People who have watched “Doraemon” must have a hard time forgetting the various magical tools in it. Among them, the arbitrary door that can instantly go to any time and space can be regarded as the highest rate of appearances, so can our current technology take it Made it? It’s still difficult to travel through time and space, so can you travel across the earth and go from one end to the other at once?

A physics problem

To answer this question, let’s first use the physics knowledge of middle and high school to calculate a physics problem. Assuming that the earth is a perfect sphere, its mass is evenly distributed, the center of gravity is centered on the center of the earth, ignoring the centrifugal force and air resistance of the earth’s rotation, making a hole from the center of the North Pole to the South Pole, and then you jump into the hole, how long does it take to reach the South Pole time?

The solution to this problem is much easier than imagined. Since we assume that the mass of the earth is concentrated in the center of the earth, the gravity of the earth on people can be considered as the universal gravitation between the center of the earth and people, and it can be calculated by the universal gravitation formula.

Human beings receive the greatest gravity on the ground, and the force they receive is zero when they reach the center of the earth, and the force they receive increases in the opposite direction after leaving the center of the earth. The whole process is similar to the compression and rebound of a spring. When the spring is in the original position, the force is zero. The greater the compression force, the greater the rebound force. A process like this is physically called simple harmonic vibration, and its motion cycle is the time it takes to go back and forth twice, and it can also be calculated with a formula. We only need to combine the gravity formula and the simple harmonic vibration formula together to calculate the result. According to calculations, it only takes 42 minutes to travel from the North Pole to the South Pole through this hole!

Can be faster

If we get closer to the actual situation, we can calculate a faster time. Physicist Alexander Klotz of McGill University in Canada proposed such an algorithm. According to seismic data, the density of the core is much greater than the density of the mantle and crust, which means that the closer to the center of the earth, the heavier the earth. Therefore, before we cross to the core, the mass of the earth below is almost equal to the mass of the entire earth, and the gravitational force received is equal to the gravitational force given to us by the entire earth; once we cross the mantle, the gap between upward and downward gravitational forces will increase. The smaller the size, the smaller the total gravity.

Therefore, Klotz proposed that the calculation of the falling process in the northern hemisphere should be divided into two stages, the free fall movement stage where the force is almost constant before crossing the mantle and the uniformly accelerated movement stage where the gravity after crossing the mantle shrinks with the decrease of the radius. . Calculating the sum of the two phases in the northern hemisphere and multiplying it by 2, we get Klotz’s time to travel through the earth, which is about 38 minutes and 11 seconds, which is 4 minutes faster than ideal.

Building gravity train

It only takes more than half an hour to get from one end of the earth to the other. If this idea can be realized, it would be so cool. So can we dig a tunnel through the earth?

At present, we do not have such conditions, because the internal environment of the earth is very harsh. First of all, the heavy pressure must be overcome. In the center of the earth, the object will bear the huge pressure generated by the inward squeeze of the rock, which is estimated to be equivalent to about 3 million times the sea level pressure. Then comes the high temperature. There is no material that can withstand the temperature of thousands of degrees Celsius for a long time, let alone human beings still ride it. Finally, there are the centrifugal force and air resistance of the earth’s rotation that we ignored in the previous calculations, which are also important influencing factors. If you imagine the earth as a runway, when the earth rotates, we run the inner circle inside the earth, and the outer rock runs the outer circle, our speed must be faster than the rock, so it is difficult to keep falling vertically when we fall in the tunnel. It’s more likely to hit the rock with one head. The air resistance will greatly reduce the speed of our advancement, and the actual time to cross the earth is much longer than ideal. For example, the time to cross the earth calculated by the scientists of Cornell University and the air resistance is as long as 1.8 years!

In fact, even such a tunnel has many insurmountable difficulties, but who knows what magical technology we will invent in the future? Maybe one day, we can really go through the center of the earth and go all over the world.