Weighing the Earth
More than a hundred years elapsed between Newton's publication of his law of universal gravitation in Principia Mathematica and its experimental verification in the laboratory. The experimental verification of a universal attractive force between two objects in a laboratory is a difficult experiment to perform because gravity is so weak. To give an example, the attractive force between two lead balls, each a foot in diameter and weighing nearly 400 pounds, is only two one hundred thousandths of an ounce (.00002 oz.) when the centers of the balls are separated from each other by 2 feet. Detection and measurement of such microscopic attractive forces between objects themselves weighing nearly half a ton creates an interesting challenge for the experimenter.
The first successful measurement of gravity in the laboratory was performed by Henry Cavendish, a wealthy recluse famous for his eccentric behavior. However, his scientific work was first rate. His early studies on "Factitious Airs" indicated that hydrogen (which he called "inflammable air") when burned with oxygen ("dephlogisticated air") forms water, the weight of the water being equal to the weight of the gases used up. (This, incidentally, is where the water in ice fog comes from: gasoline and fuel oil contain hydrogen.) But Cavendish is most noted for the gravity work he performed with a sensitive torsion balance and described in a paper published in 1798. Considering the extreme difficulty of the measurement, it is indeed impressive that Cavendish was able to measure the "gravitational constant" to within about 1% of its modern accepted value.
The torsion (twisting) balance Cavendish used for his measurement was similar to one that we constructed at the University of Alaska. It operates as follows: a horizontal rod with small test weights on each end is hung at its center by a thin metal wire: the torsion fiber. When an external mass (we used an apple) is brought up close to one of the tiny weights, the gravitational attraction causes the fiber to twist slightly. In our experiment the mass "falls" into the apple, rather than the other way around, when Newton observed an apple falling into the earth.
The Cavendish torsion balance experiment can be used to determine the weight of the earth by comparing the attraction of the tiny test mass first to the earth and then to the apple. We find by this elegant method that the earth weighs in at six thousand six hundred billion billion tons (6,000,000,000,000,000,000,000,000 kilograms).
An interesting point is that the earth weighs about twice what it should if it were made of rock. The reason for the discrepancy is that the planet has a heavy nickel-iron core.
