## Wednesday, September 23, 2015

### How much water is actually there on the Earth?

Picture this.

A recent post that has gone viral claims that this is what the Earth looks like "without water". That is, if some alien water-reallocation company--call them Spacetlé, just for laughs--were to zoom over to our fair planet tomorrow and suck out all the water from our oceans and leave us, literally, high and dry, this is what we would be standing on. Rather lumpy, ain't it, a dry Earth?

'cept it ain't correct. This is definitely not what the Earth looks like if Spacetlé were to suck it dry tomorrow. This is what the Earth looks like if it was redrawn so that, at every point on its surface, the net local gravitational field were to point perpendicular to the ground at the point. In other words, this is the Earth's geoid. Now, you might say, waittaminit! I know that at Earth's gravity is trying to pull me towards its centre everywhere on Earth. Right? Right?

Well, not quite. You see, that would be exactly correct if the Earth were a homogeneous uniform mass sphere. The gravitational field would indeed point radially inwards at each point on the surface, and you would indeed be pulled towards the very centre of the Earth. However, the Earth is not completely spherical. And it isn't completely homogeneous. You see, Earth's gravity comes from its mass {d-uh}, and depends on how that mass is distributed across its volume {hu-d; that is like, a retort to d-uh...saying it backwards, y'know}. Since the mass of the Earth isn't uniformly distributed, with some parts being denser than others, the gravitational field of the planet is also not uniform, and tends to point away from the centre at most places. Of course, the deviation is probably too small on the scale of the Earth to really matter too much.

So what is the cute colourful potato doing at the top of this post, merrily spinning away? If it isn't the Earth sans its water, what is it? I think I'll let Bad Astronomer Phil Plait explain that bit.

You might ask, what am I doing basically repeating the same thing that Plait has said so much more clearly in his post? Why does the world need another near-clone blog post on the same topic? Well, that is because I want to talk about something else. As I was reading Plait's post, a second figure caught my eye...and my attention. It is a picture of the Earth without its water. For real, this time, that is if Spacetlé had really succeeded.

 The large drop is all the water the Earth has
The graphic is originally from this article. The large drop of water is all the water that Earth has. All of it. The smaller one is the total fresh water we have, whereas the smallest, almost invisible, one is the water in lakes and rivers.

Not a lot, is it?

Well, no, not if you compare it to the Earth. But do keep in mind that the diameter of the big drop is almost 1400 km. Which means there is total of almost 1.4 * 10^18 cubic meter, or about 1.4 * 10^21 litres of water on Earth. That is indeed a lot from a human scale. However, most of this water is not drinkable. The smaller sphere can be drunk, but most of it can't be obtained easily by humans. What we can drink is the smallest sphere, which has a diameter of a mere 56 km. Which translates to 733 million billion litres of water (7.33 * 10^14 cu-m). Given that, say, an average person drinks about four litres of water per day, and there are 7 billion people on the planet, about 28 billion litres of water is drunk per day. That is about 10000 billion litres per year. At this rate, we would have drunk all the water the Earth has right now in about 73 thousand years. Of course, it doesn't quite work that way. But hey, fun exercise. If I did it right. Which I sincerely doubt.

#### 2 comments:

1. May be this will prompt the people to save some of the drinkable water on the planet ☺ the little drop doesn't look like much does it ? Also the population is only going to increase by the day !

1. That really tiny drop ain't much at all. Let's hope people to start saving up.