Is It Possible for Archimedes to Lift The Earth?

Arhimedes Trying to Lift The Earth“I would lift the earth if I had a point of support” that is a saying of legendary Archimedes, the genius of antiquity who discovered the laws of the lever. He wrote this claim to his friend, King Hiero (Some call it “King Geiron”) of Syracuse. He added that if there be another earth in the space he would go there to prove his claim!

Archimedes knew that even the weakest of force could lift the weightiest of an object by using a lever. One had only to apply this weakest force to the lever’s longer arm and that’s what would make the shorter one to act on the weightiest load. He therefore thought that by pressing with his hand on the extremely long arm of the lever he would be able to lift a weight which in this case is equivalent to that of the mass of the earth.

Archimedes might be right about his laws of the lever but the problem was that in the times of antiquity nobody knew the mass of the earth, and neither did Archimedes! If only he knew the mass of the earth, Archimedes would be likely to eat back his words. Imagine for a moment that he had at his disposal another earth and also the point of support he looked for. Further imagine that he was even able to manufacture a superlong lever that extended over  a great great distance in the space required. I wonder if you can figure out the time he would need to lift a load as massive as the earth, by at least a centimetre? He would need 30,000,000,000,000 years!!

Today scientists know the Earth’s mass. The earth possesses the mass of 6,000,000,000,000,000,000,000 metric tons or tonnes. Suppose Archimedes could lift 60 kilos directly, to lift the earth he would need a lever with a long arm that would be longer than the shorter arm by:

100,000,000,000,000,000,000,000 times! (that is \frac{6 \times 10^{24} \: kg}{60 \: kg} ).

You can easily figure it out that to have the end of the short arm rise by a centimetre, the other end must delineate through space the huge arc of

1,000,000,000,000,000,000 km!! ( that is  1 \: cm \: \times 100,000,000,000,000,000,000 \: times )

That is an unimaginable distance which Archimedes would have had to push the lever to lift the earth by just one centimetre! As a comparison the earth-sun distance is “only” 150,000,000 km apart. A tiny figure compared to that of the huge arc would Archimedes make. So the next question would be how much time would he need? Presuming he could have lifted 60 kilos one metre in one second – the work of almost one horsepower and of course naturally a man could only work much less than one horsepower! – to lift the earth by a centimetre, he would even need

1,000,000,000,000,000,000,000 seconds!! (that is  \frac{6 \times 10^{24} \: kg}{60 \:kg} \times \frac{1\: cm}{100 \:cm} \times 1 \: second )

For those who like to do simple arithmetic problems it is not hard to convert that figure above into the unit year which is equivalent to about 30 million million years! As a comparison scientists predict that our solar system would not last longer than approximately 10 billion years from the cradle to the grave. So, even if Archimedes lived past 100 years he would not have lifted the earth by much as even the thinnest of hairs. His effort would be so-called worthless since he could only lift the earth by an unnoticeable displacement in the eyes of the crowd. Even if he supposed to be able to zap in the speed of light – the nature’s fastest – he would successfully have lifted the earth by a centimetre only after ten million  (10,000,000) years of pushing! Phew!! 🙂

11 responses to “Is It Possible for Archimedes to Lift The Earth?

  1. Hi Yari,
    Very interesting post, although arithmetic is not my cup of tea (lol).
    Happy Earth Day.

  2. by putting the rationality aspect aside, i do really like this statement 😛 i read it in an encyclopedia several years ago, but i carved it in my mind

    some bombastic words would make someone seemed to be powerful and silly at once =))

    • Archimedes looked silly to the present-day science, but in the antiquity nobody knew the mass of the earth, that’s why Archimedes made a hyperbolic claim that he could lift the earth by using a lever. If only he knew the mass of the earth I’m not so sure if he would still make such claim. And probably he did not realise either that if one can gain a mechanical advantage it would be coupled with losses of other resources or dimensions, in this case distance (displacement) thus time would be lost, not to mention economic loss…. 😉

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  4. Although theoretically possible but in practice can be categorized into a mission impossible.

    • Of course it is always possible to carry it out in reality, but in the end Archimedes would only have lifted the earth by not greater than 1 angstrom, an unnoticeable displacement to the unaided eyes, an effort not worth trying…

  5. Maybe this is called Archimedes’ Postulate .. In theory it is true, but it is impossible to prove. Just as the theory that the temperature of the sun he reaches 6000 C, who is able to calculate the temperature of the sun? whether there is material that can survive until the temperature of it?

    • You have a point. No one can “close-up” with the sun.

    • Actually there is nothing wrong with Archimedes’ laws of lever. It proves fine. We do not need to lift an object as massive as the earth to see if the laws are working fine or not. The part on his ability to lift the earth is the mistake. That’s because he did not know correctly the mass of the earth, if only he knew the correct mass of the earth I believe he would not make a claim like that though he did not have to revise his laws of lever because the laws are working well!!

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