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Cavendish, 1798

How Anyone Weighed the Earth

You cannot put a planet on scales. You can watch it tug at two lead balls in a shed.

1 You cannotweigh aplanet2 Two leadballsattract3 The pull isalmost toosmall to see4 Measure it:the massfollows
Measure the smallest gravity there is, and you get the biggest.

  1. Step 1 of 5

    Everything pulls on everything — very, very weakly.

    Earth pulling on you Obvious. You cannotignore it.You pulling on a friend Real, and roughly theweight of onebacterium

    Gravity between everyday objects is real but absurdly feeble. Two people standing a metre apart pull on each other with about the weight of a bacterium. Nobody had ever managed to detect it.

  2. Step 2 of 5

    The trick was to make the tiny force twist something.

    A fine wire,easily twisted Two small ballson a roda force too weak to push can still twist

    Cavendish hung a rod with two small lead balls on its ends from a fine wire. A wire like that will twist under almost nothing — so a force too small to push anything can still turn it, and the turn is easy to see.

  3. Step 3 of 5

    Then he brought two enormous balls alongside.

    Big balls to one side The rod twiststowards themBig balls moved round The rod twists backthe other way
    Swapping the sides proves the movement is gravity, not drift.

    Two lead spheres weighing 158 kilograms each were moved close to the small ones. Their gravity tugged the small balls sideways, the wire twisted, and the rod slowly turned. The whole movement was a few millimetres.

  4. Step 4 of 5

    Everything else had to be kept out.

    Sealed shed, no aircurrentsWatched through atelescopeWorked by rope fromoutsideEven body heat wouldswamp it
    He could not be in the room. His own warmth was larger than the thing he was measuring.

    Air currents and a person's body heat would swamp the effect entirely. So the apparatus was sealed in a shed, and Cavendish observed the rod from outside through a telescope, working the mechanism with ropes and pulleys.

  5. Step 5 of 5

    From that twist, the mass of the planet.

    Cavendish's answer, 17985.45 g/cm³average densityThe modern value5.51 g/cm³

    Knowing how hard two known masses pull at a known distance tells you the strength of gravity itself. And once you know that, Earth's own pull on a falling apple gives away Earth's mass. His answer was within one per cent of today's.

    He never called it weighing the Earth. His paper is titled as an experiment to determine the density of the Earth, which is what he actually measured.

The short version

Earth was weighed by measuring how hard two lead balls pull on each other, in a sealed shed, watched through a telescope.

Try it yourself

Hang a light object on a long thread and blow at it gently. A tiny sideways force makes a visible turn — that is the whole design.

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