Most of the surface of the earth is covered with water. Some of it is pretty deep (at least by human standards). Above us is the atmosphere. It goes up. Way, way up. So if we were to make a sphere with just the earth's water and another one with the atmosphere at standard temperature and pressure (STP), how big would be spheres be? The answer seems to have surprised some people (see the comments at this link). But it shouldn't have. Volume goes up with the cube of the radius of a sphere while the surface increases by the square of the radius. This means that for larger spheres, the surface to volume ratio will almost always be small, as is the case here:
Left: All the water in the world (1.4087 billion cubic kilometres of it) including sea water, ice, lakes, rivers, ground water, clouds, etc. Right: All the air in the atmosphere (5140 trillion tonnes of it) gathered into a ball at sea-level density. Shown on the same scale as the Earth. (Dan Phiffer via Boingboing)
Here's the basis for the original calculation, although not the explanation for the surprise:
Andrew Nowicki writes:The mass of the oceans is approximately 1.35 Ã 10^18 tonnes, or about 1/4400 of the total mass of the Earth (ranges reported: 1.347 Ã 10^21 to 1.4 Ã 10^21 kg.) source
The average mass of the atmosphere is about 5 quadrillion metric tons or 1/1,200,000 the mass of Earth. According to the National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480 Ã 10^18 kg with an annual range due to water vapor of 1.2 or 1.5 Ã 10^15 kg depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27 Ã 10^16 kg and the dry air mass as 5.13 Ã 10^18 kg." source
The explanation goes to Euclid. But he doesn't have an internet connection.
- Log in to post comments
More like this
I'd like to see the spheres (balls) containing all
living organisms, all humans, all chickens, all bacteria
all viruses
anon: That prevents somewhat of a packing problem. How would you do it. Convert the mass to water? It certainly would be smaller than what you see for water, right?
My favourite analogy to show people how little fresh water there is on earth is to ask them "If all the salt water on earth is represented by an Olympic size swimming pool, and you dumped in the equivalent represented volume of all the fresh water on earth, how much fresh water would you be adding?"
By far, most people say a dozen bathtubs full, or hundreds of gallons/litres etc. It is actually about a tablespoon full or there abouts! Which I find amazing, having canoed some long distances on Lake Superior, but there you have it.
The whole biomass of the earth fits into a sphere of
diameter 8km.
Humans,birds,krill amount for roughly the same mass and
fit into a sphere of diameter 1km each.
anon: I'm not surprised, but what is the basis for the calculation?
"The whole biomass of the earth fits into a sphere of diameter 8km."
So if all life were happening on dry land, it would be about one centimetre deep. I would have expected a bit more...
revere, do we need a basis ? Assuming 1 ton = 1 m^3,
if that's what you mean.
Lassi, I got biomass=2.8*10^14kg, (=per year ?)
but now I found : 1.85*10^15kg (Wikipedia) so the diameter
would be 15km or 3.6cm all over the Earth's land-surface
(if I made no mistake)
anon: I just meant how did you do the calculations. You assumed, I guess that biomass has the density of water. Close enough. Again, I was just curious. Your answer is not qualitatively surprising to me. We are a tiny fraction of the planet and its surroundings.
"The whole biomass of the earth fits into a sphere of diameter 8km."
So if all life were happening on dry land, it would be about one centimetre deep. I would have expected a bit more...
Posted by: Lassi Hippeläinen | March 13, 2008 7:39 AM
Yep! I would have expected a lot more! Funny how spreading it around all over the place gives that illusion!
Dave Briggs :~)