This article is from the WeChat public account: China Science and Technology Expo (ID: kepubolan) , author: Chen Xing, from the cover: vision China
When it comes to measuring the “weight” of the earth, do we really have such a par? of course not! We are not going to “weigh” the mass of the earth directly, because there are no such large scales for us to use. So, seriously, how exactly is Earth’s mass obtained?
The direct benefit of the quality of the earth is that you can launch the rocket, because only by knowing the mass of the earth can we accurately determine how much fuel is needed to launch the rocket, the calculation of the orbit of the rocket after it is lifted off, and so on. Take the “Tiangong No. 1” that just crashed some time ago. Before it crashed, there were websites that announced its possible fall orbit. The calculation of this orbit also uses the mass of the earth.
Actually, the mass of the earth is obtained through clever experiments based on Newton’s gravitation. The first person to accurately measure the mass of the earth was British scientist Henry Cavendish. Yes, some students may have thought that the famous Cavendish Lab was established in memory of him.
British scientist Henry Cavendish (picture from the Internet)
It took more than 100 years from Newton’s publication of the theory of gravitation in 1687 to Cavendish’s announcement of the mass of the earth in 1798. For more than 100 years, scientists have continuously tried to measure the mass of the earth in different ways, but all have failed due to too large measurement errors. Cavendish, through clever design experiments, successfully amplified the gravitational force between the big ball and the small ball to measure the universal gravitational constant G, and calculated the mass of the earth. The experimental equipment he used is as follows:
It looks a bit complicated, right? In fact, the main part of the experiment is very simple, as shown in the figure below, and the rest is just to eliminate environmental interference.
It looks simpler than the experiment in high school experiment class! It is such a simple instrument, but the measurement accuracy is scary. The error is about one millionth. With this simple instrument, the mass of the earth can be measured. This is why this experiment by Cavendish is considered the most accurate One of the classic experiments. Let’s talk about how this experiment measures the mass of the earth.
In this process, the masses of the small yellow ball and the large blue ball are known, m and M, respectively, and the distance between their center points is also known as r. There is universal gravitation between the big ball and the small ball, which attracts each other. This force will generate a moment, which will eventually be balanced by the torque of the small ball wire. At this time the position of the ball will be biasedAway from an angle. The balance is as follows:
where is the torsion coefficient of the steel wire, L is the distance between the rods connecting the two small balls, and F is the gravitational force between the large and small balls. The expression for F is:
This gravitational force is very small, it is almost impossible to feel in real life, but it does exist.
The distance L between the two small balls and the deviation angle of the small balls are measured experimentally. The torsion coefficient of the wire can be calculated based on the properties of the wire, or it can be considered to be known. Therefore, according to the above known conditions, the universal gravitational constant G can be calculated,
Then the weight of the ball is equal to the gravitational force between the earth and the ball, we can calculate the mass of the earth is:
Cavendish estimated through his experiments that the mass of the earth is 5.965 × 10 ^ 24 kg, which is about 60 trillion tons, which is very close to the existing accepted value of 5.972 × 10 ^ 24 kg.
The rigor of Cavendish’s experiment is that he used a closed experimental device to successfully shield the interference of external factors on the measurement results, such as air flow. In addition, he successfully amplified the gravity with a mirror on the hanging line. The resulting deflection reduces reading errors. In addition, in order to overcome periodic errors, such as temperature, Cavendish’s experiments with measuring the earth lasted for several years, thereby effectively reducing the observation errors caused by the temperature and the periodic swing of the torsion scale. Impact.
The experiments were so clever that the accuracy of the experiments was unsurpassed for more than 100 years. His torsion scale experiment is still the main method for measuring the gravitational constant.
After understanding the mass of the earth, you can easily calculate the mass of the moon and the sun according to the law of gravity, and then the masses of other planets and celestial bodies in the solar system, so the significance of Cavendish’s experimental significance is self-evident. of.
In addition, the second cosmic velocity of the earth can be calculated from the mass of the earth to be 11.2 m / s. This velocity is the minimum velocity at which a satellite must break away from the gravity of the earth and enter space. Moreover, to calculate the flight trajectory of an artificial satellite or a spacecraft, the mass of the earth is used. Therefore, knowing the mass of the earth is the most basic step for launching satellites and spacecraft.
To sum up, Cavendish ’s step in measuring the mass of the earth is to first use the gravitational force between the big ball and the small ball to measure the gravitational constant G, and then use G and the mass of the ball to calculate the mass of the earth.
This article is from the WeChat public account: China Science and Technology Expo (ID: kepubolan) , Author: Chen Xing