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If all the water on Earth’s surface and in the air were put into a ball, how large would the sphere be? Could it exist in space by itself?
Garry Trethewey
Leigh Creek, South Australia
The answer is: a bit under 1400 kilometres in diameter, and no. But it’s a lovely exercise in googling and back-of-the-envelope calculations.
First, let’s see how much water there is in oceans. The US Bureau of Reclamation says 1.37 billion cubic kilometres. And how much water is there in the atmosphere? About 13,000km3. The oceans hold over 100,000 times as much water as the atmosphere, so atmospheric water is negligible.
Now, lets calculate the size of the sphere that would fit 1.37 billion km3. First, we need to calculate the size of the cube, which is the cube root of 1.37 billion. This equals a cube 1110 km on each side. For the volume of the sphere, Google provides lots of radius-to-volume calculators, not the other way around, so we must guess a radius, then adjust it up or down until we find the approximate volume. In round figures, lets start with a cube of 1000km across, so a 500km radius. We get about 500 million km3, far less than the 1.37 billion km3 we found earlier. Trying a radius of 700km, we get 1.436 billion – close enough for our back-of-the envelope calculation. Double that (diameter is radius multiplied by 2) to get a ball 1400km across.
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The state of water on Earth, something that we tend to take for granted, is highly unusual within the universe
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Next, could it exist in space by itself? As we know, the temperature at which water evaporates decreases with lower air pressure. You can’t get a good cup of tea on Mount Everest. How much air pressure would be around our water ball? Consider the moon, which is about 2.5 times the diameter, so 2.53, or 15, times the volume of our water ball. Thus, if the moon were made of water, it would be about 15 times the mass of our ball.
But the moon isn’t water; it’s rock, which is about 3.3 times the density of water, so let’s say about 50 times the mass of our water ball. Even with that mass the moon hasn’t got enough gravity to hold on to an atmosphere, so water, or even ice, evaporates quickly.
Our water ball, much smaller, would do the same. It couldn’t form in space by itself, and if some super-techno flying saucer people put it in space, it wouldn’t last long.
Pat French
Longdon upon Tern, Shropshire, UK
Were you able to accumulate all of Earth’s water – ice, liquid and vapour, plus all the water physically and chemically combined with mineral and organic substances – you might reach 1.4 billion cubic kilometres. If somehow you could store it under Earth surface conditions, it might form a sphere of roughly 700-kilometre radius.
However, these conditions would be unlikely. The state of water on Earth, something that we tend to take for granted, is highly unusual within the universe. On our planet’s surface, water can exist in its three natural states: solid, liquid and gas, all held in place by gravity. Earth’s average surface temperature is about 15°C (59°F); air pressure is one atmosphere (101,325 pascals); gravity is 1 g. These are sometimes known as Goldilocks conditions – just right for maintaining water that life, as we understand it, can use.
Over a billion cubic kilometres of water deposited in intergalactic space would experience zero gravity in an almost perfect vacuum at a temperature of -270.3°C (-454.5°F). Under these conditions, it would explode: freezing and subliming (vaporising) at the same time. Eventually, the individual molecules of water would end up about a metre apart, as are most particles in intergalactic space.
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