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# I Didn't Know That...

September 24, 1998

Q: How did scientists measure the mass of the Earth?

A: They didn't actually measure it. Instead, they calculated it using Sir Isaac Newton's universal law of gravitation.

In the early 18th century, Newton concluded that any two bodies in the universe attract each other with a force that depends on each of their masses, the distance between them, and a constant called the universal gravitational constant or G.

Newton could not calculate the Earth's weight, however, because he didn't know the value of G.

That was not determined until 1798, when English scientist Henry Cavendish devised an ingenious experiment with a torsion balance.

Cavendish suspended a light rod at the middle by a delicate wire about a yard long. At each end of the rod were 2-inch lead balls. First, he applied a tiny, known amount of force to the balls and determined how much that twisted the wire.

In a second experiment, he measured the gravitation attraction between lead balls using the twisting of the wire as a gauge. In a room with no air currents, he placed two 8-inch lead balls close to the smaller balls.

By measuring how much the wire was twisted by the attraction between the balls, he was able to calculate the value of G, obtaining a value very close to the best modern determination, which is:

0.0000000000667 m3/kg-sec2 . Plugging that into the equation, he calculated the weight of the Earth as 6,000,000,000,000,000,000,000,000 kilograms, or 13,200,000,000,000,000,000,000,000 pounds.

(BEGIN TEXT OF INFOBOX / INFOGRAPHIC)

Finding G Constant

Cavendish's 1798 experiment

A torsion balance is used to measure the gravitational attraction between lead balls.

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