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One often comes across news articles that claim that an earthquake shifted the earth's axis.


If you ignore the influence of other celestial bodies, an internal event like an earthquake surely can't change the direction of the angular momentum of the Earth (unless stuff is ejected out of Earth), since angular momentum has to be conserved in the absence of an external torque. So the axis has to remain fixed.

Am I missing something? Or are geologists trying to say that the resulting movement of tectonic plates causes a change in the point of intersection of the axis (which remains the same) and the plates that include the poles, so that it seems as if the axis has shifted?

EDIT Some articles mention the value of the shift in the axis and also the change in the length of the day. If, as Ted Bunn's answer indicates below, the shift in the axis isn't actually real but is because of the movement of tectonic plates with respect to the axis, shouldn't the shift be different at the north and south poles? How are the shifts and the change in day-length calculated?

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do you mind editing your question and ask the following extra question: "How can one compute the shift in the axis and the change in day length?" I have read some claims from news sources that a Nasa scientist computed it. I'd guess it's possible to measure it, but how can one compute it without knowing the distribution of mass prior and posterior. Sounds like a misrepresentation from the media to me or am I missing something? –  Raskolnikov Mar 12 '11 at 16:45
@Raskolnikov I'm pretty sure you need the shape and distribution of the plates to calculate the shift (which should be different at the N and S poles). I've added your question. –  dbrane Mar 12 '11 at 19:40
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4 Answers

up vote 20 down vote accepted

Angular momentum doesn't change, but the angular velocity vector does. This is effectively due to a shift in the body's moment of inertia tensor.

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Lubos, is the shift in the earth's axis related to "why a chalkboard eraser will flip axis when it is tossed in the air rotating?" (And why does that happen?) Or is it more like what would happen if a spinning symmetrical ice skater moved only one of her hands in or out a few inches? –  Jerry Mar 12 '11 at 19:00
I wasn't particularly concerned about the change in angular velocity (which would change the day length) but about the supposed shifting of the axis. –  dbrane Mar 12 '11 at 19:42
@dbrane that's why I specifically said the angular velocity vector. An appropriate shift in the inertia tensor will change the direction of rotation. –  Stingray Mar 12 '11 at 19:47
Right, sorry, missed the vector bit. –  dbrane Mar 12 '11 at 19:53
And yes, you seem to be spot on springerlink.com/content/u00824pkl1032115 You could include that or similar references in your answer for the benefit of others. –  dbrane Mar 12 '11 at 20:20
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Your explanation is right: an earthquake can't change the axis of rotation, relative to a given inertial reference frame -- that is, the axis of rotation doesn't change relative to the "fixed stars" as a result of the earthquake. What the earthquake does is to move material around within the Earth, so that the position of the rotation axis relative to any given marker on Earth's surface changes.

If you prefer, rather than saying the earthquake shifted the Earth's axis, you can say that it shifted all of the stuff on the Earth's surface. Since we find it more convenient (often!) to use points of reference that are fixed to markers on Earth's surface, it looks to us like a shift in the axis.

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See springerlink.com/content/u00824pkl1032115 –  dbrane Mar 12 '11 at 20:21
Let me backpedal a bit. @Stingray's answer is correct: you can change the (instantaneous) axis of rotation without changing the angular momentum. –  Ted Bunn Mar 12 '11 at 23:14
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There is some confusion about the term axis. The axis about which the Earth rotates of course did not change. It requires some external torque or transfer of angular momentum for that to happen. However, the Earthquake changed the shape of the Earth slightly, which changed the figure axis of the Earth. Calculations also show the Japan quake should have shifted the position of Earth’s figure axis (the axis about which Earth’s mass is balanced) by about 17 centimeters (6.5 inches), towards 133 degrees east longitude. Earth’s figure axis should not be confused with its north-south axis; they are offset by about 10 meters (about 33 feet). This shift in Earth’s figure axis will cause Earth to wobble a bit differently as it rotates, but it will not cause a shift of Earth’s axis in space-only external forces such as the gravitational attraction of the sun, moon and planets can do that.


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Now I'm confused. Isn't it possible for a change in the mom-of-inertia tensor to change the direction of the axis while keeping the angular momentum vector unchanged, as @Stingray pointed out? Also, I think it's good practice to put your text in indented quotes if you're copying verbatim from another source. –  dbrane Mar 16 '11 at 0:58
This is just a definition of the axis shift that means the configuration of the Earth changed relative to that. It means the center of mass of the Earth was displaced and so the axis of rotation now “pierces” different points at the poles. The angular momentum of course remains constant in magnitude and direction. –  Lawrence B. Crowell Mar 16 '11 at 22:59
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There is a confusion in the words "axis of rotation". These words have been used for the vector "angular momentum", which doesn't change in absence of external torque or forces. The other vector is the vector "instantaneous rotation", which can change its orientation during the movement, even if the rotating solid doesn't change its shape or mass distribution. Changing the center of gravity during the movement (as a result of earthquaques in our case) can also change that vector, but not the angular momentum.

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