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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 
just about any change that could be made at the surface. 

Does this help? 

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

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