"Wobble" of Planetary Core

**LURCH** · Sep22-03, 06:28 PM

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?

**Nereid** · Sep22-03, 10:02 PM

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** · Sep27-03, 11:40 AM

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.

selfAdjoint · Sep27-03, 12:05 PM

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.

**Nereid** · Sep27-03, 01:22 PM

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.

SelfAdjoint:

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?

**Janus** · Sep27-03, 01:28 PM

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

D_m2-Cog = D_m1-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. )

**LURCH** · Sep28-03, 01:28 PM

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.

**Nereid** · Sep28-03, 02:51 PM

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 (~5^o) to the Earth's equatorial plane. Another off-centre factor.

selfAdjoint · Sep29-03, 11:24 AM

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

**Mentat** · Sep29-03, 11:31 AM

Originally posted by SelfAdjoint
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** · Oct2-03, 11:10 PM

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?

**Nereid** · Oct3-03, 10:40 AM

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** · Oct5-03, 03:50 PM

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** · Oct5-03, 09:33 PM

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 earths 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

**LURCH** · Oct6-03, 05:54 PM

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 earths 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. He has a website 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?

**dhris** · Oct7-03, 12:45 AM

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

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 occuring on a yearly basis and I'm not sure that this is actually observed.

dhris