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

Three months ago, the editor received a question from a reader in the question-and-answer column: "what happens if the earth rotates in reverse?"

Oh, my God, that's the sun coming out in the west.

Imagination is so rich that we can only use time reversal to simulate that the sun rises in the west. It is a worthy reader of our No. 2 Middle School, which easily raises questions that I can't even dream about. At that time, I just wanted to open my head and put it in our question and answer column on Friday. As a result, this article was greatly grasped by the editor-in-chief, saying that it was a good question and suggested to expand it into writing. Well, let's think about the possible physical phenomena of the earth as a rotating non-inertial system during and after the inversion of the direction of rotation.

1 let the earth rotate and reverse

If we define the earth's rotation as a long-term process, like the braking age of the first step of the "wandering Earth" project, using a bunch of planetary engines built near the equator to give the earth a reverse torque, then we can estimate what configuration of planetary engines is needed to reverse in a reasonable time.

The engine is powered by the reverse injection refrigerant, ignoring the incalculable atmospheric resistance (a chimney can be built to send the recoil refrigerant directly into space), and the effective backinjection speed is taken as the second cosmic speed 11.2km / s to ensure that most of the refrigerant will not be pulled back by the earth's gravity. As for the estimated time of the reversal, you might as well follow the original setting and let it take 42 years to complete the "brake" of rotation. Then, according to the simple conservation of angular momentum and kinetic energy theorem, it can be calculated that it takes 83.65 years to reverse the earth, consuming a total of 1.21 × 1031J energy and 3.25% of the earth's mass, and the corresponding power is as high as 4.60 × 1021W, that is to say, it consumes 45 times as much energy per second as the global power generation for the whole year of 2021.

Assuming that the earth is a uniform sphere with a mass of the working medium collected at the outer shell of the earth, transported to the equator and ejected eastward at a relative velocity, then the conservation of total angular momentum of the system before and after the jet is given.

Omit the second-order small quantity and simplify it.

Define the injection mass flow of the engine as a fixed value, then the mass of the earth will be consumed over time. If the density of the earth is constant, then the radius of the earth will be reduced to, but the differential equation will become extremely disgusting. In order to be lazy, let's assume that the radius of the earth will not change, so that we can get it all.

Solution

cursory

Or write as

cursory

Let's start the numerical analysis. First of all, put in some reasonable values. Then determine the flux of the return injection of the working fluid. In wandering the Earth, Da Liu imagines that it will take 42 years for the earth to spin on the brakes. What is this concept? Put in, roughly, the mass of the working fluid ejected per second is equivalent to a mountain with a cone angle of 45 °and is nearly 3km high. Spraying at such a flow rate for 42 years will spray 1.634% of the initial mass of the earth, so it is true that the radius of the earth can be approximately unchanged in this process. In fact, the complete expression is substituted and thrown to the almighty Mathematica, and the solution is not much different from the rough value (although the poor mass is enough to build a hill more than 800 meters high).

Let's take the rough value of the first calculation first. Now, it takes 83.89 years to get a reverse rotation, slightly less than 84 years, because the earth's mass is already lighter in the second half of the process.

If we consider the decrease of the radius of the earth, take the second value and replace it with the complete differential equation, the result will be shortened to the year again, because the decrease of the radius will also reduce the moment of inertia. The whole process will spray off 3.246% of the earth's mass, reducing the radius of the earth by 69.7km. It doesn't seem to be enough to spray off the crust, but let's not consider this bug here.

Let's consider the energy consumption of the whole process. After the working fluid is transported from the surface to the equator and then ejected back, the kinetic energy increment obtained is

The change of the kinetic energy of the earth's rotation is

So the energy consumed in the whole process is as high as the average power. Thank you for watching the beautiful formula: -)

Of course, this calculation is too large, because in the process of calculation, we treat the earth as a uniform sphere. But in fact, the density of the earth increases with the increase of depth, so that the moment of inertia is smaller than that of a uniform sphere. But the current results are sufficient as a logarithmic estimate.

If this energy was obtained through a nuclear reaction, a mass loss of 135.1 billion tons would be required. At present, the way of energy acquisition at the top of the human science and technology tree is nuclear fusion, such as the EAST (artificial Little Sun) under development, which mainly uses DT fusion:

DT fusion schematic diagram | Image source Wikipedia even if the utilization rate of nuclear fusion energy can reach 100%, it would require 14 trillion tons of deuterium and 21 trillion tons of tritium to reverse the earth. Deuterium accounts for 0.003% of the sea water, which translates to 40 trillion tons of reserves, which should be sufficient. Although there are not many reserves of tritium on earth, tritium can be produced and sold by adding Li to the reactor.

Exothermic, but consumes neutrons to absorb heat, but not neutrons

However, at present, the proven Li ore resources are on the order of 10 million tons, so we still have to focus on the potential helium-3 deposits on the moon and use the various fusion reactions of helium-3 to power the engine.

Then consider the power of a single engine. In the original work, 2000 steering engines were arranged near the equator, and the power of each engine should reach 2.3 × 1018W. At present, the power of the largest nuclear fission power station in the world is only 8 × 109W, which translates to only 575 billion units.

Schematic diagram of 2000 steering engines, please ignore the 10000 propulsion engines on the right, but another way is to build a Dyson ball around the sun that absorbs radiation energy. Considering that the radiation power of the sun is 3.74x1026W, as long as we can use it with an efficiency of 1/100000, we can easily accomplish the feat of reversing the earth as planned.

Dyson ball that can absorb radiation energy from stars | Source: "Dyson Ball Project" 2 stars rising to the west and falling to the east after reversal

If you can't imagine, please stand on your right foot and turn yourself back with your left foot, and you will see everything around you move from right to left. This is how the stars rise and fall in the east and west on the home planet. So after the reversal, it should not be difficult to imagine that the sunrise will become weaker and weaker in the west and Dongshan. In fact, in the solar system, Venus and Uranus rotate from east to west.

The rotation direction of the eight planets of the solar system + Pluto reverses the direction of the rise and fall of the stars, which leads to an interesting phenomenon: there are two more sunrises a year and two more moonrises a month.

Now consider a small problem: Venus is known to have a rotation period of 243days and an orbit period of 224.7 days. So is there a complete sunrise and sunset in a Venus year?

You may answer without thinking that the rotation period is longer than the rotation period, but of course it is invisible. Indeed, if Venus rotates from west to east, in the same direction as its revolution, then it will look like this.

The solar day on such a Venus is equivalent to 1 / (1 dial 224.7-1 dial 243) = 2983.7 days, equivalent to 13.3 Venus years, which can be described as a real year. But when you think about it, Venus rotates from east to west, and it should look like this.

Do you see the difference? Since rotation and rotation are in opposite directions, their relative speeds are superimposed. So in fact, a day on Venus is equivalent to 1 / (1 to 224.7) = 116.7 days, which is slightly longer than half a Venus year.

So in two cases, how many Venus days are there in a Venus year? You might as well try to convert it. The former is 0.075 Venus days and the latter is 1.925. The sum of the two is exactly 2. Think about it. Is that a coincidence?

Of course not. If you think about it, if Venus doesn't revolve, the sun will revolve around Venus less than once in a Venus year, and if Venus starts to revolve in the opposite direction, the sun will turn in the opposite direction. For this problem, turning the rotation in the opposite direction is equivalent to the rotation in the opposite direction, just looking at the problem from a different point of view, but it is easy to see the source of the gap between the two laps.

Now, you can imagine that if the earth's rotation were reversed, there would be two more moonrises and moonsets in a month, and two more sunrises and sunsets in a year. Accordingly, the year on Earth will become 367.24 days, the time of the day will be shortened by 470s, and the cycle of the tide will be shortened.

If you still can't imagine, there is a serious play here, and it only takes two big pancakes to simulate this phenomenon, which may help you understand better.

3 the Coriolis force will be reversed.

What is Coriolis force? Don't be frightened by this guy's name. Look at the picture first.

The experimental demonstration of the Coriolis force shows that the above motion picture is taken in the ground reference system, and the ball flies out in the direction of its original speed after getting rid of it. The following motion picture is fixed in the rotating reference frame. In the rotating reference frame, the trajectory of the ball bends to the right, as if it was subjected to a right force. But in fact, the bending of this trajectory is caused by the rotation of the reference frame itself, and there is essentially no force acting on the ball. In order to make it easier for people in the rotating system to describe this phenomenon, we have imagined an inertia force, that is, the so-called Coriolis force, or geostrophic deflection force in geography.

The geography teacher may make you lean to the right in the northern hemisphere and to the left in the southern hemisphere, but it may be difficult for him to tell you why. The big thing teacher will "Kuang Kuang" from the differential point of view, but lacks some understanding of physical images. Don't panic, let's take the northern hemisphere as an example to talk about how this biased force comes from.

If you move toward the center of a rotating system, for example, from the equator to the North Pole, you get closer and closer to the axis as you move north, and if you maintain the same angular velocity as the earth, then your linear velocity will gradually decrease, which means you must have been subjected to a westward force. But in the earth's frame of reference, you don't deflect in the east-west direction, so in order to balance this actual force to the west, we need to pretend to be an eastward force. Conversely, if you walk from the North Pole to the equator, your linear velocity increases and you must be subjected to an eastward force, but in order to maintain balance in the Earth's frame of reference, you need an illusory force to the west. This shows that in the northern hemisphere, for radial motion, there is always a force to the right compared to the direction of motion.

But this effect is very weak on Earth. How weak is it? If you drop an object freely from a height of 200m at 40 degrees north latitude, then the falling body will only be 4.75cm to the east. Therefore, this effect mainly has an impact on large-scale phenomena.

The analysis of the radial motion is finished, followed by the tangential motion, which requires a little bit of the basis of circular motion. If you move westward, like the one on the left in the image below, you will find that your linear velocity becomes smaller or even stationary, so that the actual centripetal force required to maintain circumferential motion will be reduced. it means that you are subjected to an extra force outward along the radial direction (that is, the support force facing you increases). And in order to keep the point of view of the rotational system, and you still have a force balance, you need to imagine a force inward along the radial direction. Conversely, if you move eastward, like the one on the right in the image below, your linear speed will increase and the centripetal force you need will increase, indicating that you are subjected to a radial inward force (that is, the support force facing you is reduced). In order to maintain balance, it is necessary to imagine a force outward along the radial direction. This shows that there is always an imaginary force for tangential motion, to the right in the northern hemisphere and to the left in the southern hemisphere.

By understanding the Coriolis force, we can understand why cyclones are usually counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. The center of the cyclone is an area of low pressure, and the surrounding air is subjected to a Coriolis force as it rushes into the center, to the right in the northern hemisphere. Synthesize the motion path and it is a counterclockwise vortex.

Schematic diagram of cyclone formation in the Northern Hemisphere

The typhoons "mangosteen" and "Bailijia" in the northern hemisphere. I'm sorry to know such delicious fruit in this way.

Cyclone "Baziere" in the southern hemisphere, and the island in the picture is Madagascar. Let's see what happens after the rotation reverses. Or take the northern hemisphere as an example, the Coriolis force will change from right to left. From top to bottom, large-scale cyclones (such as typhoons) radiated inward counterclockwise, but now they radiate inward clockwise; along the direction of the river, the erosion of the right bank is greater than that of the left bank, and now the erosion of the left bank is greater. The east-west direction of the trade wind will be reversed, and the ocean current and climate will change greatly. Perhaps the water vapor from the Atlantic will accompany the southwest trade wind to descend on the Sahara, turning it into a tropical rainforest. Or maybe the Siberian winter wind will no longer blow directly southeast to the Taihang Mountains and Qinling Mountains, and the dust from the northwest will no longer accumulate on the Loess Plateau.

The theory of the birth of the monsoon on the Loess Plateau | Source: planetary Research Institute 4. May the geomagnetic field be reversed?

Why put a question mark on the title? Because the formation mechanism of the geomagnetic field is still a mystery, it was published in 2021 in Science magazine's most cutting-edge 125 scientific questions.

The wonderful thing is that this problem is classified into ecology, but this does not affect the importance of this century puzzle. Source: 125Me: Exploration and discovery | Science | AAAS the mainstream geomagnetic field origin theory is the earth core generator model, which believes that there is molten iron and nickel in the outer core of the earth's core. For these melts, the deeper the temperature is, the higher the temperature will be, so they will convect up and down under the action of the temperature difference. But they do not rise and fall vertically, but spiral up / down under the influence of Coriolis force. If at some point this spiral convection produces a seed magnetic field, the anions and cations in the melt will be subjected to Lorum magnetic force to form an electric current, which in turn will form a magnetic field and strengthen the seed magnetic field. This feedback mechanism is constantly superimposed and finally forms a stable geomagnetic field at present.

According to the discussion in section 3, after the Coriolis force is reversed, the helix direction of the current will be reversed, which may lead to geomagnetic reversal. However, at present, the internal environment of the earth's core is still a mystery, and the model of the earth's core generator has not been strictly tested by experiments, and the real origin of the geomagnetic field remains to be further studied.

The flow of conductive fluid under the Coriolis effect forms multiple spiral convection, resulting in a magnetic field 5 conclusion

The brain belongs to the brain, and the earth rotates without anyone, and those who should rush the manuscript still have to rush the manuscript. But it's also good to dream occasionally and review theoretical mechanics by the way.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: shepherd

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