Researchers Crack Newton’s Elusive ‘3-Body’ Problem That Has Baffled Scientists for Centuries

Visualization Newton Three Body Problem

Chaos Leads Scientists to New Understanding of Centuries’-Old Quandary

It’s been nearly 350 years since Sir Isaac Newton outlined the laws of motion, claiming “For every action, there is an equal and opposite reaction.” These laws laid the foundation to understand our solar system and, more broadly, to understand the relationship between a body of mass and the forces that act upon it. However, Newton’s groundbreaking work also created a pickle that has baffled scientists for centuries: The Three-Body Problem.

After using the laws of motion to describe how planet Earth orbits the sun, Newton assumed that these laws would help us calculate what would happen if a third celestial body, such as the moon, were added to the mix. However, in reality, three-body equations became much more difficult to solve.

Astrophysicist, Nicholas Stone

Hebrew University astrophysicist Dr. Nicholas Stone. Credit: Noam Chai/Hebrew University

When two (or three bodies of different sizes and distances) orbit a center point, it’s easy to calculate their movements using Newton’s laws of motion. However, if all three objects are of a comparable size and distance from the center point, a power struggle develops and the whole system is thrown into chaos. When chaos happens, it becomes impossible to track the bodies’ movements using regular math. Enter the three-body problem.

Now, an international team, led by astrophysicist Dr. Nicholas Stone at the Hebrew University of Jerusalem’s Racah Institute of Physics, has taken a big step forward in solving this conundrum. Their findings were published in the latest edition of Nature.

Stone and Professor Nathan Leigh at Chile’s La Universidad de Concepción relied on discoveries from the past two centuries, namely that unstable three-body systems will eventually expel one of the trio, and form a stable binary relationship between the two remaining bodies. This relationship was the focus of their study.

Instead of accepting the systems’ chaotic behavior as an obstacle, the researchers used traditional mathematics to predict the planets’ movements. “When we compared our predictions to computer-generated models of their actual movements, we found a high degree of accuracy,” shared Stone.

While the researchers stress that their findings do not represent an exact solution to the three-body problem, statistical solutions are still extremely helpful in that they allow physicists to visualize complicated processes.

“Take three black holes that are orbiting one another. Their orbits will necessarily become unstable and even after one of them gets kicked out, we’re still very interested in the relationship between the surviving black holes,” explained Stone. This ability to predict new orbits is critical to our understanding of how these–and any three-body problem survivors–will behave in a newly-stable situation.

References: “A statistical solution to the chaotic, non-hierarchical three-body problem” by Nicholas C. Stone and Nathan W. C. Leigh, 18 December 2019, Nature.
DOI: 10.1038/s41586-019-1833-8

8 Comments on "Researchers Crack Newton’s Elusive ‘3-Body’ Problem That Has Baffled Scientists for Centuries"

  1. Very misleading title. They didn’t solve anything. It is, by nature, impossible to solve. They developed a way of predicting outcomes. It is a ‘line of best fit’, not a solution.

  2. This article didn’t solve anything yet they added a very misleading title.

  3. Richard Chapman | January 6, 2020 at 6:16 am | Reply

    Three bodies of equal Mass and equal distance will eventually collide. The chaos gravitational effect will allow one body to reduce the orbital distance of the other two which will in turn cause at least two of the bodies to collide.

  4. Richard Chapman | January 6, 2020 at 6:27 am | Reply

    Three celestial bodies two of which have equal mass of the Earth and one the mass of the Moon are in alignment with the moon as the farthest point only the nearest Earth affects the moons orbit. When the alignment is Earth Moon Earth, the equal gravitational force of the earth allows the moon to escape as it pass beyond the equal force of the two bodies.

  5. Lying asses

  6. Three body?? LOL

    And what about the INfinite body problem?

  7. Bibhutibhusanpatel | April 20, 2021 at 9:56 am | Reply

    Thanks to the Auther for informìng 3 Body moton law.Let us take example of the sun,earth and moon.The law of motion binary system of earth rotatingaround sun is eaasy to formulate.Now moon is added.There is a radial vector force is actig is to sum with sun-earth binary vector force to get resultant vector force and formula of 3-body.Now we have a term of vector force due to constrain motion of moon around sun.Thìs is radial vectoŕ force due to mass of moon rotating sun transformed in radial direction of moon’s orbit to earth.But as in sky stars and other massive objects are present have some effect on constrain motion of moon is to be deleted.

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