NP > Surprisingly, our personal spaceship works out to be a globe only
about 1.18 kilometres in diameter
HH <<This is wrong by orders of magnitude by inspection. Such a sphere
would easily fit within a 10.6 km envelope around the earth.>>
No, one's personal space on Earth is a piece of land and ocean (30% land,
70% ocean) which is 278 metres
square - with which we both agree - with a "ceiling
height" of around 8.6km of air above it (not 10.6km - thanks for the
correction Horace!). I originally took the stated statistic (
http://en.wikipedia.org/wiki/Atmospheric_pressure ) that half the mass of
the atmosphere is below 5.3km and doubled it to get total mass. The volume
of our personal atmospheric space, a "right rectangular prism" (or tall thin
brick shape), is 278x278x8600 = 664,642,400 cu m. Convert this volume to a
sphere
and you get a radius of about 541 metres, which is a diameter of 1.08km
Q.E.D.
I found no mistake in your arithmetic below but you used the total volume of
Earth's atmosphere to get 1000km for the radius but I was trying to work out
how much atmosphere, land and ocean each person has to use and abuse...
HH> 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.
The radius of one's personal spaceship's atmospheric globe is, as above, 541
metres.
I was trying to find out what people thought of these figures - were they
surprisingly small/big/about what you expected etc?
* air pressure at sea level is about 14.7lbf/sq in = 10.3333 tonnesf/sq
metre
density at sea level is about 1.2kg/cu m
