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### Earth's Balance

```
Date: 12/20/2001 at 11:28:51
From: Thomas Kolasa
Subject: Earth's balance

Why would Earth change its orbit and turning if something as heavy as
the Ross Iceshelf moved up some amount of miles?
```

```
Date: 12/21/2001 at 11:26:56
From: Doctor Ian
Subject: Re: Earth's balance

Hi Thomas,

It wouldn't change its orbit significantly, because from the point of
view of the sun and the other planets, the mass of the earth is
concentrated at a point at its center. (It might as well be a golf
ball with the same mass as the earth.) So moving stuff around on the
surface of the earth makes no difference to the rest of the solar
system.

A redistribution of surface mass might, however, affect the earth's
rotation, if the redistribution were large enough. How would that
work?

If you've ever watched a figure skater spin, you may have noticed that
she starts out with her hands flung out to the side, and then pulls
them in toward her body. That makes her spin faster because her mass
is closer to her axis of rotation. To slow down, she moves her arms
back out.

The scientific explanation for this is called 'conservation of angular
momentum', which is a fancy way of saying that you have to work a lot
harder to swing something far away from you than you have to work to
swing something close to you.

In the same way, if you moved a lot of mass from near the equator
(away from the axis of rotation) to near the poles (closer to the
axis), you could cause the earth's rotation to speed up; and moving
stuff the other way could cause it to slow down.

Forget ice shelves. If everyone else and everything else stays put,
and you get in a car and drive from Alaska to Florida, _you_ will
cause the earth's rotation to slow down. But the interesting question
is: By how much? And the answer is: Not very much! Because you're
pretty small compared to the rest of the earth.

However, what about something as big as the Ross Ice Shelf? Wouldn't
that make a significant change?

Well, consider this: If you take something really big, and move it a
little bit, the only significant change occurs at the ends. (Imagine
that you live under the Ross Ice Shelf, near the middle, and it moves
by a mile or two. You're still under about the same amount of ice,
right?) So moving an ice shelf a few miles is the same as moving a few
miles of ice from one end of the shelf to the other.

(In fact, think about a warehouse full of boxes,

+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+

Moving the whole warehouse by the length of one row of boxes is the
same thing as just moving one row of boxes,

+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+--+--+--+  ^
|                               |
+-------------------------------

isn't it?)

So to really get a big enough change to make a difference, you'd have
to move the ice shelf by an appreciable fraction of its size.

But even then consider this: If you move something, something else
will occupy the space where it used to be.

If you dig a lot of stone out of the ground, you're replacing the
stone with air, which has a much lower density. So if the hole is big
enough (like the Grand Canyon), you've made a significant change in
the distribution of mass on the surface of the earth.

However, if an ice shelf releases an iceberg (thus 'moving' the
shelf), the ice that used to be there is gone, but it's replaced by
water, which has almost the same density. And most of the iceberg is
below water, so the change in the distribution of the surface mass of
the earth is pretty insignificant.

In any case, we're talking about the surface of the earth while
ignoring its center, which is like worrying about the skin of a water
balloon and ignoring the water inside. The effects of whatever goes on
down there in the earth's core would be much more significant than

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Physics/Chemistry

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