Newton's century problem
Since Newton put forward the law of universal gravitation, it is easy for people to calculate the motion of two celestial bodies in the universe under the action of gravity and get their orbits. But if there is a third celestial body, the situation is completely different. The relationship between the three celestial bodies is very complicated and difficult to solve. With more celestial bodies, the problem becomes complicated.
In the actual starry sky, the celestial system is often composed of many celestial bodies. For example, the sun, the earth and the moon constitute a "three-body", and the Ka Rong, a satellite of the sun, Pluto and Pluto, also constitutes a "three-body". There are few systems consisting of only two celestial bodies. But when calculating the orbits of these stars, it can be calculated according to the situation of two celestial bodies. For example, when calculating the earth's orbit, you don't need to consider the influence of the moon; Calculate the moon's orbit around the earth without considering the influence of the sun.
However, if you really need the influence of a third party, how to calculate it? After Newton conquered the two-body problem, he immediately began to study the three-body problem. However, due to the difficulty, even if the headache is splitting, the answer can't be found, so the cautious Newton left no discussion on this issue.
In fact, calculating the trajectory of three-body motion has greatly simplified the physical reality, and only the motion equation of particles needs to be considered, and no other factors need to be considered. When scientists study the trajectory of celestial bodies, they usually regard celestial bodies as a point with mass, which is called "particle". However, as long as we study the actual earth motion, it is much more complicated than particles. The earth is not a point or even a sphere. It seems to be an ellipsoid with a fat circle on the equator. Therefore, under the gravity of the moon, the direction of the earth's rotation axis is not fixed, so Polaris will not always be that one (astronomers have calculated that 4800 years ago, Polaris was not the current alpha star of Ursa major, but the alpha star of Draco; In the future, around 4000 AD, Cepheus gamma star will become the North Star; By 14000, Vega, the alpha star of Lyra, will gain the reputation of Polaris. When considering the tidal action, the earth is not "hard" and its rotation is getting slower and slower. If all these problems are taken into account, then no equation can accurately calculate the movement of the earth.
However, even the extremely simplified three-body, from Newton's time, in the following 200 years, Euler, Lagrange, Laplace, Poincare and other mathematical masters racked their brains and failed to conquer.
It took a lot of trouble to find a special solution.
Because the three-body problem is difficult to solve, people begin to try to solve some simplified three-body problems, that is, the so-called restricted three-body problem. We consider a situation: two massive celestial bodies (such as the sun and the earth) revolve around each other, and the mass of the third celestial body can be ignored, but this small celestial body is influenced by the gravity of the two large celestial bodies and is a restricted three-body motion. /kloc-Lagrange, a French mathematician in the 0/8th century, made a breakthrough contribution to this issue. He studied the so-called restricted three-body of elliptical orbit, which is a common orbit of celestial bodies in the universe.
During the period of 1767 ~ 1772, Lagrange obtained five special solutions to restrict the motion of three-body in elliptical orbit, and calculated five so-called "Lagrange points" in the three-body system. If an object is placed on the Lagrangian point of a three-body system, it will remain relatively stationary.
These five Lagrangian points are called L 1-L5 for short. Among them, L 1-L3 is located on the connecting line or extension line of two large celestial bodies, and L 1-L3 is unstable, that is, if the object deviates from this position due to external disturbance, it will not return to this position, but gradually move away. L4 and L5 are located in the orbits of the smaller celestial bodies around the larger celestial bodies, respectively, and form a very stable equilateral triangle with the two larger celestial bodies. At that time, due to the limitation of observation conditions, it was impossible to verify this calculation result. However, after 100 years, astronomers discovered an example in the solar system, that is, the Trojan asteroid group. These asteroids are divided into two groups, which are located on L4 and L5 of the Jupiter-sun system, and just form two equilateral triangles with Jupiter and the sun. Nature is really amazing!
In 1980s, astronomers discovered that there were several similar equilateral triangles in Saturn's satellite system. It is further found that all kinds of motion systems (including micro-motion) in nature have Lagrangian points. Even in the Earth-Moon system, there are two thin gas clouds in the orbit of the moon, 60 degrees in front and 60 degrees behind, and the distances from the earth and the moon are equilateral triangles. Two clouds take the moon around the earth, maintaining this equilateral triangle relationship with the earth and the moon forever.
"Butterfly Effect" of Three-body System
Lagrange found several finite special solutions, so can the three bodies find the general solution? 1885, Swedish king Oscar II, who loves mathematics, offered a reward to solve the stability problem of the solar system, which is actually a variant of the three-body system. Poincare, a 33-year-old young scholar from France, accepted this challenge. Because this problem is too complicated, he decided to start with a relatively simple restrictive three-body like Lagrange, trying to break through the special solution and find a universal general solution.
But in the process of research, Poincare found it almost impossible. After three years of hard work, he concluded that the problem could not be completely solved and decided to call it a day. Poincare sent his research results to the paper review Committee and wrote a sentence at the beginning of the paper: "The stars cannot be surpassed."
Poincare did not solve the three-body problem, but he still won the 1888 Swedish King Award for his contribution to this problem.
This is not over. In the follow-up study, Poincare found that the root of the three-body system is that as long as the initial data of a celestial body changes slightly due to the mutual interference of gravity, the subsequent situation may be very different, and the calculation results will be very different, resulting in meaningless calculation results. At that time, Poincare tried to draw some trajectories, but found that the graphics were too complicated and chaotic to draw at all!
In fact, this is a typical chaotic system, which will infinitely enlarge the minimum difference of initial conditions. With the passage of time, this initial change will make the motion of the whole system completely different, which makes us unable to calculate. Just like the famous saying describing chaos theory: "A butterfly flapping its wings in the Brazilian rainforest may cause a tornado in Texas." The same is true of three bodies.
Chaos theory is the third basic scientific achievement after relativity and quantum mechanics in the 20th century, but Poincare proved the sensitivity of the initial conditions of the system by studying three bodies, which is the earliest study of chaos theory.
Unbelievable planetary orbits
From Newton to Poincare, those talented mathematicians made various attempts, and finally admitted that it was impossible to find a general solution of three bodies, but only a special solution (special orbit under specific conditions).
However, it is also difficult to obtain a special solution, and it is difficult to find any solution. There are countless ways to display three objects in space, so it is necessary to find suitable initial conditions (such as starting point and speed). ) the system can return to the starting point and run repeatedly. Lagrange first proposed some solutions, and it was not until 1970s that scientists found some new solutions with the help of modern computers. What Lagrange discovered was that three equidistant objects were rotating in an elliptical orbit, just like a merry-go-round; The newly discovered one is called figure 8, and three objects chase each other in the figure 8 orbit; There is a more complicated one. Two celestial bodies rampaged back and forth in orbit, and the trajectory was messy, but the third celestial body rotated more regularly in the outer layer.
After decades of exploration, not long ago, scientists discovered more special solutions to the three-body problem. The orbits of these special solutions are very strange, and one of them is complex and changeable, which looks like a mess of noodles, but the three-body can still return to the initial state from the initial condition after passing through this messy "noodle orbit".
Can these strange trajectories be found in the real universe? So far, except for the three-body type calculated by Lagrange, all other types in the solar system are theoretical models. Scientists speculate that those grotesque three-body systems can only appear in dense globular clusters, where there are so many stars that there is almost no room for planets, let alone life. As a novel, it is possible to set a three-body civilization with superb technology, but there is no scientific basis. The scene on the three-body planet described in the novel is impossible in the universe.