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

Happy New year. If there is anything to celebrate on the first day of the Lunar New year, I believe those of you who love physics will blurt it out-"wandering Earth 2" has been released. I just got out of the cinema, and it's really a good science fiction movie.

Here are the settings for readers who don't know the background of the story. According to the story lines shown in the film production notes [1] and trailers: as early as 1977, some astronomers speculated on the acceleration of solar core fusion based on the historical records of solar activity; in 2026, a solar storm exceeding the G5 level broke out. The international began to pay attention to the helium flash crisis, and gradually formed a spaceship school fleeing in a spaceship and an earth school wandering with the earth. In 2030, the Earth plan was adopted and began to build the planetary engine that propelled the Earth; in 2039, the braking age, the earth's rotation was stopped by the engine; in 2042, it was planned to start month by month; in 2044, the space elevator crisis; in 2058, the moon fell crisis; in 2065, the earth stopped, propelling the engine to ignite, entering the era of acceleration; in 2075, Jupiter gravitational crisis; and in 2078, the solar helium flash crisis.

Let's start with the motivation of the whole story, that is, the rapid expansion and aging of the sun, that is, helium flash.

1. Helium flash: why does the sun age? Our sun is in its prime, which is astronomically called the main sequence star stage. It is about 3/4 hydrogen, 1/4 helium and contains small amounts of oxygen, carbon, neon and iron. The energy source of the sun's glow and heat is mainly due to the fusion of the hydrogen in it, and every four hydrogen (protons) converge into a helium nucleus, which is called the proton-proton chain reaction.

The inner layer of the sun can be fused to produce helium at high temperature and high pressure, while the outer environment is not high enough for hydrogen to fuse. Because of the large mass of the sun, the helium produced in the inner layer is trapped by gravity, and the hydrogen in the outer layer cannot get into the interior. Therefore, when the hydrogen in the inner layer of the sun is depleted and all turns into helium, the heat produced by the inner fusion cannot resist gravity and collapses.

Inner and outer layers of the sun | Source: bilibili@ Bard Kidd but this does not mean that the sun will shrink, because the collapsed inner layer will become hotter, heating up the hydrogen in the outer layer and igniting the fusion reaction, which instead causes the sun to expand thousands of times, and the surface can even reach the orbit of Venus. At this point, the sun enters the red giant phase. Red giant stars usually last 1 billion years. At the end of the red giant, the temperature of the sun's core can be as high as 100 million degrees, enough to ignite the nuclear reaction in which helium aggregates into carbon and oxygen, which is called helium flashover.

So, according to current star theory, long before helium flashes, the sun expands into a red giant, roasting life on Earth.

According to the current theory, solar energy lasts for 11 billion years in the main sequence star phase, but now that the sun is only 5 billion years old, there is no need to worry about its expansion and aging.

two。 Planetary engine: is heavy nuclear fusion feasible? To propel Earth, a total of 12000 planetary engines have been built, of which 10, 000 are built in the Northern Hemisphere for propulsion and 2, 000 near the equator for steering. The height of these engines is more than 10,000 meters and covers an area of about 1,000 square kilometers.

Steering and propulsion engines, as hard-core fantasies, we estimated six months ago that the first step in the earth's wandering is how to brake rotation (how to make the sun rise in the west). We assume that the engine uses the old aerospace favorite refrigerant propulsion scheme, and that the engine can eject the working fluid at the second cosmic speed 11.2km / s, and then calculate how much power this requires.

According to the film production notes, it took people 26 years to complete the brakes, but in the original novel it took 42 years to complete, and here we use the time of the novel. After calculation [2], two thousand steering engines need to emit a total of 73.36 billion tons of working fluid per second, with an average power of 4.6 × 1021W.

You may have no idea about this number, which, for example, is equivalent to 45 times the amount of electricity generated worldwide in 2021 per second. Compared with the current engineering technology, this is the installed capacity of 200 billion three Gorges power stations, or 575 billion nuclear fission power plant units (measured by the Kashiwazaki Kariwa nuclear power plant with the largest installed capacity at present). But for the sun, this is only 1/100000 of its radiant power.

In other words, the total thrust of the engine should reach 8.21 × 1017N, so the thrust of a single engine should reach 41 billion tons. However, both the original book and the movie set the thrust of an engine at 15 billion tons [1]. To be on the safe side, I suggest tripling this setting.

Engine start-up will generate a huge amount of heat, so at the beginning of the plan, the surface temperature will rise to 70 or 80 degrees Celsius, polar glaciers will melt, coupled with the tides caused by rotation, some coastal cities will be submerged.

The submerged Shanghai and the huge planetary engine have such a huge thrust, where can we get the energy? Wandering Earth imagines a technology-heavy nuclear fusion, that is, "burning rocks". Let's talk about what a nuclear reaction is.

The nucleus is made up of protons and neutrons, which are collectively called nucleons. Nuclei combine to form nuclei, which release energy. In the process of nuclear reaction, the binding mode of nucleon will change, and the reorganization process of this binding mode will be accompanied by the change of energy. If a nuclear reaction absorbs energy, it means that the energy of the initial state is lower than that of the final state. If the nuclear reaction releases energy, it means that the energy of the initial state is higher than that of the final state.

Because of the conservation of the number of nucleons in a nuclear reaction, we divide the energy released by the binding of a nucleus by its number of nucleons, thus defining the average binding energy of nucleons in that nucleus. The higher the average binding energy is, the lower the nucleon energy is and the worse the reaction activity is. The smaller the average binding energy is, the higher the energy of the nucleon is and the more likely the nuclear reaction is.

The specific binding energies of different nuclei can be seen from the diagram that H1 has the lowest average binding energy (because it has only one proton and there is no binding yet), and the average binding energy of Fe56 is the largest. Any nucleus whose average binding energy is less than Fe56 can approach Fe56 and release energy through nuclear reaction. The nucleus on the left of Fe56 can be fused into Fe56, while the nucleus on the right can be transformed into Fe56 by fission.

We have just talked about the hydrogen nuclear fusion of the sun, and it can also be seen from the picture that helium nuclei can continue to coalesce into carbon, nitrogen, oxygen and so on, but the subsequent reactions require higher pressure and temperature.

The same is true of the carbon-nitrogen-oxygen cycle in stars heavier than the sun, where the main oxygen and silicon in rocks can be fused and moved closer to iron at extremely high temperatures and high pressures. But at present, people have not even mastered light nuclear fusion. At present, there are three generations of fusion technology being studied, the first generation is mainly deuterium-tritium fusion, which requires relatively low temperature and pressure; the second generation is the fusion of deuterium and helium 3, and the third generation is the fusion of two helium 3, the reaction conditions of these two generations are more stringent.

3. Monthly plan: Roche limit? Ignite the lunar nucleus? The gravity between the sun and the moon is about 2 × 1020N, and the full power operation of all engines can not directly offset this force. In order to eliminate this uncontrollable factor, wandering the Earth sets a monthly plan.

The three bright spots on the moon are three lunar engines, but we can know from the trailer that there was a lunar fall crisis in 2058, and one of the moon was not accidentally pushed out, but crashed into the earth.

This picture is very interesting, the red circle is the Roche limit of the moon relative to the earth. What is the Roche limit? Let's take the first film as an example.

In the first movie, when the earth is growing with Jupiter's gravitational slingshot, it accidentally miscontrols its trajectory and is about to fall into the Roche limit. If you don't find a way to exert more thrust to escape, it will be torn apart by Jupiter's gravity and become part of Jupiter's ring.

This shredding force comes from the non-uniformity of gravity. Jupiter's gravity on the earth is uneven, the gravity far away from Jupiter is small, the gravity close to Jupiter is strong, and this gravitational difference will form a tidal force. Yes, the name is precisely because the tide on the earth is caused by the tidal force of the moon on the earth, and the rise and fall of the moon leads to the rise and fall of the tide.

The tide-generating force will increase with the decrease of the distance between the two celestial bodies, and when the distance decreases to the Roche limit, the tide-generating force will exceed the earth's own gravity, thus causing the earth to collapse. For rigid bodies and fluids, the Roche limit is calculated as follows:

Rigid body Rosie wood ground

Fluid Loxi wood ground

But there's a bug in the movie. The average density of the Earth is 5.514g / cm3, while the average density of Jupiter as a gaseous planet is 1.326g / cm3, so the Roche limit is smaller than the radius of Jupiter, that is, there is no Roche limit before the Earth collides with Jupiter. Of course, if you consider Earth's fluids, such as Earth's atmosphere, it will indeed be torn apart by Jupiter's gravity before the collision.

The Earth's atmosphere and Jupiter's atmosphere are pulled back to the second film. The average density of the moon is 3.340g / cm3. It can be calculated that its rigid body Roche limit for the Earth is 1.49 times the radius of the Earth. So in the movie, when the moon falls to the earth, the moon will be torn apart by tidal force before it touches the earth.

The month-by-month plan finally succeeded with difficulty. People first install thousands of nuclear bombs on the lunar surface, detonate through a phased array, and concentrate the shock waves on the lunar nucleus, triggering lunar nuclear fusion. Although director Guo Fan said frankly that it was a crazy idea to let the moon collapse, it would take at least 1 billion times the current reserves of nuclear weapons to destroy the moon directly. But this plot shows that in the face of global crisis, countries finally "put aside their obsession with history, the present and the future" and choose a rational way of cooperation.

"Today people do not see the ancient moon, this month once according to the ancients." Since then, the earth has embarked on a lonely wandering journey.

4. Mountain removal Project: pushing the Earth out of the Solar system? Now that all the preparatory work has been done, it is time to leave the solar system. So where should the engine be sprayed?

Intuitively, if you want to escape from the sun, of course you have to spray at the sun. But the problem is, according to our estimate in the second section, the thrust of 10,000 propulsion engines is only 4.1 × 1018N, which can only provide the earth with an acceleration of 0.7 μ m / S2, compared with about 3.5 × 1022N between the sun and the earth. So it is not feasible to push it off the earth in a daze.

A more practical solution is to make the acceleration direction follow the speed direction of the earth's revolution, so as to maximize the kinetic energy. There are two points here: first, it is not necessary for velocity to turn back to the source of gravity to get rid of gravitational bondage. As long as the kinetic energy is large enough to exceed the gravitational potential energy, as long as the direction of velocity does not blankly point to the source of gravity, the object can break free from gravity. Second, under the condition of the same engine power, the momentum increment obtained by the back injection is the same, which can be approximately understood as the constant velocity increment of the earth. When the direction of the velocity increment is the same as that of the original velocity, the kinetic energy increment will be the largest.

Today's aerospace technology also uses this acceleration direction to achieve the ascent from low orbit to high orbit. In most cases, this is the most fuel-efficient way to change orbit, also known as Horman transfer orbit.

Horman transfer orbit I imagined the process of ascending the Earth to the orbit of Jupiter, which would take at least a hundred years according to the engine thrust calculated in the second section. In order to catch up with the timeline of the movie, regardless of the thrust of the engine, we directly assume that each recent ignition can generate a 3km / s growth rate for the earth, then it only takes three times to change the orbit.

The reason why it is ignited only in the past few days is that the speed of the earth is the highest, the mechanical energy increased by the same speed increment is the most, and the farthest point can be lifted. In the original work, people get nervous every time they pass perihelion because they don't know when the helium flash will explode, which is likened to "cosmic Russian roulette."

Jupiter's gravitational slingshot acceleration effect (as an illustration, there is no ignition in the picture) the Earth will have a slingshot interaction with Jupiter's gravity as it approaches Jupiter, gaining some of Jupiter's momentum and speeding up. This process is actually like waving a racket when you play. If the mass of the ball is very small compared to the racket, then the ball can grow up to twice the speed of the racket.

Earth's mass is only 3/1000 of that of Jupiter, so it can be thought of as a light ball hit by Jupiter's racket, so it can get a considerable speed increase from the gravitational slingshot.

5. Wandering destination: Samsung system? Through Jupiter's gravitational slingshot, the earth officially broke away from the gravitational shackles of the solar system and headed for a new sun. In wandering Earth, people regard Proxima, which is 4.2 light-years from the sun, as their new home.

The idea is wonderful, but there is a thorny problem: Proxima Centauri and Alpha Centauri A (South Gate II A) and Centauri α B (South Gate II B) constitute the three-star system. This alpha-Samsung Centauri system is the site of the three-body civilization set in the science fiction "three-body". The reason why the trisomy people want to invade the earth is because their three-star system will move irregularly under the action of gravitation. we have introduced it in "finding a stable solution for the three-body before the three-body broadcast". Of course, at present, Proxima is relatively far away from the South Gate 2 AB binary, and it is still in the permanent era according to today's orbital parameters.

Alpha Samsung Centauri system | Source: KOSMO, but there is a joke:

On the way to wander the earth, people encounter the trimaran fleet.

Earthlings: our sun is aging rapidly and we are moving to neighboring galaxies.

Trisomy: our star system is unstable and we have to move to the solar system.

Earthlings and three-body people look at each other.

Several galaxies closest to the Sun | Source: KOSMO considering that the book "wandering Earth" was written earlier than the "trisomy", it is estimated that Da Liu himself did not expect such a coincidence. So is there a better choice? The second closest star observed to Earth is Barnard, six light-years from Earth. Like Proxima, it is also a red dwarf with a mass of about 0.144m ☉ and a surface temperature of about 3000K.

In November 2018, it was discovered that Barnard also had a planet named Barnard b by the apparent velocity method (Doppler shift method). It is more than three times the mass of the Earth and its surface temperature is about-170 ℃.

Barnard star b art imaginary map, if the earth is parked into the orbit within Barnard star b, it should also be able to obtain a good living environment. This avoids the chaotic operation of the Samsung system, but requires an extra 1.8 light-years of wandering, or about 400 years.

Throughout the entire wandering earth project, people accelerate to 5/1000 of the speed of light in 500 years, then 2/3 of the journey in 1, 300 years, and then decelerate into the gravitational range of Proxima in 700 years, adjusting the course of the earth and bringing it into a stable orbit. The whole process lasted 2,500 years and spanned 100 generations.

Some people in the film questioned whether it could be finished. Teacher Li Xuejian replied, "I believe that my child will believe it, and so will my child's child." This spirit of Yugong moving away from the mountain is not only a gene engraved in traditional culture, but also our precious spiritual wealth in real life.

Reference:

[1] Shuo Fang et al. Notes on the production of wandering Earth movies. People's Communications Publishing House, 2019

[2] Shepherd sheep. How to make the sun rise in the west. Institute of Physics, Chinese Academy of Sciences, 2022.10.10

[3] talk to Guo Fan! Reunited after 4 years to decipher the behind-the-scenes story of wandering Earth 2!

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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