The moon's orbital speed is much lower than the first cosmic speed, so why doesn't it fall from the sky?

This is in response to a question from a netizen. He said: The moon's orbital speed is 1.02 kilometers per second, which is much lower than the first cosmic speed of 7.9 kilometers per second. It is not supposed to orbit the earth, so how come it doesn't fall down? I don't understand.

Let’s talk about this issue now.

The so-called first cosmic velocity, second cosmic velocity, and third cosmic velocity are calculated based on the earth's surface through the gravitational equation, that is, Newton's law of universal gravitation. This law is expressed as: F=MmG/r^2, which means that the magnitude of gravitational force is directly proportional to the mass of the object and inversely proportional to the square of the distance between objects.

That is to say, the greater the mass of a celestial body, the greater its gravitational force; but the greater the distance between two celestial bodies, the gravitational force decays exponentially. This makes it easier for us to understand that the first cosmic velocity, the second cosmic velocity, and the third cosmic velocity on the surface of the earth are constantly changing and decaying as they move away from the surface of the earth. The greater the distance, the smaller the speed requirements.

Now let's talk about the first cosmic speed, which is 7.9 kilometers per second on the surface of the earth, which means that an object taking off from the earth needs to reach 7.9 kilometers per second to fight against the earth's gravity. However, this speed cannot get rid of the earth's gravity, and can only achieve a balance with the earth's gravity. It can neither be pulled down by the earth's gravity nor escape the restraint of the earth's gravity, and can only revolve around the earth.

Therefore, the first cosmic velocity is also called the orbital velocity, and the formula it follows is derived from Newton's law of universal gravitation, expressed as v²=GM/r. Here v represents the speed required for orbiting, which is the so-called first cosmic velocity; G is the gravitational constant, M is the mass of the celestial body to be escaped, that is, the mass of the earth; r is the distance between the object to be escaped from the mass of the earth and the center of gravity of the earth, that is, the center of the earth.

The radius of the earth is about 6371 kilometers, which can be regarded as the distance from the center of the earth to the surface. According to this formula, we can calculate the first cosmic velocity on the surface of the earth. The calculation formula is: v^2=（6.67*10^-11）*（5.965*10^24）/6371000≈62449458, v≈7902 meters/second.

This is the origin of the so-called first cosmic velocity. If an object flies 20,000 kilometers above the earth's surface, the so-called first cosmic velocity only needs to be about 3,844 meters per second. The moon is 384,000 kilometers away from the earth on average, and the earth's gravity on it is much weaker. According to the orbital formula, its revolution speed only needs to reach 1018 meters per second to reach the orbital speed. This is why the moon's revolution speed is only about 1.2 kilometers, but it will not be sucked down by the earth's gravity.

In fact, the moon is moving away from the earth at a speed of 3.8 centimeters per year. There are many different opinions on the reasons. One theory is that this phenomenon is mainly caused by the periodic tidal effect between the earth and the moon. That is, the gravity of the moon causes the ebb and flow of the earth's sea water, which consumes the energy of the earth's rotation. The earth's rotation speed continues to decrease, causing the moon to gradually move away.

But another theory is that gravity is only related to mass and distance, and has nothing to do with the speed of rotation. The reason why the moon gradually moves away is very complicated, and it is not due to the slowdown of the earth's rotation as some people say. This is another topic, and it is a long story, so I won't go into it today.

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