Shulou(Shulou.com)11/24 Report--

The measurement of the earth's mass plays an important role in the history of science. In order to explain the whole story, let's start with a famous bet.

One day in 1683, three academicians of the Royal Society met in London and then made an appointment for dinner. The three men are Edmundo Harley, Robert Hook and Christopher Lane.

The first two names may sound familiar to you. Edmundo Halley is the Halley of Halley's comet, and Robert Hook is the Hook of Hook's law. Both of them are giants in the history of science, and their scientific achievements are much more than that.

The lesser-known Christopher Lane was an early professor of astronomy at Oxford University. But in 1666, a fire broke out in London and the whole city of London was set ablaze. At the appointment of the king of England, Rehn presided over the post-disaster reconstruction; since then, he has changed careers as an architect. There are many famous buildings in Britain, such as St. Paul's Cathedral, the Greenwich Observatory and the Cambridge Library, all of which are the works of Ryan. Although Ryan did not do much research in astronomy, as a veteran of the Royal Society, he was elected president of the Royal Society in 1680.

Once, three academicians talked about the motion of celestial bodies in the solar system. As early as the beginning of the 17th century, the great astronomer Kepler had discovered that the major planets in the solar system were orbiting the sun in an elliptical orbit. But more than half a century later, no one has been able to explain why their orbits are oval.

Ryan made a bet at dinner: if anyone could explain why the planet was moving in an elliptical orbit, he would reward that person with 40 shillings, equivalent to half a month's salary of a university professor at the time.

Hooker, a "boast", said on the spot that he had solved the problem. However, he was reluctant to release the answer to this question right away. His reason is that if the answer is published too early, it will deprive others of the fun of finding the answer. Of course, after this dinner, Hook forgot about the answer to be announced.

But Harley was fascinated by the problem. He didn't believe that Hook could find the answer to the problem, but he knew that there was a man in the world who was able to solve the mystery. So one day in August 1684, Harley made a special trip to Cambridge University to visit this extraordinary man who could not see the end of the dragon. The man who changed the course of history was Isaac Newton.

Isaac Newton was the second scientist in the world to be knighted (the first was Francis Bacon) and the first scientist in the world to enjoy a state funeral.

Voltaire, a French enlightenment thinker, witnessed Newton's funeral and wrote in his memoirs: "the British mourn Newton like a king." There are countless praises of Newton for later generations. One of the most popular is a poem by the English poet Alexander Pope: Nature and nature's laws lay hid in night; Godsaid "Let Newton be" and all was light. (Tao is natural, old Tibet is mysterious; born Newton, all things are born bright. )

There are many earth-shaking events in the world, all of which stem from some rather inconspicuous little things. Newton gained such a reputation in large part from Harley's visit.

Let's start with a brief review of the study of gravity in the 17th century. There is gravity between any two objects, and the magnitude of gravity is directly proportional to the mass of the two objects and inversely proportional to the square of their distance, which is the inverse square law of gravity.

Now many textbooks say that the inverse square law of gravity was put forward by Newton. In fact, this statement is wrong. As early as 1645, three years after Newton's birth, the French astronomer Brio proposed this inverse square law. But Brio made a big mistake: he mistakenly thought that sometimes there was gravity and sometimes there was repulsion between two objects.

Later, Italian physicist Borrelli guessed in his book that all the planets in the solar system are gravitated by the sun, and that the sun's gravity satisfies the inverse square law.

Borrelli in the 1770s, Hook also began to promote the inverse square law; he even explained the theory to Newton in a private letter. But like Brio and Borrelli, Hook cannot prove the correctness of the inverse square law.

Why can't Hook and others prove that the inverse square law is correct? The answer is actually very simple. As early as the beginning of the 17th century, Kepler put forward the famous three laws of Kepler, which revealed that all the planets in the solar system are revolving around the sun in an elliptical orbit. To prove the inverse square law of gravity, it is necessary to prove that the orbit of a planet affected by this gravity must be an ellipse.

In other words, it is necessary to derive Kepler's three laws from the inverse square law. But the problem is that in order to achieve this goal, we must use a mathematical tool that did not exist at that time, that is, calculus.

At this point, the most famous problem in the history of science, you can understand what makes Newton special. As the inventor of calculus, Newton was the only "chosen man" in the world who had the ability to solve this super-century puzzle.

But Newton had a peculiarity: he didn't like to publish his research. Therefore, although he has long solved this famous century puzzle in the history of science, he has kept it a secret. If there had been no accident, it would probably have been taken to the grave by Newton as a secret.

So the meeting between Harley and Newton in August 1684 was a real turning point in history. The whole history of human science, and even the whole history of human civilization, has been rewritten.

After a few pleasantries, Harley asked Newton bluntly, "what will the orbits of these planets look like if the gravity between the sun and other planets satisfies the inverse square law?"

Newton replied without thinking, "of course it's an ellipse."

Harley was surprised and immediately asked, "how do you know that?"

Newton replied, "I did the math a long time ago."

Excited Harley immediately asked to see Newton's calculation process. While Newton rummaged through the old paper for a long time, he couldn't find anything. However, he promised Harley that he would recalculate it and write it into a paper. Two years later, Newton kept his promise.

In fact, he did much more than he promised. What he gave Harley was not a paper, but a book, the Mathematical principles of Natural philosophy. In this greatest academic work of all time (none), Newton proposed the three laws of Newtonian mechanics and the law of universal gravitation based on the axiomatic system pioneered by Euclid, thus completing the first revolution in the history of physics.

The book impressed Harley with admiration. After that, he told everyone that Newton was the closest person to God in the world. A similar view was held by the great mathematician Leibniz, who later competed with Newton for the right to invent calculus. He once said that Newton made more contributions to science than all the people before him combined.

Harley's greatest contribution to human civilization is that he contributed to the publication of the book the Mathematical principles of Natural philosophy. The Royal Society had agreed to publish the book, but it was not long before it changed its mind. This is because the Royal Society has just lost a lot of money on a book called Fish Chronicles, for fear of continuing to lose money on a book that is extremely obscure. So Harley simply advanced the full cost of publishing the book. In 1687, this epoch-making scientific masterpiece was officially published. This immediately made Newton famous all over the world and ascended directly to the altar of science.

A bet on the Mathematical principles of Natural philosophy finally led to the publication of the greatest academic work of all time. This should be the best example of the butterfly effect.

Something funny, by the way. Because the Royal Society lost so much money on Fish Records that it was unable to pay Harley's salary as a secretary of the Society, it sent him some unsold "Fish Records" as his salary.

Let's get back to the point. Now that we know the concept of gravity, we can talk about how to measure the mass of the earth.

As we all know, all objects on the earth are affected by gravity, which comes from the gravitation of the whole earth. This can be described by a very simple formula:

On the left side of this formula is the gravitational force on an object, and on the right is the gravity on it. Where m is the mass of the object, which can be eliminated during simplification; g is the gravitational acceleration, which is about 10m / S2; R is the radius of the earth, which is about 6400 kilometers. As a result, there are only two unknown physical quantities: the Newtonian gravitational constant G and the mass of the earth M. In other words, as long as the Newtonian gravitational constant can be measured in other ways, the mass of the earth can be calculated.

The first person in the world to measure the mass of the earth was the British physicist Henry Cavendish. Cavendish has two very distinct characteristics. First, he does not pursue any fame or fortune at all, no matter what he does, he starts from his personal interests. This is not surprising, for he himself is one of the richest aristocrats in England, and there is no need to pursue fame and fortune at all.

Second, he suffers from a very serious social phobia. How serious is it? He didn't want to meet anyone, and even his housekeeper could only communicate with him by letter. Cavendish attends only one social event, the weekly scientific gathering held at the home of naturalist Banks. But all people who want to communicate with him must use the way they treat "invisible people". You have to wander carelessly around him and talk to the air around him without looking at him. Otherwise, Cavendish would scream and run away to no one.

These two characteristics led to a very strange consequence: Cavendish made a lot of important scientific research results in his life, but only in manuscripts, not published. He is more extreme than Newton in his reluctance to publish a paper. As a result, these scientific achievements were later rediscovered by others, and then named after those people. For example, Coulomb's law, Ohm's law and Dalton's law, which were learned in high school physics textbooks, were first discovered by Cavendish.

Of course, there are always exceptions. Cavendish's most famous scientific experiment in his life, that is, the accurate measurement of the gravitational constant G, the original idea did not belong to him, but to a priest named John Mitchell.

Since Michelle did not leave any portraits, no one knows exactly what he looks like; only some written records tell us that he is a short, dark-skinned fat man. But this unattractive person has an extraordinary past. He taught at Queen's College of Cambridge for many years and became the dean of the college. However, due to some unexpected changes, he had to resign from the University of Cambridge and go out of town to become a church director.

Michelle was the first to suggest that there could be a star with such a large mass that even light could not escape from its surroundings. In this way, people will never see it. Michelle calls this invisible star a "black star". This is the origin of the famous concept of "black hole".

He also made his own experimental device and wanted to use it to measure the magnitude of the gravitational constant G. Unfortunately, Michelle died of illness before she could do the experiment. After several twists and turns, the device came into Cavendish's hands. In 1797, Cavendish improved it and then used it to complete the famous Cavendish torsion scale experiment.

The following diagram is the schematic diagram of the Cavendish torsion scale experiment. You can see that the device has an inverted T-shaped light rod, with two m-shaped balls of the same mass at both ends, and a small plane mirror at the end protruding from the middle. Hang the device up and shine a beam of light on the plane mirror; the light will be reflected by the plane mirror and hit on a ruler next to it.

Next to the Cavendish torsion scale experiment, two large balls of the same mass, both M, were placed next to the two small balls. Due to the gravity of the big ball, the hanging inverted T-bar will have a slight deflection. In this way, there is a slight change in the angle between the incident light and the plane mirror, which shifts the position where the light hits the ruler. By measuring the offset of this position, the gravitational force between the big ball and the small ball can be calculated, and then the Newtonian gravity constant G can be measured.

The subtlety of this experiment is that it converts the magnitude of gravity, which is very difficult to measure, into a lot of easily measured position changes, thus making it possible to accurately measure Newton's gravitational constant.

The results measured by Cavendish more than 200 years ago have a margin of error of only 1% compared with the latest results. Using the measured value of the Newtonian gravitational constant, it can be calculated that the mass of the earth is about 6 × 10 to the 24th kilogram.

Author: Wang Shuang part of the source network copyright belongs to the original author editor: Zhang Runxin ★ book introduction ★

The Universe Odyssey walks the Solar system author: Wang Shuang Tsinghua University Press this is a magical journey that begins with the earth and will eventually travel around the universe, and this book is the beginning of this journey of the cosmic Odyssey. This is a brief history of the solar system, which consists of 40 articles and is presented in the form of "biography". What I want to show you is not some fragmented knowledge about the solar system, but a complete knowledge system about the solar system. With 40 topics carefully selected from hundreds of primary topics, I hope you can understand the coordinates of these major celestial bodies in the history of human civilization: what important role have they played in the history of human civilization? What are the particularly important scientific events? How to change man's view of the whole universe? What kind of connection does it have with our real life? A brief introduction to ★ authors ★

Wang Shuang, Associate Professor and doctoral Supervisor, School of Physics and Astronomy, Sun Yat-sen University. He has devoted himself to the study of cosmology for many years. At present, 35 SCI papers have been published, with a total of more than 1800 references. Popular science writer, author of the Universe Odyssey: walking in the Solar system, telling Children about the Universe and the Theory of Relativity. He has won a series of popular science awards, including "China Publishing Association's 30 good Books in 2017" and "the State Press and publication Administration recommended 100 excellent publications to teenagers across the country in 2018." Sina Weibo, a well-known science blogger with nearly 2 million followers, is a speaker at the standard meetings of Phoenix Satellite TV, Shenzhen Satellite TV and TEDx. This article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Wang Shuang, Editor: Zhang Runxin

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