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Author Topic: Will melting the Antarctic ice sheet slow the rotation of the Earth?  (Read 7097 times)

Artful Dodger

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Hi folks,

Conventional estimates of the mass of the Antarctic ice sheet are around 30 million cubic kilometers (and perhaps 10% of that for Greenland's ice sheet, so we'll simplify this question by ignoring it).

Assuming ~1000 kg / m3 density of pure ice, that would be roughly 30 * (1016) tonnes = 3.0 × 1020 kilograms of mass at or very near the South pole (you can calculate the polar moment of inertia if you wish to refine this initial state, radius is about r = 2100 km, distribution mostly flat but again refine away if you choose)

Now, if all this land ice melts over the coming X millennia, that mass will be redistributed Northward as it spreads out upon the world ocean. The new center of gravity for that mass would shift from near the pole to near the equator (i think this is the appropriate assumption, but see also below about 45 degrees latitude).

Now comes the real sticky part. The rotational speed of the Earth at the pole is zero, while the speed of Earth's rotation at the equator it is about 465 m/s or 1,674 km/h.

So then, the Earth would have to accelerate about 3.0 × 1020 kilograms mass to about 230 m/s or 830 km/h (this is half the equator's speed based on melt water moving to an average of about 45 degrees latitude, roughly). This energy would come from the Earth's rotational inertia, thereby slowing Earth's rotation by some amount.

Given the mass of Earth = 5.97219 × 1024 KG and rotational speed 465.1 m/s (and its to-be-defined density layers down to the heavy nickel-iron core), how much does the Earth's rotation slow down when the Antarctic ice sheet melts completely?

Anyone? Bueller? Ooh, and PLEASE, show your work... ;)
Cheers!
Lodger

gfwellman

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #1 on: April 12, 2013, 10:22:46 AM »
One can get a good ballpark estimate without a calculator.  Just say you're taking some mass with close to zero angular moment and distributing it at roughly the average moment (actually it might be more like twice the average moment considering it's all at the surface so let's go with that).  So the ratio of twice that mass to the whole mass is about 1/10000.  So the earth should slow down by about that factor, so days would be 8 seconds longer or so.  I'm guessing that's probably good to a factor of 2.

Artful Dodger

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #2 on: April 12, 2013, 11:17:06 AM »
Ooh, baseball analogies! I Love it! Snow ball Earth? Screw ball Earth? jus' sayin'...



I bet the only 'moment' Bueller ever studied was with his comb in a mirror. ;)

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Lodger

ivica

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #3 on: April 12, 2013, 11:39:15 AM »
What is oddity, then, for Dzhanibekov effect on planetary level...
Uuups, gone too far, going off now ;-)

Artful Dodger

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #4 on: April 12, 2013, 12:12:53 PM »
What is oddity, then, for Dzhanibekov effect on planetary level...
Hi ivica,

Yes, I expect the dynamics could get quite complicated, what with the water sloshing about. Two other considerations come to mind:
  • the water may not accelerate to match the Earth's rotation. This would imply a momentum drag current, and
  • the mantel, outer core, and inner core are not tightly coupled at their boundary layer. The Earth's crust slows down, but the heavy mantel, and even heavier core keeps right on truckin'...
This last implies the Earth's crust rips open, coming unstitched at the seems (tectonic plates), just like a baseball that's been hit too hard. The horse-hide is dragged along, flapping as it goes.  :o

WHOOPS!
« Last Edit: April 12, 2013, 03:05:27 PM by Artful Dodger »
Cheers!
Lodger

Jim Williams

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #5 on: April 12, 2013, 02:30:21 PM »
When was the last period of extreme vulcanism, and how does it relate to the last time the Earth thawed?

Artful Dodger

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #6 on: April 12, 2013, 03:00:30 PM »
When was the last period of extreme vulcanism, and how does it relate to the last time the Earth thawed?

Maybe the Late Heavy bombardment?

... and "i have no idea" ;) I have no realistic sense of the energies involved.

What do you think, Jim?
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Lodger

johnm33

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #7 on: April 12, 2013, 04:32:19 PM »
Jim there was a lot of activity the last time the' laacher see' went off, don't think it would qualify as extreme though.

Jim Williams

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #8 on: April 12, 2013, 06:04:51 PM »
What do you think, Jim?

I think I have a headache.

Too much data for me....and too much of it doesn't fit.

Glenn Tamblyn

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #9 on: April 17, 2013, 03:53:09 AM »
Interestingly, oceanographers have used changes in the Earth's rotation to estimate past ice quantities and sea levels.  Astronomy gives them when past eclipses should occur. Archaeology lets them explore when the ancients reported eclipses.

They have been able to see a drift in the Earth's rotation that fits with the transfer of ice mass from the poles - close to the Earths axis - to the equator, farther from it's axis. Sea ice might have an impact on this but much smaller, it is the mass that matters, not its volume. It is land ice that makes the most noticeable change.

pikaia

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #10 on: April 17, 2013, 10:21:16 AM »
Interestingly, oceanographers have used changes in the Earth's rotation to estimate past ice quantities and sea levels.  Astronomy gives them when past eclipses should occur. Archaeology lets them explore when the ancients reported eclipses.

They have been able to see a drift in the Earth's rotation that fits with the transfer of ice mass from the poles...
The Earth's rotation is gradually slowing down due to tidal friction, and it also varies up and down slightly due to convection of the magma. By looking at the dates of ancient eclipses we can tell how much the rotation has changed, but I had not heard about measuring the transfer of ice mass by this method. How do you separate the different effects? Do you have link?

Glenn Tamblyn

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #11 on: April 17, 2013, 11:20:44 AM »
pikaia

General presentation by Jerry Mitovica here:

Tidal friction is a very steady process and magma movement is slow. Where as ice melt to water allows mass transfer over large distance pretty quickly. Particularly when you factor in the bulging effect at the equator for any fluid.
« Last Edit: April 17, 2013, 12:20:58 PM by Glenn Tamblyn »

pikaia

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #12 on: April 17, 2013, 12:25:33 PM »
A fascinating video! It is amazing that melting Greenland's ice would actually lower sea levels there, and by such a huge amount.

However, it does make calculating the effect of the original question more complicated!

Artful Dodger

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Re: Will melting the Antarctic ice sheet slow the rotation of the Earth?
« Reply #13 on: April 17, 2013, 09:33:00 PM »
General presentation by Jerry Mitovica
Excellent dig, Glenn.  :D

So does Dr. Mitovica present a finding for historical changes in the Earth's rotation due to melting of the Polar ice sheets?
Cheers!
Lodger