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. >> >> >> >> >
