimensions that are perpendicular to that axis of spin, collapse from gravity has opposition so it does not flatten in those two dimensions. this is why these spiral galaxies are sort of flat. same for solar systems.

as far as comparing Gravity to God, even if the fundamental interaction has no currently known source (why does matter curve spacetime?), there is at least a mathematically described interaction that can be used to predict physical outcomes. that is different from saying "God did it". it is not equally unhelpful.

 

[Paulibus]

... even if the fundamental interaction has no currently known source (why does matter curve spacetime?), there is at least a that can be used to predict physical outcomes. that is different from saying "God did it". it is not equally unhelpful.

Not equally, perhaps. You're right, rbj, I was overstating the case. But still unhelpful; the "mathematically described interaction" so far seems to have been unhelpful for explaining the "physical outcome" of ubiquitous astronomical circular motions. I'm trying to provide an explanation, rather than attributing it all to primeval turbulence. Old Henry Ford said "History is bunk" and maybe he had a point!

In a gravitational context a simple mathematical treatment of turbulence is doubly impossible because of the non-linearity of both the Navier Stokes equations and Einstein's field equations, but the effect of the shearing character of Newton's law on gravitational collapse doesn't seem to have been noticed.

Is it too simple? But then it probably has (there's nothing new under the sun). If so, does anyone know where and by whom?

 

[codex34]

Rotate in what way?
If it's only down to collision interactions wouldn't you get a rotation in more than one axis?
By applying a gravity well to an interacting cloud of molecules, surely your predetermining the results, since the gravity well is essentially planar, axis driven.
Applying a gravity well seems like circular logic unless you use a spherically symmetric gravity well, but then you don't get the shear forces.
The observations show that most, if not all, rotations are planar, the moons, planets, galaxies, nebulae.
So I'm going to assume you mean 'highly planar' rotations?
If you want to use Newtonian mechanics then I think Newton answered this already, in a round about way, but ask this question, what caused the gravitational collapse in the first place?
If you take the three descriptions of rotations described by Newton and apply each of them to a gas/dust cloud (using the Bernoulli principle), the only real conclusion you can make is that the shear forces have to be there in the first place to cause the gravitational collapse.
So where do shear forces come from? At the point other rotations intersect? Where did the other rotations come from?

 

[Paulibus]

Hi, Codex ... thanks for your reply. Hope this answer helps.

...Applying a gravity well seems like circular logic unless you use a spherically symmetric gravity well, but then you don't get the shear forces

There is a misunderstanding here. To see where you went wrong think of Saturn's gravity well. Close to the planet, where its moons and rings revolve around the planet, all in coplanar orbits, Saturn's gravity makes a well that is spherically symmetric about the planet's centre. And the planar rings provide the classic example of Keplerian shear. This was verified very long ago by the observation that the rings are made of particles rather than being solid. Keplerian shear is the reason for this: it breaks solid orbiting bodies up into particles via tidal forces. Keplerian shear is just a particular kind of tidal distortion.

Conclusion: you do indeed get shear with a spherically symmetric gravitational well! If you consider a small enough piece of a ring, the Keplerian shear in it approximates to what is called simple or engineering shear, as in a pack of cards made to slide over each other. Simple shear can be described mathematically (with a tensor) as the sum of what is called pure shear , plus a rotation. The rotation of a piece of Saturn's rings has an axis that lies normal to a radius from Saturn's centre.

So it's all old classic stuff. I still don't know why this hasn't been noticed in connection with the gravitational condensation of just about all astronomical objects.

 

[Chronos]

Conclusion: you do indeed get shear with a spherically symmetric gravitational well! If you consider a small enough piece of a ring, the Keplerian shear in it approximates to what is called simple or engineering shear, as in a pack of cards made to slide over each other. Simple shear can be described mathematically (with a tensor) as the sum of what is called pure shear , plus a rotation. The rotation of a piece of Saturn's rings has an axis that lies normal to a radius from Saturn's centre.

So it's all old classic stuff. I still don't know why this hasn't been noticed in connection with the gravitational condensation of just about all astronomical objects.

It was noticed centuries ago. It's called the ecliptic.

 

[Paulibus]

Chronos, please spell this out for stupid old me, for whom your reply now seems a Cryptic Ecliptic! I can only guess that accretion discs form with this geometry to minimise disruptive inter-element collisions by confining Keplerian shear to a plane? If so, who first realized this, centuries ago?

 

[codex34]

Hi, Codex ... thanks for your reply. Hope this answer helps.

There is a misunderstanding here. To see where you went wrong think of Saturn's gravity well. Close to the planet, where its moons and rings revolve around the planet, all in coplanar orbits, Saturn's gravity makes a well that is spherically symmetric about the planet's centre. And the planar rings provide the classic example of Keplerian shear. This was verified very long ago by the observation that the rings are made of particles rather than being solid. Keplerian shear is the reason for this: it breaks solid orbiting bodies up into particles via tidal forces. Keplerian shear is just a particular kind of tidal distortion.

Conclusion: you do indeed get shear with a spherically symmetric gravitational well!
SNIP
The rotation of a piece of Saturn's rings has an axis that lies normal to a radius from Saturn's centre.

Yeah, I don't understand that at all, one the one hand you have a spherically symmetric gravity well, and on the other hand you have differential rotation caused by (or causing) the rotation of the planet on it's axis, so what causes the planet to rotate on it's axis in the first place?
A spherically symmetric gravity well wouldn't produce a galaxy/star/planet that rotates on a single axis surely? Even the slightest addition to the collapsing mass above or below the normal to the center of the axis of rotation would produce a secondary rotation, it would tumble, as you have more than one axis of rotation. That might be ok for globular clusters but what about disc galaxies. Statistically you would have less disc galaxies than clusters.
It's as if the internal mechanism of fluid bodies have a single axis rotation but produce an external spherical gravity well.
If the cosmic web model is correct however I might see where you get the shear from to produce rotating bodies with single axis of rotation, but space would have to have a minimum density/maximum tension which cannot be exceeded (solid space).

 

[Chronos]

Kepler is the short answer.

 

[Paulibus]

...what causes the planet to rotate on it's axis in the first place?

Remember this?

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on."

I'm reminded of this rhyme because the universe matured as a hierarchy of structures. The fact is that the centralisation of mass by gravitational collapse proceeds, on all scales that have time to collapse in the universe's age, according to Newton's inverse square law. This law comes with baggage, as it were, in the form of a shear-inducing character.

What causes galaxies to rotate is that they're condensations ruled by Newton's law, which, (I think) is also why stars, planets etc. rotate while spawning lots of smaller rotating stuff as they collapse. Condensations shear surrounding, collapsing, orbiting matter.

Perhaps Kepler didn't notice this, Chronos.

...If the cosmic web model is correct...

I don't know this model, sorry.

 

[Chronos]

Perhaps you you failed to notice the Navier-Stokes equations, Paulibus.

 

[Paulibus]

Chronos, these equations are non-linear and you may be aware that they can't be easily solved by analytic methods. Notice; yes. Draw simple conclusions from, about any problem involving turbulence or gravity: I don't know of any such .

 

[codex34]

Paulibus, yes my grandfathers favorite saying.
Condensation theory requires the shear to be there in the first place,

Some external influence, such as the passage of another interstellar cloud or perhaps the explosion of a nearby star, starts the fragment contracting, down to a size of about 100 A.U. As the cloud collapses, it rotates faster and begins to flatten (just as described in the old nebular theory).

Even if you just go by angular momentum, that has to come from somewhere, and you get right back to turbulence.

Can gravity form non-axial rotations such that any stars, planets and moons do not rotate in planar orbits but orbit in any orbital direction they wish?

 

[Chronos]

Random axial rotation would be a logical conclusion. Have you examples to the contrary? Shear only affects the process of collapse.

 

[Paulibus]

Can gravity form non-axial rotations such that any stars, planets and moons do not rotate in planar orbits but orbit in any orbital direction they wish?

. There's a bit of confusion here. In an empty model universe the orbits for two masses attracted to each other by gravity are always "planar" and "axial; relative motion then lies in a plane defined by two lines: one joining the two masses and the other along their relative velocity as seen by any observer (assuming the two lines to not be collinear). You might say that a lump traveling in any direction "it wishes" orbits a central attracting mass it encounters in a plane determined by what this "wish" was when they first met and began perceptibly to gravitate, but this is a bit wooly, don't you think?

Random axial rotation would be a logical conclusion. Have you examples to the contrary? Shear only affects the process of collapse.

Random axial rotation would be logical only if one took a large enough average over many independently-formed systems. Logical in the case of planetary systems formed by gravitational collapse in different parts of a galaxy, yes. But not in planet formation in say, our solar system. Henry Ford was wrong: history is not bunk, and planetary formation initiated by gravitational shear in a single rotating disc is a process with a shared history.

Don't most of our planets rotate (roughly -- ignore their seasons) in the same sense (clockwise or anticlockwise) if viewed from a distance, along the ecliptic axis? With their moons? I'll check. If so, that's your example. Just remember, shear and gravity go together, like a horse and carriage.

 

[Paulibus]

I came across http://www.sjsu.edu/faculty/watkins/solarspin.htm that could provide an example?

One of the most remarkable features of our solar system is that nearly all of the revolutions and rotations are in the same direction. From a point high above the north pole of the solar system the planets are revolving about the sun and rotating about their axes in a counterclockwise direction. This holds true also for the asteroids. If the planets and asteroids were formed from merely random accretions the would be an even mixture of the directions of revolution and rotation. The sun itself also rotates in a counterclockwise direction. The satellites of the planets also generally revolve and rotate in a counterclockwise direction. Of the thirty something satellites only six do not do so; they are said to have retrograde motion. Of the six exceptions five are outer satellites likely to be captured asteroids.

The Exceptions
Venus and possibly Uranus are the exceptions to the counterclockwise rotations of the planets. Venus travels around the sun once every 225 Earth days but it rotates clockwise once every 243 days. This pecular combination gives it a day with respect to the sun of 117 Earth days. Uranus is tilted on its side about 90° so its direction of rotation is ambiguous. Its angle of inclination is usually given as 98° which would mean that its direction of rotation is not retrograde. If its direction of rotation is presumed retrograde then its angle of inclination would be 82°.