Technion-Israel Institute of Technology

Professor Hagai Perets and Yonadav Barry Ginat. The three -object problem is one of the oldest mysteries in physics. It concerns the motion of a system of three objects, such as the Sun, Earth, and Moon.

**Nationalgeographic.co.id—**The problem is three things is one of the mystery oldest in physics. This problem concerns the motions of systems of three bodies – such as the Sun, Earth, and Moon – and how their orbits change and evolve due to their mutual gravity.

When one large object approaches another, the relative motion of the two objects follows a trajectory determined by their mutual gravitational attraction. But when the two objects move together and change their position along their trajectory, the force between them, which depends on their mutual position, also changes. In the end this affects their trajectory and others.

For two objects (such as the Earth moving around the Sun without the influence of another object), the Earth’s orbit will continue to follow a very specific curve, which can be described with mathematical accuracy (ellipse).

However, once one adds another object, this complex interaction gives rise to the three-object problem. This is referred to as a problem because the system becomes chaotic and unpredictable. One cannot simply determine the evolution of the system over a long time scale.

Problem physics This so-called triple body problem has been the subject of scientific research for over 400 years. In the past, physicists including Isaac Newstom have tried to solve mystery which are called three -thing problem this.

In 1889, King Oscar II of Sweden even offered a gift, in commemoration of his 60th birthday, to anyone who could provide an overview of the mystery physics the. In the end, it was the French mathematician Henri Poincaré who won the competition.

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Technion

An example of the motion of a three-body system in the universe.

Poincaré presents a solution that proves precisely that the interaction is chaotic, in the sense that the end result is essentially random. His findings then opened a new field of scientific research, called theory *chaos*.

The absence of a solution to the three-body problem makes it impossible for scientists to predict what will happen during the close interaction between a binary system (formed from two stars orbiting each other such as the Earth and the Sun) and a third star. Unless they simulate it on a computer and follow the evolution of the system step by step.

Such simulations show that when such an interaction occurs, it takes place in two phases. The first phase is a chaotic phase when the three objects are strongly attracted to each other, until one star is ejected and then a second phase occurs. If the third star is in a bound orbit, it eventually descends back toward the binary system so that the first phase occurs once again. The recurrence only ends when, in the second phase, one of the stars escapes in an unbound orbit and never returns to the binary system.

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In a paper recently published in the journal *Physical Review X*, PhD student **Yonadav Barry Ginat** and **Professor Haggai Perets of** The Technion-Israel Institute of Technology uses this randomness to provide a statistical solution for the entire two-phase process. They calculated the possible outcomes given from each phase-1 interaction.

Although chaos implies that a complete solution is impossible, its random nature allows one to calculate the probability that the interaction of a three-body system ends in one particular way, rather than another. Then, a whole set of approaches can be modeled using a particular type of mathematics, known as random walk theory, which is sometimes referred to as “the drunkard’s path.”

The term theory gets its name from mathematicians who think of a drunken walking. He regards the drunkard’s walking process as a random process with each step being unconscious of the drunkard himself. It doesn’t realize where it is and then also takes the next step in some random direction. Basically, the three-body system behaves in the same way.

After each close encounter, one of the stars is randomly ejected (but with three stars collectively still maintaining the energy and momentum of the entire system). One can think of a series of close encounters as the path of a drunkard. Like a drunkard’s move, a star is randomly ejected, returns, and another (or the same star) is ejected in a possibly different random direction (similar to another step taken by a drunkard) and back, and so on, until a star is completely properly ejected into never to return (and the drunk fell into the ditch).

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What Ginat and Perets show in their new research is how random walk theory can be applied to solve three -thing problem. They calculated the probability of each phase-2 single-binary configuration (e.g., the probability of finding a different energy), and then compiled all of the individual phases, using random walk theory, to find the final probability of each possible outcome.

“We came up with a random walk model in 2017, when I was an undergraduate student,” Ginat said, as quoted by SciTechDaily.

“I took a course taught by Professor Perets, and there I had to write an essay about three -thing problem. We didn’t publish it at the time, but when I started my Ph.D. studies, we decided to expand the essay and publish it.”

Now, with the results of a recent study by Ginat and Perets, all three-body, three-body, or multi-stage interactions, can be completely statistically resolved.

“This has important implications for our understanding of gravitational systems, and particularly in cases where multiple encounters between three stars occur, such as in dense clusters of stars,” said Professor Perets.

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