AZING SPACE: Understanding Orbital Motion

[nitinshetty]

Why does the Earth rotate?

 

[Astronuc]

The rotation is a consequence of the rotational momentum/kinetic energy that existed at the time the formation of the Earth and Solar System.

We live in a dynamic universe.

 

[russ_watters]

Since our solar system came from a collapsed cloud of gas and dust, the tiniest asymetry in the structure of the cloud would cause the entire system to rotate about its center. The rotation caused some of the matter to end up in orbit around the sun - no rotation and all of that matter would have fallen into the sun. Similarly, the condensing of the Earth in an asymetric way caused the Earth to rotate.

 

[Gokul43201]

The short answer is : to conserve angular momentum (as astronuc has stated).

The long answer is to go through the various stages of the formation of the solar system (which russ has summarized above) and see what the dynamic evolution would have to be like if it satisfied all the conservation laws.

 

[Andre]

Then why does Venus not (barely) rotate?

 

[dextercioby]

Then why does Venus not (barely) rotate?

But it does,the 'other way around' as the other planets,yet it does.The magnitude of the angular velocity is however impossible to predict from theory,because the equations that would govern,let's say,the dynamics of the particle cloud that eventually became "Earth" are nonlinear,which means non integrable.
It's just like the equations which describe the dynamics of the atmosphere.Assuming thy were linear and integrable,we could predict weather without having those satellites into orbit.

Daniel.

 

[Andrew Mason]

Since our solar system came from a collapsed cloud of gas and dust, the tiniest asymetry in the structure of the cloud would cause the entire system to rotate about its center. The rotation caused some of the matter to end up in orbit around the sun - no rotation and all of that matter would have fallen into the sun. Similarly, the condensing of the Earth in an asymetric way caused the Earth to rotate.

Here's a good question:, since angular momentum is conserved, how do you 'create' angular momentum from an original system containing zero angular momentum? (ie: you can't). So where does angular momentum come from?

AM

 

[dextercioby]

What do you mean "original system containing zero angular momentum??
Which system??The initial cloud of particles from which our Solar system evolved??

Daniel.

 

[Andrew Mason]

What do you mean "original system containing zero angular momentum??
Which system??The initial cloud of particles from which our Solar system evolved??

Any isolated system containing 0 angular momentum.

Is it possible that the cloud of gas from which the solar system was formed started out with 0 angular momentum?

AM

 

[Astronuc]

Is it possible that the cloud of gas from which the solar system was formed started out with 0 angular momentum?
It would be unlikely.

There was probably some initial angular momentum. How much depends on the particular theory of the formation of the solar system.

Furthermore, with assymmetry in mass distribution and under the influence of gravity (not everything converging at an equal rate to the same center of mass), the consequence is non-zero angular momentum.

 

[dextercioby]

There was probably some initial angular momentum. How much depends on the particular theory of the formation of the solar system.

Furthermore, with assymmetry in mass distribution and under the influence of gravity (not everything converging at an equal rate to the same center of mass), the consequence is non-zero angular momentum.

The simplest analysis which i can imagine would start from the Boltzmann equation and would yield only in the simplest possible case (frition proportional to gradients of velocity field) the Navier-Stokes equations in which the gravity term would appear given by Newton's law.Essential would be turbulence (with vortices) and how would initial nonhomogeneities in density would evolve under the influence of gravity and strog rotational velocity fields.

Daniel.

 

[Andre]

The mere fact that the mass of the solar system is not completely at it's centre but instead is orbiting it, signifies that the system as a whole had an significant angular momentum as of it's birth.

Assuming no external torque forces the total angular momentum of the solar system is still the same. As the norm is positive orbit and positive spin for the majority of the bodies planets, asteroids, moons, the retrograde spin is an exception true only for Uranus Pluto and Venus and an odd small moon perhaps.

The axial tilt of Uranus of almost 90 degrees suggests that a obliquity swing though the 90 degrees may have been possible in the chaotic motions of certain resonances. That would indicate that the planet may have been born with a normal prograde spin.

Pluto is in tidal lock with it's moon Charon, indicating that much transfer of momentum had taken place, enough to change prograde spin into retrograde.

So, again, remains Venus, what about it's enimatic retrograde spin of 247 days versus an orbit of 225 days?

Oh and

There was probably some initial angular momentum. How much depends on the particular theory of the formation of the solar system.

Odd that the physical truth adapts to a particular theory

 

[marlon]

The simplest analysis which i can imagine would start from the Boltzmann equation and would yield only in the simplest possible case (frition proportional to gradients of velocity field) the Navier-Stokes equations in which the gravity term would appear given by Newton's law.Essential would be turbulence (with vortices) and how would initial nonhomogeneities in density would evolve under the influence of gravity and strog rotational velocity fields.

Daniel.

I think this is a bit of an overstatement. If you were to examine everything i am sure you will get it right but this is waist of time...pardon the french here but really

The best explanation has been given quite some times. It is possible for a system to have net zero momentum but due to internal inhomogeneous distributions of (for example) matter forces will start to act on these distributions because they are a deviation of the lowest and most stable energystate. This is what will lead to a generated local angular momentum that is nonzero. Due to the conservation of momentum the opposite value of this generated momentum needs to be present in the system and therefore something else will happen besides these disturbances in distribution of matter. Hence the rotation of the earth...

regards
marlon

ps : this is just one way to look at it but the essence is there : conservation of momentum
:tongue:

 

[Andrew Mason]

The best explanation has been given quite some times. It is possible for a system to have net zero momentum but due to internal inhomogeneous distributions of (for example) matter forces will start to act on these distributions because they are a deviation of the lowest and most stable energystate. This is what will lead to a generated local angular momentum that is nonzero. Due to the conservation of momentum the opposite value of this generated momentum needs to be present in the system and therefore something else will happen besides these disturbances in distribution of matter. Hence the rotation of the earth...

Exactly. Since angular momentum cannot be created or destroyed the solar system still has the original angular momentum of the gas cloud from which the solar system formed (assuming no outside forces have acted on it in the last 4 billion or so years).

Has anyone determined what the total angular momentum of the known part of the solar system is? It would be interesting to see what the amount of mass that exists beyond Pluto would be if one assumed that the total angular momentum is 0.

AM

 

[nitinshetty]

What would the Earth be like if it did not rotate?

 

[Andrew Mason]

What would the Earth be like if it did not rotate?

If the Earth did not spin at all there would be more mountains because the Earth surface would contract. The moon would be closer. We would weigh more (except at the poles). We would have semi annual rather than semidiurnal tides. And we would all have to live as nomads because if we stayed in the same place, we would have days and nights that last for 6 months at a time where the days would be very hot and the nights unbearably cold. Nights would be very dry and calm and days would be very cloudy and turbulent.

If the Earth did not spin we would probably not be asking that question, because we would probably not be here.

AM

 

[FZ+]

If the Earth did not spin at all there would be more mountains because the Earth surface would contract.

Huh?

If the Earth did not spin, then it would have been shaped differently throughout its formation - in short it would be rounder. I don't see why there would be more mountains, though.

 

[Astronuc]

Mountains are formed when the Earth's crust is force upward (up-thrust) as two tectonic plates collide (put fingers tip-to-tip, and push inward) and the intersection pushes up. Also, one plate may overide the other - e.g. subduction zone.

Mountains may also form as a result of volcanic action - e.g. Cascade mountain range in US.

Elsewhere, the tectonic plates are pushing apart - e.g. mid-Atlantic ridge.

The Earth is a very dynamic body - the ground is not as solid as some might think, but like glass - the ground can flow, be it slowly. Even concrete creeps! The Earth's rotation and gravitational interaction (e.g. tides) are also factors.

 

[Andrew Mason]

If the Earth did not spin, then it would have been shaped differently throughout its formation - in short it would be rounder. I don't see why there would be more mountains, though.

The Earth radius is 6377 km at the equator which is about 22 km greater than at the poles. Work out the area of a sphere 6355 km in radius and then subtract that from the known area of the Earth surface. That is how much real estate you would lose if the Earth stopped rotating. Where would it go? The only place is up.

Which raises an interesting point. The Earth used to have an 18 hour day about 2 billion years ago. So it must have had a greater equatorial bulge and, therefore, a greater surface area. The loss of that area by the reduction in Earth rotation seems to be to be a better explanation for the mountains than continental drift.

AM

 

[russ_watters]

The Earth radius is 6377 at the equator which is about 22 km greater than at the poles. Work out the area of a sphere 2355 km in radius and then subtract that from the known area of the Earth surface. That is how much real estate you would lose if the Earth stopped rotating. Where would it go? The only place is up.

That mass would go to the poles, and the Earth would turn into a more perfect sphere. That's it.

 

[Andrew Mason]

That mass would go to the poles, and the Earth would turn into a more perfect sphere. That's it.

Are you saying that the surface area would not be less?

AM

 

[Andre]

Most excellent hypothesis! Andrew.

On second thought though, the mechanism of plate tectonics should be well capable of compensating for surface area change due to the shape change.

 

[russ_watters]

Are you saying that the surface area would not be less?

AM

No, but I am saying the difference would be utterly insignificant. And besides which:

On second thought though, the mechanism of plate tectonics should be well capable of compensating for surface area change due to the shape change.

We're not talking about a change, we're talking about what the Earth would be like if it hadn't been rotating to start with. Ie, before plate tectonics. (as FZ+ said)

In fact, with less dynamic forces on the earth, there would likely be less plate tectonics and smaller mountains as a result.

 

[Andrew Mason]

Most excellent hypothesis! Andrew.

On second thought though, the mechanism of plate tectonics should be well capable of compensating for surface area change due to the shape change.

The plates would have to compensate. If the total surface are did not change and the plates could move quickly enough, then no problem, the plates just move around.

The interesting thing is that the surface area of a spheroid (earth) is smaller than a perfect sphere of the same volume (I just worked it out - the formula for area of a spheroid is complicated). BUT the circumference at the equator is greater. So in becoming more spherical, the Earth would experience contraction at the equator and expansion toward the poles. So it looks to me that mountains would tend to be created nearer the equator and rifts would tend to develop nearer the poles.

Now here is an interesting thing to think about: what if the Earth was hit by a large asteroid so that its spin slowed rapidly all of a sudden. The plates would not be able to move quickly enough and there would be a lot of crunching of surface area and mountain making nearer the equator and sudden rifts opening nearer the poles. The opposite would occur if the asteroid caused the Earth spin to increase.

AM

 

[Andrew Mason]

No, but I am saying the difference would be utterly insignificant.

I worked it out and the area of the equivalent sphere (equal volume) is actually greater than the area of the spheroid Earth by about 600,000 km^2.

And besides which: We're not talking about a change, we're talking about what the Earth would be like if it hadn't been rotating to start with.

The question was "What would the Earth be like if it did not rotate?". That could be if the Earth never rotated in the first place or if it suddenly stopped rotating.

In fact, with less dynamic forces on the earth, there would likely be less plate tectonics and smaller mountains as a result.

I agree, if the Earth did not rotate to begin with. But not if a rotating Earth stopped rotating.

AM

 

[Andre]

what if the Earth was hit by a large asteroid so that its spin slowed rapidly all of a sudden.

The big problem with that scenario is inertia and propagation speed of impulses. It would take 90 minutes for the other side of the Earth to react on any impulse and it would continue to spin with the original speed whereas the hit side would have slowed down

Conclusion: the Earth would break up.

Another interesting though about that is from Rich Muller: Core-mantle boundary avalanches

 

[Andrew Mason]

The big problem with that scenario is inertia and propagation speed of impulses. It would take 90 minutes for the other side of the Earth to react on any impulse and it would continue to spin with the original speed whereas the hit side would have slowed down

Conclusion: the Earth would break up.

If it hit vertically, the Earth would acquire all of the asteroid's momentum in the time it takes for the asteroid to stop. Why would it be any different for angular momentum? In other words, where does the momentum "go" in that 90 minutes?

AM

 

[Andre]

Okay the mssing step here is that the Astroid has to hit at a rather oblique angle to exert a momentary torque force to change the angular momentum of the Earth to change the spinning rate. Inertia would spoil that scenario. The vertical hitting asteroid would only change the lateral momentum but not the angular momentum. Consequently a spin change would only be minor if at all.

 

[Andrew Mason]

Okay the mssing step here is that the Astroid has to hit at a rather oblique angle to exert a momentary torque force to change the angular momentum of the Earth to change the spinning rate. Inertia would spoil that scenario. The vertical hitting asteroid would only change the lateral momentum but not the angular momentum. Consequently a spin change would only be minor if at all.

Of course. But my point was: why does the Earth angular momentum not change as soon as the asteroid begins impacting the earth? Why does one side wait 90 minutes to begin spinning faster?

AM

 

[Andre]

Well the fastest way a mechanical impuls travels is with the speed of the P-waves, about 5 km/sec in granite. The average for the Earth is about 3,5 km/sec (source not available at the moment).

If a impuls would tend to slow the spinning it would be no good if it went the shortest way, though the middle of the Earth because it would not have a effective component that would change the spinning. So our impuls has to follow the surface of the Earth to change the speed over there. To the other side of the Earth, that's 20,000 km or 4000 seconds (5 km/sec) or 5714 seconds (3,5 km/sec), or 67 mins resp 95 minutes, okay?

 

[Andrew Mason]

Well the fastest way a mechanical impuls travels is with the speed of the P-waves, about 5 km/sec in granite. The average for the Earth is about 3,5 km/sec (source not available at the moment).

If a impuls would tend to slow the spinning it would be no good if it went the shortest way, though the middle of the Earth because it would not have a effective component that would change the spinning. So our impuls has to follow the surface of the Earth to change the speed over there. To the other side of the Earth, that's 20,000 km or 4000 seconds (5 km/sec) or 5714 seconds (3,5 km/sec), or 67 mins resp 95 minutes, okay?

Okay. I see what you are saying. But I think what would happen is that there would be an enormous matter wave that would keep going around the Earth until it died out eventually.

The Earth would still receive the angular momentum impulse from the asteroid. It is just that the angular momentum would be in the matter wave (ie. in the momentum x radius of all the matter in the wave). The increase in rotational speed of the Earth would occur gradually as that matter wave was absorbed.

I still don't see why the Earth would break apart. The moon is thought to have come from a large asteroid impact on the Earth about 4 billion years ago, sending up a chunk of the Earth into space. That is one theory, at least. Obviously, the Earth did not disintegrate then.

Am

 

[Andre]

Would be interesting to model that hypothetical event. Perhaps the Earth may have been shattered initially by that event due to the mentioned inertia but gravity may have rebuild the heap of big chunks into the present Earth - Moon system.

Only a thought

 

[Andrew Mason]

Would be interesting to model that hypothetical event. Perhaps the Earth may have been shattered initially by that event due to the mentioned inertia but gravity may have rebuild the heap of big chunks into the present Earth - Moon system.

If the moon is the result of the Earth being struck by a giant asteroid, where do you think it hit? ie. where is the largest expanse of low lying ground on earth? What shape (generally) is it? Just a thought.

AM

 

[Andre]

Well if you suggest the pacific, there is a small problem. Plate tectonic has send the continents drifting over the globe the last couple of billion years, forming super continents and breaking them up again roughly with 500 Ma intervals.

 

[russ_watters]

The question was "What would the Earth be like if it did not rotate?". That could be if the Earth never rotated in the first place or if it suddenly stopped rotating.

I agree, if the Earth did not rotate to begin with. But not if a rotating Earth stopped rotating.

Ok, fair enough: I was trying to conform this question to physical reality. Ie, it doesn't break any laws of the universe to speculate on if the Earth hadn't been rotating when it formed, but to speculate on it spontaneously stopping does break the laws of the universe. I don't consider such speculation useful, since (for example), if the Earth suddenly stopped rotating, earthquakes wouldn't be your first worry: stopping yourself before hitting your wall at 1,000 mph would be...

If it hit vertically, the Earth would acquire all of the asteroid's momentum in the time it takes for the asteroid to stop. Why would it be any different for angular momentum? In other words, where does the momentum "go" in that 90 minutes?

That momentum distributes itself through the Earth for 90 minutes. Consider a tennis ball hitting a wall - the point where the ball hits the wall stops immediately on hitting the wall, but the other side of the ball is still moving toward the wall and the ball compresses. Consider a nail: when you hit it with a hammer, the far end of the nail does not start moving instanly: the nail compresses and the far end starts moving when the pressure wave reaches it at the speed of sound.

So too for the earth.

I still don't see why the Earth would break apart. The moon is thought to have come from a large asteroid impact on the Earth about 4 billion years ago, sending up a chunk of the Earth into space. That is one theory, at least. Obviously, the Earth did not disintegrate then.

The fact that such a large chunk of the Earth out in space implies that it did disintegrate. Because of gravity, this disintegration was not necessarily permanent (as Andre said).

If the moon is the result of the Earth being struck by a giant asteroid, where do you think it hit? ie. where is the largest expanse of low lying ground on earth? What shape (generally) is it? Just a thought.

Any such impact would be far too big to leave a crater. The Earth would have essentially been pulverized and reformed spherically.