1889, the famous mathematician Henry Poincare proved that in a three-body system, we can't find any formula to accurately judge its future position. Even if the complexity of the whole solar system is not considered, even if it is simplified, the three-body is still difficult to solve. With this paper, he also won the grand prize sponsored by the King of Sweden.
For many years, scientists have been trying tirelessly to simplify the three-body system. Including science fiction works, it is inevitable to mention this problem, such as the famous novel Three-body, which is also named after it, and the three-body man is also troubled by the irregular illumination of three stars.
Three-body correlation problem
Special case of three-body: When the mass of one of the three celestial bodies is negligible compared with the mass of the other two celestial bodies, such a three-body is called a restricted three-body. Generally, this kind of small-mass celestial body is called infinite small-mass body, or small celestial body for short; Two massive celestial bodies are called finite mass bodies.
If the mass of a small celestial body is regarded as infinitesimal, then its attraction to two finite mass bodies can be ignored, that is, it does not affect the motion of the two finite mass bodies. Therefore, the discussion of the motion state of two finite mass bodies is still a two-body problem, and its orbit is a conic curve focusing on its center of mass.
According to the four different situations of circular, elliptical, parabolic and hyperbolic conic curves, the corresponding restricted three-body problems are divided into four types: circular restricted three-body, elliptical restricted three-body, parabolic restricted three-body and hyperbolic restricted three-body.
Hill studied the motion of the moon according to the restricted three-body theory, ignoring the eccentricity of the solar orbit, the solar parallax and the inclination of the lunar orbit. In fact, this is a notice restricting the three-body special plane. The periodic solution he got is the middle track of Hill's theory of lunar motion.
In the theory of asteroid motion, it is often discussed in terms of elliptical restricted three-body The motion of the Toro sheep asteroid is an example of the equilateral triangular solution of an elliptic restricted three-body composed of the sun, Jupiter and asteroids. Brouwer also discussed the gap of the asteroid ring according to the elliptic restricted three-body theory.
Parabolic restricted three-body and hyperbolic restricted three-body are rarely used in celestial mechanics. After the appearance of artificial celestial bodies, the restricted three-body has a new use, which is often used to study the simplified mechanical model of the motion of lunar rockets and interstellar vehicles. See the motion theory of lunar rockets and interstellar spacecraft.