Earth Weighing Experiment

In June 1798, the English chemist and physicist Henry Cavendish successfully calculated the mass of the Earth through the experiment measuring the constant of gravity (G). Scientists call this experiment the Cavendish Experiment or the Earth weighing experiment.

Henry Cavendish (1731-1810) was a scientist with a rather shy and eccentric personality. The clothes he usually wears are clothes with a style that is about 50 years old. He does not like to associate with strangers, especially women. He often went for a walk at night so that the neighbors could not see him, and even built a staircase in his house to avoid meeting the servants on the stairs.

Contrary to these strange personalities, Cavendish is a great scientist. He was capable of making extremely precise experiments and measurements, something impatient people could not do. He enjoys making and repairing scientific tools, and is always trying to improve them. He worked very carefully, never feeling satisfied when the job was completed.

Like many scientists at the time, Cavendish was born into an aristocratic family, so he inherited a large enough talent to comfortably conduct chemistry and physics experiments. He turned most of his house into a laboratory, leaving only a small part of the house for living space.

Among Cavendish's works, the most prominent was the experiment that helped him determine the mass of the Earth. This experiment is known today as the 'Cavendish Experiment'.

Newton published the law of universal gravitation in 1687, but he did not make any attempt to determine the gravitation constant (G) or the mass of the Earth. By the 1700s, astronomers wanted to determine the mass of the Earth to calculate the masses of other planets in the solar system. In addition, when the Americas were newly discovered and colonized, world cartographers needed to know the size and mass of the Earth. In 1763, two British surveyors Charles Mason and Jeremiah Dixon were hired to survey and determine the border between the two colonies of Maryland and Pennsylvania in North America. Cavendish looked at how accurate Mason and Dixon's measurements were. He noticed that the Allegheny Mountains exerted a slight drag on their survey instruments due to the gravitational pull. This may affect the measurement,

In 1772, the Royal Society of England established a commission to measure the mass of the Earth. In the field of physics, knowing the gravitational constant (G), we can easily calculate the mass of the Earth according to the following formula: M=gR2/G (where: M is the mass of the Earth, g is the acceleration due to gravity at the Earth's surface with a value of 9.8 m/s2, R is the radius of the Earth equal to 6,384 km). To calculate the density of the Earth, simply divide the mass of the Earth by the volume of the Earth.

So the problem is how to calculate the exact value of the gravitational constant (G). Many people have proposed the idea of ​​finding a symmetrically shaped mountain, and measuring by how many degrees it deflects the plumb [a small weight attached to the end of a soft rope] by an angle. The impact of the mountain on the plumb is not great due to the very weak gravitational pull. Committee members conducted the experiment using a large mountain in Scotland. After measuring the deflection angle, they easily calculated the value of G, from which the density of the Earth was equal to 4.5 that of water. However, Cavendish believes that this experiment is prone to error and inaccurate results.

The experiment to determine the gravitation constant (G) based on measuring the gravitational force between objects in the laboratory was first proposed by geologist Reverend John Michell, who built torsion springs to measure torque was precisely small, but it was lost in 1793 before his experiment could be performed. The torsion spring was then transferred to Francis John Hyde Wollaston, and then to Cavendish.

Cavendish thought about Michell's method of measurement for a long time. It was not until 1797 that he began to perform his own experiments. He realized that Michell's previous experimental setup was not precise enough to measure the gravitational force between two small metal spheres, so he sought to improve it.

Cavendish attached two metal balls to the ends of a 1.8m-long wooden stick. He used a thin rope to hang the whole system up and keep the wooden bar horizontal. Then he used two lead balls, each weighing 159 kg, to move closer to the two marbles at the ends of the wooden stick. To avoid the wind blowing and causing experimental errors, he placed the system in an airtight room and observed it with a telescope through a window. The room was also kept dark to avoid temperature differences in different parts of the room, affecting the experimental results.

The force of gravity exerted by the two lead balls on the two balls causes the wooden stick to rotate by a small angle. Cavendish measured this angle with a telescope and calculated the moment of force acting on the torsion spring, from which the gravitational constant was calculated based on the mass of the lead ball and the ball.

After determining the value of the gravitational constant (G) and the acceleration due to gravity (g) on ​​the Earth's surface, Cavendish calculated the mass of the Earth to be 6×1024 kg. Cavendish detailed the results of his experiments in a 57-page paper published in the Proceedings of the Royal Society in June 1798. This result gave Cavendish's experiment another name, the Earth Weighing Experiment. The measurement of the Earth's mass also allows the mass of the Moon and other celestial bodies in the solar system to be inferred through the laws of mechanics and the law of universal gravitation.

The Cavendish experiment was the first to accurately measure the value of the constant of gravity (G), based on the principle of measuring the gravitational force between two mass carriers. Many other scientists repeated Cavendish's measurement, but none came up with any improvement over the experiment he established.

Today, instructors often have students majoring in physics repeat Cavendish's experiment when they want to measure the G value. Cavendish's name is given to the Hernry Cavendish Laboratory at the University of Cambridge, one of the few The most modern research laboratory in the UK.

More on Cavendish Experiment

The device built by Cavendish was a torsion scale made of a 1.8 m long wooden rod suspended horizontally on a string, with two fuse balls 51 mm in diameter and 0.73 kg in weight attached to each end. Then two other balls of lead, 300 mm in diameter and 158 kg in weight, were placed near the small spheres, the chamber holding them was 225 mm and held in place by a separate suspension. Accordingly, this experiment will measure the fuzzy gravitational attraction between the small spheres and the larger spheres.

Two large spheres are placed on alternating sides of the horizontal wooden bar of the scale. Their mutual attraction to the small spheres causes the arm to rotate and twist the rope supporting the arm. The arm stops rotating when it reaches an angle where the rope's torsion force equals the combined attraction between the large and small fuses. By measuring the angle of the stick and knowing the torsion force (torque) of the string at a given angle, Cavendish was able to determine the force between pairs of masses. Since the Earth's gravity acting on the small sphere can be directly measured by weighing it, the ratio of the two forces allows the Earth's specific gravity to be calculated using the Law of Gravity. by Newton.