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 / m

^{3} density of pure ice, that would be roughly 30 * (10

^{16}) tonnes = 3.0 × 10

^{20} 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 × 10

^{20} 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 × 10

^{24} 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...