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Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes

How long would that lever have to be?

That is to say, how long a lever would be needed on Earth, to lift a sphere with the mass of Earth if a human of average size were to sit on the other side of the lever?

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    $\begingroup$ I'm pretty sure Archimedes was speaking metaphorically. From the standpoint of actual physics, this is not a well defined question, so there's really no meaningful answer to give. (I can reopen this if other people feel that there is a meaningful answer, or if you can make it more specific.) $\endgroup$
    – David Z
    Commented Feb 8, 2011 at 21:51
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    $\begingroup$ While I understand that the quote was metaphorical, a long lever would reduce the amount of energy needed to lift an object, Would it not? To raise a sphere with the mass of Earth how long a lever would be needed such that a human of average strength could lift it? $\endgroup$
    – Adam
    Commented Feb 8, 2011 at 21:59
  • $\begingroup$ That's much better :) I've reopened the question. $\endgroup$
    – David Z
    Commented Feb 8, 2011 at 22:04
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    $\begingroup$ Recent XKCD gives alternative version: xkcd.com/857 $\endgroup$
    – gigacyan
    Commented Feb 9, 2011 at 9:50
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    $\begingroup$ The statement that has come down is:Δος μοι πα στω και ταν γαν κινησω, which translates : Give me where to stand, and I can move the earth. $\endgroup$
    – anna v
    Commented Feb 9, 2011 at 14:27

4 Answers 4

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The mass of Earth is $6\times10^{24}kg$. If Archimedes can lift 60 kg, he would need a lever with an arm ratio of $10^{23}:1$. So if the short arm is one meter long, the lever length will be $10^{23}$ meters plus one. Also, note that he would have to push the lever for $10^{20}$ meters to shift the Earth just by one millimeter.

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    $\begingroup$ You are off by a factor of two for a cute reason. If the weight weighed as much as Earth, Earth would get pushed down as much as the weight would go up. $\endgroup$
    – Mark Eichenlaub
    Commented Feb 8, 2011 at 22:19
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    $\begingroup$ I'd prefer a lever with 10⁻23 meters and 1 meter :=) Hopefully Adam has understood that the length is irrelevant, only ratio of the ends counts. $\endgroup$
    – Georg
    Commented Feb 8, 2011 at 22:19
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    $\begingroup$ @Mark: at these orders of magnitude it is excusable to be wrong by a factor of 2 :) $\endgroup$
    – gigacyan
    Commented Feb 8, 2011 at 22:26
  • $\begingroup$ @Giga I agree. I just thought it was a nice point to include in terms of physics. $\endgroup$
    – Mark Eichenlaub
    Commented Feb 8, 2011 at 22:29
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    $\begingroup$ This calculation is straight forward, but it caries an implicit assumption that the whole Earth lies "near the Earth's surface" as that is the condition needed to use the usual value of $g$. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 9, 2011 at 0:27
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In addition to @gigacyan answer: length of the lever, as he said, $10^{23}$ meters or 10 million light years. For comparison - Andromeda Galaxy is the nearest spiral galaxy to the Milky Way approximately 2.5 million light-years away. It takes 10 thousand years to push the lever for $10^{20}$ meters at the speed of light.

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Technically any leaver that lifts an object away from the earth also lifts the earth away from said object.

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    $\begingroup$ A very physical answer :) $\endgroup$
    – user20499
    Commented Jun 16, 2014 at 7:04
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The amount needed to lift the Earth is negligible. Move the lever a modest amount 3 or 4 feet and the Earth would be moved the equivalent of an electron; not much but still moved.

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