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How much does the Earth weigh?

Does the Earth's mass change when we dig stuff up or send a rocket into space? Dr Karl puts planet Earth on the scales.

Blue marble Australia

Earth is not quite a 100 per cent closed system (Source: NASA)

It's a very reasonable question. You see something enormous that we humans have built (say, a huge passenger ship, or a gigantic hydroelectric dam) and the question just naturally pops into your head: "How much weight did we just add to the planet Earth?"

The answer is none at all. In fact, rather surprisingly, the Earth is getting lighter all the time.

So, first of all, how do you weigh a planet?

Luckily, Isaac Newton devised a formula that allows you to work out the weight of the planet, once you work out the force of attraction between two other bodies (such as two lead balls in a lab).

Newton never thought it would be possible to actually measure this attractive force between two other bodies with an experiment on Earth. That's because this tiny attraction between the two lead balls would be swamped by the absolutely gigantic attraction caused by the huge mass of our planet.

However, Isaac Newton didn't account for the cleverness of the Reverend John Mitchell.

Mitchell lived in the 1700s, and was not only the "Father of Seismology", but also was the first person to make a reasonable estimate of the distance to another star other than our Sun. He was also the first person to float the possibility of black holes.

In the early 1780s, Mitchell devised and built an experiment to measure the attraction between two lead balls. He was a busy man, and died before he could use his apparatus, which upon his death, passed to Henry Cavendish.

Cavendish rebuilt the apparatus with some minor improvements, and successfully measured the force of attraction between two lead balls that weighed 0.73 kilograms and 158 kilograms. He then plugged his results into Newton's formula and came up with a very close estimate for the weight of the Earth — and this was back in 1798. He was within about one per cent of the true result, which is about six billion trillion tonnes.

So, when you build something really big, does the Earth get heavier? No. All you're doing is just shifting atoms from one location on the Earth to another location. It's like, for example, when you build a giant ship, you just shift iron ore from Western Australia to blast furnaces in Korea to shipyards somewhere else. Overall, nothing gets added to or taken away from our planet, because the Earth functions almost as a perfectly closed system.

But it's not quite a 100 per cent closed system. There are inputs, and there are outputs. There's stuff falling out of the sky, and there's junk going up, such as all those space craft we launch into space.

So let's do all the major numbers.

The Earth gains about 40,000 tonnes of dust each year. A decent meteor storm can add a tonne in a single go. But the vast majority of this dust is stuff left over from when our solar system was formed. The gravitational field of our Earth just sucks it in.

What about losses?

Each year about 95,000 tonnes of hydrogen and 1600 tonnes of helium leave the Earth for outer space. They're gone forever.

As another loss, what about the rockets that we send into the space? After all, the Saturn V that took us to the Moon weighed just under 3000 tonnes on the launch pad. But the overwhelming majority of that fell back to Earth. If you do the numbers, it works out that each year about 65 tonnes of payload (very expensive payload) leave the Earth forever.

So basically each year the Earth gains about 40,000 tonnes, and loses about 95,000 tonnes, which gives us an overall loss of (ballpark figure) of about 55,000 tonnes. If the average weight of a human on our planet is about 62 kilograms, that works out to about 890,000 people, or about half the weight of one of those giant passenger liners, or a percentage you would write down as about 0.000000000000001 per cent of the mass of our planet.

But it's not enough to translate into a lucrative best seller on the massive weight loss industry charts.

Tags: planets-and-asteroids, physics

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Published 19 June 2013

© 2015 Karl S. Kruszelnicki Pty Ltd