Experiment 'weighing' the Earth more than 200 years ago

In 1798, scientist Henry Cavendish conducted experiments with spheres in a dark, sealed room, and calculated an approximate density of the Earth.

Earth and Moon. Photo: NASA — Earth and Moon. Photo: *NASA*

In the late 1600s, scientist Isaac Newton proposed the law of universal gravitation: Every particle attracts every other particle in the universe with a force (F) determined by their mass (M) and the square of the distance between the centers of the objects (R). With G being the gravitational constant, the equation for this law is: F = G(M1xM2/R ² ).

Thus, if one knows the mass of one of the objects and the other information in the equation, one can calculate the mass of the second object. Assuming a person has a known mass, this person can calculate the mass of the Earth if he knows how far he is from the center of the Earth. The problem is that in Newton's time, scientists had not yet determined G, so weighing the Earth was impossible.

Knowing the mass and density of the Earth would be extremely useful to astronomers because it would help them calculate the masses and densities of other objects in the Solar System. In 1772, the Royal Society of London established the "Committee on Gravitation" to study this.

In 1774, a group of experts attempted to measure the average density of the Earth through Schiehallion Mountain in Scotland. They found that the massive mass of Schiehallion attracted pendulums towards it. So they calculated the density of the Earth by measuring the motion of the pendulum and surveying the mountain. However, this measurement was not very accurate.

Illustration of scientist Henry Cavendish and his Earth weighing experiment. Photo: Wikimedia — Illustration of scientist Henry Cavendish and his "weighing" Earth experiment. Photo: *Wikimedia*

The geologist Reverend John Michell also studied the mass of the Earth but was unable to complete it before his death. The English scientist Henry Cavendish used Michell's equipment to perform the experiment.

He constructed a large dumbbell, with two 5cm wide lead spheres attached to the ends of a 183cm long wooden rod. The rod was suspended from a string in the center and allowed to rotate freely. Then a second dumbbell with two 30cm wide lead spheres, weighing 159kg each, was brought close to the first dumbbell so that the larger spheres attracted the smaller ones, exerting a slight force on the suspended rod. Cavendish watched the rod oscillate for many hours.

The gravitational attraction between the spheres was so weak that even the slightest air current could have ruined the delicate experiment. Cavendish placed the apparatus in a sealed chamber to avoid outside air currents. He used a telescope to observe the experiment through a window and set up a pulley system to move the weights from outside. The chamber was kept dark to avoid temperature differences between different parts of the chamber that could affect the experiment.

In June 1798, Cavendish published his results in the journal Transactions of the Royal Society in a study entitled "Experiments on the Determination of the Density of the Earth". He presented that the density of the Earth was 5.48 times that of water, or 5.48 g/cm3, quite close to the modern value of 5.51 g/cm3.

Cavendish's experiment was important not only for measuring the density and mass of the Earth (estimated at 5.974 quadrillion kilograms), but also for demonstrating that Newton's law of universal gravitation also holds at scales much smaller than the scale of the Solar System. Since the late 19th century, improved versions of Cavendish's experiment have been used to determine G.

Thu Thao (According to IFL Science , APS )

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