How was the mass of the Earth measured? It's a long process of calculation that began in ancient Egypt

What is the mass of the Earth? It is about 5.965 times 10 to the 24th power of the kilogram.

This result can be easily obtained by searching, but many people may have doubts about how this number was obtained. We know that the earth is a very irregular sphere, and this sphere is composed of a large number of different substances, on the surface, there are oceans, mountains, deserts, swamps, and below the surface, there is a layered structure composed of the crust, mantle and core, such a sphere where the mass of each part of the material is different, how can we accurately calculate its mass? It is a long process of calculation, the beginning of which can be traced back to the ancient Egyptian period.

As we know, the ancient Egyptians were very advanced in mathematics, physics and astronomy, so at a very early stage, they knew through observation and deduction that the Earth was round, and after learning this, they began to try to calculate the size of the Earth, and to calculate the size of the Earth, the first thing they had to know was the radius of the Earth.

Even in today's highly developed science and technology, humans still can not penetrate the earth's crust and explore the part under the crust, so in the ancient Egyptian period want to go deep inside the earth to measure the radius of the earth is completely impossible, but for the highly developed mathematics of the ancient Egyptians, want to know the radius of the earth, do not need to personally enter the earth.

In Egypt there was a very famous city, Alexandria, and above the same meridian there existed another city called Aswan. The sunlight shining on the Earth's surface is parallel light, and when the sunlight shines directly on Alexandria, it cannot shine directly on Aswan, so the sunlight makes an angle with the ground of Aswan, which is easy to measure and we can call it angle A. Now we can draw two lines from the center of the Earth, connecting Alexandria and Aswan, and the angle made by these two lines is the same as angle A. is the same. Now that we know the angle between Alexandria and Aswan from the center of the Earth's sphere, the ground distance connecting the two cities, Alexandria and Aswan, can be easily measured.

Since the earth is round, the ground distance between the two cities is the arc length of the earth's surface connecting the two cities, and now it is only necessary to divide the arc length by the angle A to find the radius of the earth.

The ancient Egyptians measured the radius of the Earth, but it was still far from being able to calculate the mass of the Earth.

Time passed, and in a flash, thousands of years later, Newton appeared. Newton proposed the law of gravitation, he believed that any two objects have a mutual gravitational effect between them, and accordingly proposed the universal gravitational formula: F = G(m1m2/r∧2), in this formula, F is the universal gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between them. So what is the relationship between the universal gravity formula and the mass of the Earth? The relationship is very close.

Including ourselves, any object located on the surface of the earth is subject to a gravity, the formula of this gravity is very simple, that is, F = mg, where m is the mass of the object, g is the acceleration of gravity, which is 9.8m/s∧2.

So why are the objects on the surface of the Earth subject to gravity? In fact, this so-called gravity is the gravitational force between the object and the Earth, that is, gravity and gravity these two F is actually equal, so we can substitute the two formulas into each other, that is, G (m1m2/r∧2) = m2g. m1 in this formula is the mass of the Earth, m2 is the mass of any object on the surface of the Earth, r is the distance between people and the center of gravity of the Earth, so the requirement Earth's mass only needs to deform this formula: m1=(gr∧2)/G. g is the acceleration of gravity, which is 9.8m/s∧2, and r is the mass of an object on the Earth's surface, for example, if we take ourselves as the object in this formula, then it is our own mass. Now if we know the universal gravitational constant G, we can find out the mass of the Earth.

Although Newton proposed the law of gravity, he did not calculate the magnitude of the universal gravitational constant, because it is indeed quite difficult to calculate this constant.

The gravitational force is so weak that the gravitational force of the whole earth is pulling the phone down, and we can easily overcome the gravitational force to pick it up, so we can see how weak the gravitational force is, so the universal gravitational constant is a very small number and very difficult to measure. It was not until more than 100 years after Newton's death that the physicist Cavendish measured this constant. He used a wire to hang a crossbar, placed two lead balls at the ends of the bar, and placed a mirror on the wire and shone a beam of light through the mirror.

After the device was assembled, Cavendish used two other lead balls to approach the lead balls at the ends of the rod, and gravity made the rod rotate very slightly. It is this tiny rotation makes the light reflected by the mirror a visible change in angle. In this way, Cavendish was able to measure the gravitational constant by magnifying the small deformation, and with the gravitational constant, the mass of the Earth was calculated, so Cavendish was honored as the person who measured the mass of the Earth.

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