# Wobble of Planetary Core

"Wobble" of Planetary Core

Friend of mine was asking about the Earth-Moon system, and he brought up an interesting question. As the Moon orbits the Earth, it imparts a slight wobble to the planet, much like the wobble used to infer the presence of planets aroubd distant stars. So he was wondering about the solid metal at the Earth's core, which is sarounded by the fluid mantle. Does the core wobble withtin the planet, going slightly off-center in a little circle once a month?

I told him I thought that the wobble of the core caused by the Moon would be exactly the same as the wobble of the rest of the planet, and so the core remains stationary relative to the outside of the globe. Is this correct?

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The Earth and the Moon move around a common centre, the centre of mass of the system. It happens to lie ... well, that's an interesting question. Can anyone give the calculation?

Liquid on the surface of the Earth has twice-daily tides. What about the liquid core of the Earth - does it have tides too (since there's a solid core beneath it)?

Mentat
Let's remember that there is only one gravitational pull coming from the Moon. Thus, it cannot accelerate things toward it at different rates. This would be necessary to cause the core to "wobble" within the center of the Earth (I think). So, LURCH, I think your original answer was probably right.

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Dearly Missed
The Earth is oblate, and some points are therefore closer to the moon than others. These closer points will receive a stronger force from the moon's gravity. But the location of the closest points varies as the Earth spins and the two bodies change relative positions during the moons orbit. Hence the wobble.

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LURCH:
As the Moon orbits the Earth, it imparts a slight wobble to the planet, much like the wobble used to infer the presence of planets aroubd distant stars. So he was wondering about the solid metal at the Earth's core, which is sarounded by the fluid mantle. Does the core wobble withtin the planet, going slightly off-center in a little circle once a month?
I told him I thought that the wobble of the core caused by the Moon would be exactly the same as the wobble of the rest of the planet, and so the core remains stationary relative to the outside of the globe.
Hence the wobble
Five wobbles, only three (?) are the same.

LURCH's first (two) wobbles ("used to infer the presence of planets aroubd distant stars"). This arises from the motion of the objects about their common centre of gravity/mass (take you pick; both are used). In the case of the Earth-Moon system, this centre is located ~ 4,700 km from the centre of the Earth (relative mass ratio ~81:1; centre to centre distance ~380,000 km).

LURCH's other wobbles: Start with SelfAdjoint's comment, add fluids (the liquid core, the oceans, the atmosphere; tides and more), add further bumps etc (small compared with the oblateness, but not zero), ... and you get a whole lot of wobbling, some only indirectly caused by the Moon. Add the Sun, and there's more.

LURCH again:
so the core remains stationary relative to the outside of the globe
No it doesn't, and it can't. The first order effect is the tides (unless you define 'the outside of the globe' to average out both water and land tides).

Mentat:
Let's remember that there is only one gravitational pull coming from the Moon. Thus, it cannot accelerate things toward it at different rates. This would be necessary to cause the core to "wobble" within the center of the Earth (I think).
The Earth is not a point, nor is it a perfectly rigid sphere. Where do you think the tides come from?

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Originally posted by Nereid
The Earth and the Moon move around a common centre, the centre of mass of the system. It happens to lie ... well, that's an interesting question. Can anyone give the calculation?

Basically, the Cog can be found by

Dm2-Cog = Dm1-m2 m1/(m1+m2)

if m1 is the moon and m2 the Earth, than the Cog is

4670 km from the center of the Earth or 1708 km below its surface, on average (it changes slighty do to the eccentricity of the moon's orbit. )

Tidal forces have been brought up by my friend, as well. My reaction is that tidal forces do not make the oceans "off-center" form the Earth's center of gravity. There is a high tide directly under the Moon, and another on the opposite side of the planet. If I understand tidal forces properly, it would seem that the high tide directly beneath the Moon should be (very slightly) higher than its opposite, but also last slightly less time, resulting in an egg-shaped ocean around the globe. But the center of this shape should be the Earth's center of gravity.

The crust also has tides but, being more rigid, it holds more cloesly to a circular shape around the equator. Shouldn't this also mean that the mantle will be slightly oblate, but the core will hold more to a cirular shape, both because of its greater rigidity and its smaller circumfrence? But this discrepency should not place the center of the core somewhere other than the center of the planet, by any means I have yet seen.

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LURCH, let's take them one by one ...
My reaction is that tidal forces do not make the oceans "off-center" form the Earth's center of gravity
The oceans are not completely free, there's the small matter of land. Some bays experience tides of over 10m, others ...
There is a high tide directly under the Moon, and another on the opposite side of the planet
close, but not exactly 'under' (there's a lag - look up the tide tables and lunar almanac for your nearest/favourite bit of seashore).
The crust also has tides but, being more rigid, it holds more cloesly to a circular shape around the equator. Shouldn't this also mean that the mantle will be slightly oblate, but the core will hold more to a cirular shape, both because of its greater rigidity and its smaller circumfrence?
.. but not perfectly circular, perfectly rigid, ...

One other thing: the Earth's equatorial radius is greater than its polar radius (a.k.a. oblate), as SelfAdjoint said. However, the Moon's orbital plane is inclined (~5o) to the Earth's equatorial plane. Another off-centre factor.

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And since we're bringing up all therse variances, don't forget the noticabole "masscons" distributed unsymmetrically through the Earth's mantle.

Mentat
The Earth is oblate, and some points are therefore closer to the moon than others. These closer points will receive a stronger force from the moon's gravity. But the location of the closest points varies as the Earth spins and the two bodies change relative positions during the moons orbit. Hence the wobble.

Now that does make sense. Hmm...I guess it would make sense for a "wobbling" effect to occur at the core.

zoobyshoe
Here are some outlandish speculations completely free of any knowledge of Celestial Mechanics:

The only thing I can imagine that is preventing this core from drifting completely over to one side of the Earth's interior (in response to either the sun' gravity, or that of the moon) is the rotation of the Earth itself. This causes the situation to resemble a fluid bearing.

To the extent this core lags behind the rotation of the crust, if it does, we would have the dynamo situation whereby the Earth's magnetic field is generated.

If there is any difference in the rotation of the crust and core the potential exists for whatever irregular projections there may be on the surface of the core to bang into the inverse mountains sticking inward on the underside of the crust, which ought to create some nasty earthquakes. I'm thinking this failure of the fluid bearing situation would come about from time to time due to the irregularities of the surfaces themselves, how these would affect the fluid dynamics of the molten layer, in conjunction with whatever new and interesting vector is resulting from the combined gravity of the moon and sun.

Whackiest speculation of all: could this core ever flip over for any reason thereby causing the occasional reversals in polarity of the Earth's magnetic field?

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More geology and geophysics than celestrial mechanics.
The only thing I can imagine that is preventing this core from drifting completely over to one side of the Earth's interior (in response to either the sun' gravity, or that of the moon) is the rotation of the Earth itself.
By analogy with the tides, the Earth's own gravity keeps the inner core from moving very far.
If there is any difference in the rotation of the crust and core the potential exists for whatever irregular projections there may be on the surface of the core to bang into the inverse mountains sticking inward on the underside of the crust, which ought to create some nasty earthquakes.
The Earth's structure is, from the inside out:
- inner core (solid), ~1,250 km
- outer core (liquid), ~2,200 km
- mantle (solid but somewhat plastic), ~2,900 km
- crust (solid), ~<100 km.
http://pubs.usgs.gov/publications/text/inside.html

While the inner-outer core and mantle-outer core transition layers aren't well understood, there certainly aren't any >1,000 km (inverse) mountains!

BTW, the deepest earthquakes occur ~700-800 km below the Earth's surface.
http://pubs.usgs.gov/gip/earthq1/how.html

dhris
Actually, the core does indeed have this "wobble". In fact, we can observe the misalignment of the core's and the Earth's rotation axes when we see that magnetic north and true north are different (and magnetic north appears to randomly drift). The core is also thought not to spin at the same rate as the rest of the planet, but is constantly exchanging its angular momentum with the mantle, via various mechanisms, resulting in fluctuations in the length of the day.

As for someone's speculation that the core "flips over" resulting in magnetic reversals, this is not likely, and the reversal mechanism is thought to be more complicated than that. But there are reputable geophysicists who believe that the core actually spins in the opposite direction from the rest of the planet (a phenomenon they call super-rotation).

dhris

zoobyshoe
Originally posted by dhris
The core is also thought not to spin at the same rate as the rest of the planet, but is constantly exchanging its angular momentum with the mantle, via various mechanisms, resulting in fluctuations in the length of the day.
This is fascinating.
As for someone's speculation that the core "flips over" resulting in magnetic reversals, this is not likely, and the reversal mechanism is thought to be more complicated than that.
The early electrets that were made of aluminum plates and carnuba wax were observed to spontaneously reverse polarity at irregular intervals, and I once read a geologist speculating that the same mechanism, whatever it be, was probably at work behing the Earth's magnetic polarity flip.
But there are reputable geophysicists who believe that the core actually spins in the opposite direction from the rest of the planet (a phenomenon they call super-rotation).
Even more fascinaing. Are they thinking this is the only way to account for the strength of the magnetic field,(by which I mean they don't think a mere "lag" would generate the field strength actually observed) or is it based on the presence of some other effect they've observed?

-Zooby

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Originally posted by zoobyshoe
The early electrets that were made of aluminum plates and carnuba wax were observed to spontaneously reverse polarity at irregular intervals, and I once read a geologist speculating that the same mechanism, whatever it be, was probably at work behing the Earth's magnetic polarity flip.
-Zooby

Yeah, that's the leading theory at this time. It is a characteristic of dynamos to invert their field polarity. Therefore, it is thought that plantary cores generate magnetic fields the way a dynamo does. One of the leading authorities on this area of research is a Dr Daniel Perry Lathrop. http://complex.umd.edu/dynamo/index.html [Broken] on which he documents his progress.

DHris, are you saying the anagonic angle is proof that the Earth's core is not in the center of the planet, or only that the two rotational axes do not line up?

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dhris
Oops. It seems I misspoke up there. Super-rotation refers to the phenomenon of the solid inner core rotating at a different rate from the rest of the planet, not necessarily in the opposite direction. It seems that it was predicted in some numerical simulations, and the debate now is whether or not it's what actually happens inside the core.

And reversals are indeed a generic feature of chaotic systems that produce a magnetic field. The main point is that the equations (in the case of the Earth's fluid outer core, the Navier-Stokes and induction equations) are unchanged upon changing the sign of the magnetic field. That means that if a steady-state exists of one polarity, then a steady state of the other also exists. Since the source is chaotic, reversals may result. An interesting chaotic system with reversals is the double-disc dynamo:

http://setiathome.berkeley.edu/~pauld/etc/210BPaper.pdf [Broken]

Chapter 6

And by "wobble", I meant the wobble of the core's rotation axis, which upon re-reading is not what you were talking about. I don't know the specific answer to your question, although if the entire core did move around inside the Earth due to tidal effects, we might expect to see a systematic change in magnetic north occurring on a yearly basis and I'm not sure that this is actually observed.

dhris

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zoobyshoe
I just saw a program about two guys chasing magnetic north on PBS about two weeks ago and, unless I hallucinated it, I heard them say it meanders around by as much as 44 miles per annum, which startled me.

dhris
Yeah, that's quite a lot! I think that's a pretty random variation, though, and some of it is due to continental drift. But I wonder if there is an annual or monthly periodicity in there that could be attributed to the effect that Lurch was asking about.

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zoobyshoe
Originally posted by LURCH Yeah, that's the leading theory at this time. It is a characteristic of dynamos to invert their field polarity. Therefore, it is thought that plantary cores generate magnetic fields the way a dynamo does. One of the leading authorities on this area of research is a Dr Daniel Perry Lathrop. http://complex.umd.edu/dynamo/index.html [Broken] on which he documents his progress.
Lurch,

I don't understand his thinking in how he has designed these devices.
He has no metal core in them. He is cooling the interior. He is applying the exiting field from the outside.

He seems to be shooting for some kind of convection - wants the sodium to move around by convection. I don't understand.

It is completely unclear where he expects the generated electricity that would give rise to a magnetic field, to be flowing. In the sodium? In the metal container?

Likewise, with no disconnected metal core there is no possibility of this feature contributing to the result.

To generate electricity there must be relative motion between a conductor and a magnetic field, and, a circuit for the electricity to flow around. I can't figure out where any of these are in his devices. To read that he has not been able to generate a magnetic field is exactly what I'd expect from the way he has designed them.
I definitely don't get the ones with the propellers inside.

Do you know his thinking about these things that are baffling to me?

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dhris
Well, the Earth's magnetic field is believed to be generated solely in the fluid outer core. You do not need a solid inner core for regeneration. The turbulence that arises in rotating convection has properties that make it suitable to act as a dynamo. The fluid just needs to be a good conductor.

And a dynamo is something that REgenerates and amplifies a given magnetic field, not necessarily that generates a field out of nothing. Even if your fluid flow is a good dynamo, you still need a "seed" field. So what he's doing is giving the system an initial field and measuring the decay rate. The slower it decays, the more regneration is going on inside the fluid.

dhris

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Chandler wobble

IMHO lots more work to be done before the origin of, and changes in, the Earth's magnetic field is well understood.

A nice factino for LURCH: The Chandler wobble, the movement of the Earth's rotational pole. Why it hasn't damped down to nothing was a mystery until a few years ago; now understood to be caused by the oceans. See:
http://www.jpl.nasa.gov/releases/2000/chandlerwobble.html

zoobyshoe
Originally posted by dhris
Well, the Earth's magnetic field is believed to be generated solely in the fluid outer core.
This, I'm sure, is what's represented by the molten sodium in his devices.
The turbulence that arises in rotating convection has properties that make it suitable to act as a dynamo. The fluid just needs to be a good conductor.
This only half accounts for the relative motion between a conductor and a magnetic field needed in a unipolar dynamo. It provides the moving conductor. I have been assuming the solid metal core of the Earth was taking on the function all ferrous cores fullfill in electromagnets - to greatly amplify the magnetic field. Current in the conductor would give rise to a weak magnetic field. This would be amplified by a ferrous core, and would in turn
induce more current in the moving conductor.
Even if your fluid flow is a good dynamo, you still need a "seed" field.
This is true when you're deaing with a system being started from scratch. You can "seed" it with an external magnetic field once it is turning, or give the coils a zap from a capacitor. Provided the rotation is not stopped the field will not decay once it is started.
So what he's doing is giving the system an initial field and measuring the decay rate. The slower it decays, the more regneration is going on inside the fluid.
If there were a proper core to amplify the field providing lines of magnetic force for the moving conductor to cut through I don't think he'd have any problems with decay at all. I bet there would be an excellent magnetic field at considerably slower speeds. As it is now the conductor is being asked to use whatever magnetic field it is able to generate to cut across its own motion. I suppose that could happen in a turbulent situation but the resulting field would also be turbulent containing many poles much like the sun. The more regular the motion of the fluid the "nicer" the magnetic field, but the less able to cut itself, I really think he needs a core, or else two distinct, neat fluid motions that could possibly exite each other.

If the wobbling of the core of the Earth actually does account for the meandering of magnetic north it seems logical to conclude it is acting like the core in any electromagnet. If the rotation of the core lags behind the crust it is also lagging relative to the molten layer. Any magnetic field it possessed would be inducing current in whatever conducting media were in relative motion with it.

Zooby

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Originally posted by dhris

And by "wobble", I meant the wobble of the core's rotation axis, which upon re-reading is not what you were talking about. I don't know the specific answer to your question, although if the entire core did move around inside the Earth due to tidal effects, we might expect to see a systematic change in magnetic north occurring on a yearly basis and I'm not sure that this is actually observed.

dhris

Yeah, and I should think there would be easily obtainable siesmic evidence, as well.

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Originally posted by LURCH
Yeah, and I should think there would be easily obtainable seismic evidence, as well.
Why? What sort of evidence?

If the core is off-center, in the direction towards the Moon, then it completes only one orbit per month, while the Earth around it revolves once a day. Applying relativity, this means that the core is a solid metal ball in the fluid mantle, going around in a little circle once every 24 hours. It should push a bow-wave which ought to hit the bottom of the crust once a day. Siesmometers should be able to detect that.

Regarding the generation of magnetic field, and the work of Dr Lathrop, there is another Topic in Geology about that. This Topic is more about orbital dynamics, so I put it here in CM.

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LURCH: Siesmometers should be able to detect that.
Do you have any references to the detection of seismic events which originate anywhere near the mantle/core boundary?
LURCH: If the core is off-center, in the direction towards the Moon, then it completes only one orbit per month, while the Earth around it revolves once a day. Applying relativity, this means that the core is a solid metal ball in the fluid mantle
The core comprises a solid inner core and a liquid outer core. Above the liquid core is the mantle. Could you restate these two sentences please, distinguising between the solid and liquid core?