A new theory for solving the three-body problem - one of the oldest problems in science

                                                                                                                                           An Israeli study led by Prof. Barak Kol from the Hebrew University heralds a new approach to the problem of the three bodies and accurately predicts the statistics of the system's behavior

The three-body problem is necessary for the understanding of a variety of astronomical processes and even for the understanding of a wide class of problems in mechanics, which is why it has occupied the best physicists, astronomers and mathematicians for over three hundred years. Their experiments led to the discoveries of several important fields of science, but its solution remains a mystery.

At the end of the 17th century Sir Isaac Newton was able to explain the movement of each of the planets around the sun by a single and simple law describing the force of attraction between them. He also sought to explain the movement of the moon, and since its movement is determined by both the earth and the sun, he was interested in the problem of predicting the movement of any three bodies moving in space under the influence of the mutual gravitational force between them (see the attached figure), a problem that was later named "the problem The three-body". However, unlike the two-body problem, Newton was unable to find a closed and general mathematical solution for it. If so, The three-body problem is easy to define but difficult to solve.

At the end of the 19th century, after about two hundred years of fruitful research in the field including by Euler, Lagrange and Jacobi, the great mathematician Poincare discovered that the problem shows a high sensitivity to the initial position and speed of the bodies. To speak has a far-reaching meaning - this sensitivity shows that there is no deterministic (fixed in advance) and exact solution to the three-body problem. In the 20th century, the development of computers made it possible to re-examine the problem with the help of simulations simulating the movement of bodies. The simulations showed that usually a three-body system will experience periods of chaotic (random) motion and in between periods of regular motion until finally The system decomposes into a pair orbiting around the common center of mass and a third body moving away or escaping from them. Due to the sensitivity to initial conditions, the computer simulation also does not provide a reliable solution for a single three-body system, however, performing simulations for large collections of systems led in 1976 to the idea that it is possible to predict the statistics of the system's movement, and in particular to predict the survival chance of each of the three bodies. In this sense, the original question, to find a deterministic solution, turned out to be incorrect, andIt was recognized that the right question is to find a statistical solution.

Determining the statistical solution proved to be no easy task due to several elements of difficulty that exist in this problem: the system presents a chaotic movement that alternates with a regular movement, and the system is not blocked and allows disintegration. A breakthrough in the subject happened when Dr. Nicholas Stone from the Rakah Institute of Physics at the Hebrew University and his partners They used a new calculation method, and obtained for the first time a closed mathematical expression for the statistical solution. Recently, this method was even improved by Yondav Bari Ginat and Prof. Hagai Peretz from the Technion. But this method, like all its predecessors in the subject of the statistical solution, is based on certain assumptions. Inspired by the results of Alohal Prof. Barak Kol from the Rakah Institute of Physics at the Hebrew University In a reexamination of the assumptions. It was found that the assumption that the movement is random is inaccurate because it does not take into account the regular movement after the breakup, and that one of the variables has an arbitrary component.

In a study that will soon be published in the scientific journalCelestial Mechanics and Dynamical Astronomy, was offered A new theory for the statistical solution, which corrects these defects by a different conceptual basis. The chances of survival predicted by this theory are different from all the works that preceded it, and Prof. Cole emphasizes that "Examination by millions of computer simulations showed a high agreement between the theory and the simulation". This adjustment proves that understanding the system requires a perceptual change and that the new conceptual basis describes the system well. It becomes clear, then, that it is possible to innovate even with regard to the foundations of such an old problem.

The implications of this research are broad. It is expected to influence both the solution of a variety of astrophysical problems and the understanding of a whole class of problems in mechanics. In astrophysics, it may be used to find the mechanism that creates pairs of compact bodies that are a source of gravitational waves, as well as to deepen the understanding of the dynamics within star clusters. In mechanics, the three-body problem is a prototype for a variety of chaotic problems, so progress in it is expected to radiate to other problems in this important department.

for the scientific article

More of the topic in Hayadan:

• Theory: the universe is like football - and it is finite
• Researchers from Israel and Chile solved Newton's three-body puzzle from 330 years ago
• The problem of the three bodies - why, despite the crash, this is a great achievement