Researchers from Israel and Chile solved Newton's three-body puzzle from 330 years ago

This problem was first presented by Newton in his article "Principia" in which he described the laws of gravity and the motion of the planets. The statistical solution was discovered by Dr. Nicholas Stone from the Rakah Institute of Physics at the Hebrew University in collaboration with the researcher Nathan Lee from the University of Concepcion in Chile

The oldest problem in astrophysics receives a solution on paper and pen for the first time: researchers from the Hebrew University and Concepción University in Chile have published an article in the prestigious journal "Nature" describing for the first time a statistical solution to the famous problem in the scientific world, known as the "three-body problem".

When the famous scientist Sir Isaac Newton published the three laws of motion, he was able to use them to describe the elliptical orbit of the Earth around the Sun. Despite the scientific success of his time, when Newton added the moon, another third body, to the equations, the problem became complex and difficult to solve. This is how the famous problem got its name "the three-body problem" and remained open for about 330 years until today.

The main obstacle facing those trying to solve the "three body problem" stems from the system's chaotic software. Chaotic systems are difficult to describe because small changes in their initial state lead to huge changes in their final state. In recent years, researchers have managed to avoid the chaos of the "three-body problem" by carefully choosing the masses of the stars, but general systems containing three stars will usually be chaotic and difficult to predict. In order to overcome the difficulty and predict their position and speed over long periods of time, the scientist must make a fairly accurate measurement of their initial state, which is not possible as an experiment. Along with technological developments in the 20th and 21st centuries, researchers have used computer simulations to describe how three or more bodies in space move through space.

The computer simulations taught the scientists that over long periods of time systems with three bodies will disintegrate into a pair of stars and a third star separated from them. The interesting software allowed Dr. Nicholas Stone and Dr. Nathan Lee to turn the bowl upside down and treat the chaotic feature of the system as a tool instead of an obstacle. Chaotic systems have an interesting feature that allows the stars to be at all speeds and positions under the limitations of the laws of nature and the structure of the system. Thanks to this feature, the researchers discovered a formula with which they can predict the probability of the stars' velocities, their positions, the scattering angle at which the pair of stars separates from the third star, and more. The mathematical development was not at all simple and to make sure that the formulas correspond to the laws of physics, the researchers built simulations that simulated three stars in space and indeed the results corresponded to the theory.

The "three-body problem" is a very common problem in astrophysics. One of the open problems in space research examines the physical processes for merging black holes, and the conditions that would create a system of a pair of black holes in the first place. The main explanation given today focuses precisely on the statistical properties of the three bodies because over long periods of time such threes can form pairs of stars or black holes.

Dr. Stone excitedly described that "we hope that the solution we presented will be useful for problems in astrophysics and for researchers who wish to delve deeper into three-body systems, the dynamics of black holes and other objects in the universe. Beyond that, we are happy to present for the first time significant progress in the famous problem. A solution that can be written with a pen on a page, even if it is a probabilistic solution, is always better and even more useful for physicists with which they can imagine complex systems. In addition, I think there are those who will find a little satisfaction in our formulas because for the first time we used chaos as a tool and not as an obstacle to finding a statistical solution to the 'three-body problem'."

Dr. Nicholas Stone is a young researcher at the Rakeh Institute of Physics at the Hebrew University of Jerusalem. Dr. Stone is funded by the NASA research fund and his research deals with many theoretical problems in astrophysics starting with gravitational waves, radiation bursts from black holes and unique systems in space.