Nate Holt's Blog

July 5, 2009

Melting glaciers and not enough hours in the day

Filed under: Musings — nateholt @ 9:25 am

(this originally appeared in May 2006 on the old blog)

If you’re like me, it seems that sometimes there just aren’t enough hours in a day (especially in the weeks before an AutoCAD Electrical release). The high-priced consultants say “work smarter, not harder”… but I wonder if they really have a clue.

Is there hope? Donno, but I got to thinking that maybe, with patience, this problem will self-correct. The solution may be in melting glaciers. The water run-off might slow the earth’s rotation down (and make days longer!).

The key is an immutable law, the Law of Conservation of Angular Momentum. This stuff can neither be created nor destroyed… and the earth has a fixed quantity of it.

Here’s an analogy… a figure skater spinning on the ice. Her arms and hands held closely together and stretched out above her head. In this pose, her “moment of inertia” is small and the spin rate is very high. Her fixed angular momentum is the product of these two values. Now she slowly pulls her arms down, elbows go out, hands start to separate. Her moment of inertia increases. Since the angular momentum is fixed (i.e. conserved), the spinning rate has to decrease to keep a constant momentum value. She flings her arms straight out, maximizing her moment of inertia, and the spin nearly stops.

Let’s say the figure skater is the planet earth and her arms and hands represent the polar ice pack at the top and bottom of the planet. Since these are pretty much on the axis of rotation, they don’t contribute much to the overall moment of inertia. But, when the polar ice caps melt and the water spins out toward the mid section of the planet (like the figure skater pulling her arms down and out), this now begins to seriously contribute to an increase in the planet’s moment of inertia. The earth’s rotation would have to slow down to avoid breaking the conservation of angular momentum law.

So, let’s try to figure out how much extra time we can get in a day if we wait around for the ice caps to melt…

One of the more dire predictions is that glacial melting will contribute about a 2.5 inch rise in sea level. If this were spread out over the whole planet (which is 30% land, 70% oceans), it would be about a 2 inch rise overall. So, we need to compare the moment of inertia of the planet earth with this water frozen at the poles (current condition) versus the new moment of inertia with the equivalent of an extra 2 inches of melted glacier water spread out over the whole planet.

Google provides some numbers for crunching. The mass of the earth is 5.98×10^24 kg, radius is 6.4×10^3 km and the weight of 2 inches of water spread out over the earth’s surface calculates to be something like 7×10^16 kg. Moment of Inertia calculations for a solid sphere (full earth) and a spherical shell (the 2 inches of water) are here and work out so that the difference is about 0.00000000071 between the two scenarios (earth sphere+fozen poles versus earth sphere+2″ water shell).

So, the angular velocity of the earth would have to slow down by this factor, 0.00000000071, in order to maintain its fixed angular momentum. What does this work out to? 365 days in a year x 24 hrs x 3600 seconds = 1,227,600 seconds in a year. Multiply by the slow-down factor and we end up with a year that is 0.009 seconds longer.

Is this right? Doesn’t seem like much.

Guess will have to try to work smarter.

UPDATE:

In original post above I suggested that this problem might self-correct if we were patient. Melting glaciers at the poles would raise the ocean level world-wide. Since total angular momentum can neither be created nor destroyed, the earth’s rotation would have to “slow down” due to the redistribution of mass away from the poles.
Well, now they say that warming water becomes less dense and alters the distribution of water between the equator and polar regions. They say this will speed up the earth’s rotation: http://www.sciam.com/article.cfm?articleID=E4337790-E7F2-99DF-3D1E8E32CEBF832A&chanID=sa003

So, I guess this cancels my theory out. Since we can’t look forward to being able to work longer, I guess we’ll have to work smarter.

UPDATE2: But wait!… Harvard University scientists say it’s true… here (16-Dec-2015)

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