PostHeaderIcon Earthquakes and the Length of a Day

The fabulous and illustrious duo Beth and James requested that I educate you all further on the relationship between the Chilean Quake and the rotation of the Earth. A worthy topic.

In Short

The big earthquake in Chile shifted enough of the mass of the Earth far enough that (like a figure skater bringing her arms in toward his body) the Earth actually sped up slightly – shortening our day by 1.26 microseconds. Maybe – the number will be refined further.

Quote

JPL research scientist Richard Gross computed how Earth’s rotation should have changed as a result of the Feb. 27 quake. Using a complex model, he and fellow scientists came up with a preliminary calculation that the quake should have shortened the length of an Earth day by about 1.26 microseconds (a microsecond is one millionth of a second).

Perhaps more impressive is how much the quake shifted Earth’s axis. Gross calculates the quake should have moved Earth’s figure axis (the axis about which Earth’s mass is balanced) by 2.7 milliarcseconds (about 8 centimeters, or 3 inches). Earth’s figure axis is not the same as its north-south axis; they are offset by about 10 meters (about 33 feet).

-JPL Media

In Detail

Overwhelmed? I’ve highlighted the pieces you should pull out of that.

Conservation of Angular Momentum

You cannot create energy or matter out of nothing. These laws are called “conservation of matter” and “conservation of energy.” We’ve got one for spin (angular momentum) too. If you’re spinning you either keep spinning (at the same speed) or you pass off some of that momentum to another object. This causes the oft-referenced effect of the figure skater’s pirouette. She begins to spin with her arms out, gets up some speed, and then pulls her arms and legs in tight. She spins significantly faster in this configuration. Later she puts her arms out again and slows down.

You can do this at home. Grab two cans of food and a spinning office chair. If you do not also find yourself at least fifteen by fifteen feet square of clear space, I take not responsibility for your bruised knuckles (you WILL knock into something if you don’t have plenty of room around, so don’t hurt yourself). Get a friend to start you spinning, with the cans held at arms length in your hands. As soon as you’re going, pull the cans in to your body. Try it the other way – starting with your arms in too.

This is conservation of angular momentum.

Figure Axis

Why were we talking about that? Because of the figure axis. You know the Earth is round, and you also know the Earth is not a perfect sphere because of that hill you had to bike up to get to work today. The Earth rotates on its axis, once a day, and that axis is pointed at the North star.

Now, imagine your washing machine – it spins too. Where is that axis? Yup, right down the middle. The figure axis is different though – it’s the axis around which the mass is all balanced. In a normal situation for your washing machine, these two axes are about the same. Now imagine it gets off balance – all your clothes end up on one side of the drum.

First, where is the spin axis? Yes! Same exact place – right down the middle (sorta, you hope). The mass (your soggy clothes) have changed places though, and they’re all on one side. Imagine a line that intersects the middle of the clothes pile. It’s off to one side, and in fact, as the washing machine spins, the figure axis is rotating around the spin axis with the clothes.

Re-balance your load of laundry so it doesn’t make your washing machine walk and let’s talk about the Earth.

The Earth’s figure axis (balance of mass) is very close to its spin axis, but they aren’t the same. If you move one of the Earth’s plates a lot – it’s like moving the towel in the laundry around, you’re messing with the balance of the mass. In the case of the Chilean earthquake we have one plate subducting under another, which means some mass moving closer to the center of the Earth. It’s not moving far, it’s not getting that much closer to the Earth, but if you’re doing minute calculations it is definitely enough to have that conservation of angular momentum effect (spin a little faster as mass moves in) due to the shifting of the mass of the Earth.

Calendar Change

A student came up and asked today if that meant the atomic clocks needed to change. Well, no, but the atomic clocks are pretty much just counting time passing anyway, in oscillations specific atoms. The question you want to ask is, are the “atomic calendars” going to change?

First off, I must point out I don’t know if there are calendars kept to the level of accuracy that is implied in the term “atomic calendar.” Perhaps these folks?

Second, no, not yet. Richard Gross’s calculations are preliminary. Once they are solidified, the next leap second will take care of it. Does that mean a leap second isn’t actually exactly a second?

Want More?

The JPL Release

Microseconds – a measure of time

Milliarcseconds – a measure of angle (like a degree is a measure of angle)

International Earth Rotation and Reference Systems Service

I’m embarrassed to say, but I got the idea for the  washing machine analogy off Yahoo Answers. I was just going to use the figure skater till I read the concept there. I’m also going to have to talk about the ways the Earth moves sometime.

~ A l i c e !

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