On Mar 22, 2008, at 11:01 AM, Horace Heffner wrote:
Using an earth radius of 6371 km.
http://en.wikipedia.org/wiki/Earth
The density of air at the earth's surface is 1.2 kg/m^3, The mean
mass of the atmosphere is 5.1480×10^18 kg.
http://en.wikipedia.org/wiki/Earth's_atmosphere
The surface area is 4 Pi (6371 km)^2 = 5.1x10^14 m^2. The volume
of the earth's atmosphere at average humidity and temperature
conditions is (5.15x10^18 kg)/(1.2 kg/m^3) = 4.3x10^18 m^3. The
per capita volume for 6.6 billion people is then (4.3x10^18 m^3)/
(6.6x10^9) = 6.5x10^8 m^3. The per capita surface area for 6.6
billion people is (5.1x10^14 m^2)/(6.6x10^9) = 77272 m^3, or 278
meters square. If each person gets a 77272 m^2 room, then the
ceiling height is (6.5x10^8 m^3)/(77272 m^2) = 8411 m, or about 8.4
km. so that's a long way between floors.
The volume V of a sphere to hold all that gas is V = 4/3 Pi r^3, so
r = ((3V)/(4 Pi))^(1/3) = (3(4.3x10^18 m^3)/(4 Pi))^(1/3) = 1x10^6
m, or about 1000 km.
You really don't need all that gas for a space ship, because it can
recycle. Suppose each person gets 278 meter cube. That's a total
volume of (6.6x10^9)(278 m)^3 = 1.4x10^17 m^3, and r = ((3V)/(4 Pi))^
(1/3) = (3(1.4x10^17 m^3)/(4 Pi))^(1/3) = 3.2x10^5 m, or about 320 km.
Suppose each person only gets a 3 m ceiling. That's a total volume
of (6.6x10^9)(3 m)(278 m)^2 = 1.5x10^15 m^3, and r = ((3V)/(4 Pi))^
(1/3) = (3(1.5x10^15 m^3)/(4 Pi))^(1/3) = 7.1x10^4 m, or about 71
km. That's a sphere 142 km in diameter.
Horace Heffner
http://www.mtaonline.net/~hheffner/
