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Asked by vishutha to Daniel, Jon, Louise, Sharon, Zoe on 18 Jun 2010 in Categories: General.
Question: WHAT IS THE MAXIUMUM WEIGHT THE EARTH COULD BE?
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Jon Copley answered on 14 Jun 2010:
Hmmm… to answer this one, I think it’s worth looking about the difference between “weight” and “mass”.
“Mass” is a measure of how easy (or difficult) it is to change the motion of an object by exerting a force on it. But “weight” is the force created when gravity pulls an object.
Here on Earth, “mass” and “weight” often mean the same thing, because everything gets pulled by the Earth’s gravity. But to define a “weight” for the Earth, you’d need to consider the force created by the gravity of another object, such as the Moon or the Sun. I’ve no idea what the answer would be there.
However, people have estimated the “mass” of the Earth – and it’s roughly 6,000,000,000,000,000,000,000,000 kilograms. That’s from knowing the structure of the Earth and the density of the materials that make up its different layers.
As for the maximum possible mass of the Earth – well, if you made a sphere the same size as the Earth out of the most dense substance in the Universe (the stuff that neutron stars are made of, which is called “neutronium”), it would have a mass of around 4 x 10^38 kg (that’s a 4 with 38 zeros after it, if I’ve done my sums right!).
But I think it would then inevitably collapse under its own gravity to form a black hole (it would be even more massive than the “supermassive” black hole that astronomers have detected at the centre of our Milky Way galaxy). So I’m afraid it wouldn’t last for long…
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Louise Dash answered on 14 Jun 2010:
Hmm – there’s a few ways of looking at this question! There’s a difference between “weight” (which is the force exerted on an object by the earth’s gravitational field) and “mass” (which is a fundamental property of an object), so I’ll assume you mean mass.
(Watch out, there’s some maths coming, which I hope is OK! It’s not too easy to write maths in plain text so I hope you can understand what I’ve written :))
The best way to calculate the mass of the earth is to use Newton’s law of gravitation, which states that the force between two objects due to gravity, F = (GmM)/r^2, where m and M are the masses of the two objects, G is the gravitational constant (= 6.67×10^-11 m^3 kg^-1 s^-2) and r is the distance between the two objects.
If we take an object whose mass we know, like a 1kg sphere, and measure the force F if we drop it on the ground, we can work out the mass of the earth! If we put m = 1kg, then the force F will be this mass times the acceleration, i.e. 1 x 9.8 kg m s^-2. If we know the radius of the earth (and we do, it’s 6371 km) we can now plug all these values into Newton’s equation and solve for M, and you should get:
6×10^24 = 6,000,000,000,000,000,000,000,000 kg
(That’s heavy! :D)
As to the maximum mass the earth could have, if it was substantially different to what we showed above, then the orbit of the earth around the sun would be different too and so life on earth would be very different (or even non-existent!) so I think I’d say that the mass that it has is the maximum mass, otherwise it wouldn’t be our earth any more! I hope that’s OK as an answer.
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Sharon Sneddon answered on 15 Jun 2010:
Good question!!! I have no idea!! I know that the earths mass is continually increasing but I’ve no idea how heavy it could get, I’m hoping that one of the other scientists will know!!’
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