The earth is so big, it is certainly impossible to invent a scale that weighs the whole earth. How did cavendish weigh the earth?
After Newton put forward the law of gravity, he and many scientists at that time found that the mass of the earth could be calculated by using the formula of gravity.
Before this, scientists have proposed a method to calculate the weight of the earth.
Because radius of the earth can calculate the volume of the earth as 1.08× 102 1 m3, if we know the density of the earth, we can use "mass = density× volume" to calculate the mass of the earth. The idea looks easy, but it doesn't work in practice. Because scientists have found that the density of substances that make up the earth is different and the proportion of substances in the whole earth is different, it is impossible to know exactly what the average density of the whole earth is. So, at that time, some scientists asserted that man could never know the weight of the earth.
Newton's discovery of the law of universal gravitation gave this work of weighing the earth another ray of hope.
First of all, Newton analyzed the following numerical values: one is the gravity of the earth to a known mass, which is actually the gravity of an object and is easy to measure; One is the distance between the earth and the object, which can be replaced by radius of the earth approximation; Another key value is the gravitational constant g, which was unknown at that time, but can be obtained by directly measuring the gravitational force between two objects with known mass on the ground. (It turns out that Mr. Newton didn't know the value of G, so who measured the value of G? )
In order to directly measure the gravity between two objects, Newton carefully designed several experiments, but the gravity between general objects is very small and it is impossible to measure it in experiments.
Later, Newton had to express his disappointment. If he wanted to use gravity to calculate the mass of the earth, he would never get the result.
1727 after Newton's death, some scientists continued to study this problem.
1750, French scientist Bougle (1698 ~ 1758) came all the way to Ecuador in South America. He climbed the steep Qin Boraso, and a long rope hung down the cliff with a shot put tied to its lower end.
He wanted to measure the distance of the shot put deviating from the gravity of the mountain under the vertical line first, and then calculate the mass of the mountain according to the density and volume of the mountain, and then calculate the gravitational constant g, but because the gravity is too small, the distance from the vertical line can hardly be measured, and even if it is measured, it is very inaccurate. Bougle's experiment was still unsuccessful. (See Famous Experiments in the Development of Classical Physics, edited by Shen, and, Press, p57~80 (Determination of Gravity Constant)).
The first person who successfully "weighed" the weight of the earth in the world was British physicist cavendish (1731~1810). How did he succeed?
Cavendish has a reputation as a "freak" in the scientific community. He is the descendant of several generations of British bureaucrats and his family is very rich. However, he wore old clothes and was untidy. There is hardly a piece of clothing that doesn't lose its button. He set up a laboratory and a library at home. Although he is in disorder, the library is in good order. A large number of books are numbered in different categories, no matter who borrows them or even who reads them himself, they must be registered.
Cavendish became interested in "weighing" the earth when he was still in college.
He carefully analyzed the reasons for the failure of predecessors, and thought that the main reason was unscientific experimental methods. In order to make a breakthrough in this problem, new experimental methods must be adopted.
1750, there was a professor named John Michel at Cambridge University. When he was studying magnetism, he observed a very weak force change in a clever way. When cavendish got the news, he immediately went to the door for advice.
Professor Michel introduced the experimental method to young Cavendish. He hung a bar magnet horizontally with a time line, and then forced a magnet to attract it. At this time, the time line is distorted, and the magnitude of magnetic attraction is clearly visible. Cavendish was greatly inspired by this, and he thought, can we use this method to measure the weak gravity between two objects?
Shortly after returning from Michelle, cavendish copied a set of devices: put a small shot put at both ends of a slender rod to make something similar to a dumbbell; Then hang dumbbells horizontally from the middle with timely steel wires. He believes that if two larger shot puts are moved closer to two smaller shot puts, according to the law of universal gravitation, the "dumbbell" will swing for a while under the action of gravity, and the time line will also be twisted accordingly. At this time, as long as the torsion degree of the time line is measured, the gravity can be further calculated. (See Famous Experiments in the Development of Classical Physics, edited by Shen, and, Press, p57~80 (Determination of Gravity Constant)).
This inference is valid in theory, but cavendish tried many times and failed.
What is the reason? Or because the gravity is too weak, for example, when two one-kilogram shot puts are ten centimeters apart, the gravity between them is only one millionth of a gram, and even the dust in the air can interfere with the measurement accuracy. Therefore, under the conditions at that time, if we observe and determine the subtle changes of silk with the naked eye, the experiment will inevitably fail.
Time has passed for decades without knowing it.
1785, Coulomb put forward Coulomb's law (note 1). Cavendish (1731~1810) was inspired by the invention of coulomb torsion meter. But gravity can't be measured by Coulomb method, because gravity is nearly 40 times smaller than electricity, and the instrument needs to be more precise!
Cavendish thought about how to enlarge the tiny twist of the silk. But it never worked.
Until one day in 1798, cavendish attended a meeting of the royal society. On the way, he saw several children playing an interesting game:
Each of them has a small mirror in his hand to reflect sunlight and play with each other. As long as the small mirror rotates slightly, the position of the distant light spot will change greatly.
Seeing this, suddenly an idea flashed through his mind, and he remembered the problem of twisting and amplifying the timely silk. Can't it be solved with the help of a small mirror? Unable to restrain his excitement, he turned and ran back to the laboratory to improve the experimental device again. He fixed a small mirror on the timely silk and irradiated it with a beam of light. The light is reflected by a small mirror and shines on a scale. In this way, as long as the time line is slightly distorted, the reflected light will be clearly displayed on the scale. Cavendish called this device a "torsion scale".
Torsion scales are highly sensitive. Using this device, cavendish finally successfully measured the gravitational constant g as (6.754 0.04 1) × 10-8 dyne cm2/g 2, which is the same as the modern value (6.6732 0.003 1 )× 650. According to the gravitational constant, cavendish further calculated that the weight of the earth was 5.976× 1024 kg.
Cavendish began to ask this question when he was a teenager in college. Until 1798, he "weighed" the earth by experiment for fifty years. It has been about 100 years since Newton put forward the law of universal gravitation.