Hi James,

Actually, even if you can assume the earth is a sphere, you have your 
geometry wrong.  You're correct that the volume of a sphere goes as the 
radius cubed:
V = 4/3 * pi * r^3
however, you may remember from calculus that to calculate the change in 
volume as a function of radius, you must take the derivative of this 
equation, and you find:
(change in V) = 4 * pi * r^2 * (change in r)
The earth's radius, r, is ~6400km ~ 21,000,000 feet.
So if the ocean levels rise by 1 foot, the increase in the volume of 
water would be
dV(1 foot) = 4 * pi * (21,000,000)^2 * 1
on the other hand, if it rises by 20 feet, you can approximate the 
increase in volume by
dV(20 feet) = 4 * pi * (21,000,010)^2 * 20
If you divide these by each other, the ratio you find is 20.00002, which 
means that the increase in volume of a spherical ocean from a rise in 
sea level of 20 feet is 20.00002 times larger than the increase in 
volumes from a rise in sea level of 1 foot.  The large size of the earth 
is what makes this so different than your estimate of 8,000.

On the other hand, the earth is not spherical, and ~1/3 of the earth is 
covered in land, which makes the problem more difficult to solve.

Best regards,
Mike

-- 

Michael Niemack
Princeton University
Physics Department, Jadwin Hall
Washington Road
Princeton, NJ 08544
office (609) 258-5077
fax    (609) 258-6853

Maren N Vitousek-Bemis ([EMAIL PROTECTED]) wrote:
> 
> ------------------------------------------------------------------------
> 
> Subject:
> Re: Ocean Level Rising
> From:
> "L. Brian Patrick" <[EMAIL PROTECTED]>
> Date:
> Wed, 21 Mar 2007 18:52:48 -0400
> To:
> [email protected]
> 
> To:
> [email protected]
> 
> 
> Hi James,
> 
> While I think that your first point is essentially true, the second 
> point assumes that the whole of the earth is covered with water, when 
> only 2/3 of the earth's surface is water.  Further, most of the ice 
> locked up in the arctic and antarctic ice caps sits above sea level.  
> Thus, as ice calves from those repositories, they add to the ocean.  The 
> amount of ice locked up in those polar caps is staggering, though I 
> don't know the numbers.  Further, I don't know whether there is enough 
> to actuate a change even when correcting for the terrestrial surface 
> subtracted from the sphere used in your calculations.  In short, I 
> neither agree nor disagree with what you have said, only offering some 
> corrective calculations.  :-)  I'll let the experts argue your points.
> 
> Best, Brian
> 
> James T. Conklin wrote:
> 
>> Inconvenient Facts  regarding rising ocean level:
>>
>> 1.  The ocean level is unchanged when floating ice melts.
>>
>> 2.  The ocean is a spherical body of water.  The ocean volume varies as 
>> the cube of the ocean radius.  Therefore, for the ocean radius to increase 
>> 20 feet, the ocean volume must increase 8,000 times more than for a 1-foot 
>> radius increase.  For the ocean radius to increase 40 feet, the ocean 
>> volume must increase 64,000 times more than for a 1-foot radius increase.
>>
>>
>>  
>>
> 

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