For more than three centuries, Newton's laws of motion have helped scientists understand the relationships between body of mass and the forces that act on it, like the forces acting on a planet orbiting the sun.

Newton's equations weren't perfect, however.

When trying to account for three bodies -- a moon orbiting a planet orbiting a sun, for example -- Newton struggled to solve the equations related to mass and motion.

Simply put, neither Newton's laws of motion, nor any physical laws, explain the movements of three bodies in orbit. The equations don't compute.

Fast forward 350 years, and scientists have made one of the largest steps yet in solving Newton's three-body problem.

For the new research, scientists focused on recent discoveries related to unstable three-body systems, chiefly, that models suggest unstable three-body systems will eventually expel one of their members, with the remaining two forming a stable relationship.

Astrophysicists Nicholas Stone, a professor at the Hebrew University of Jerusalem's Racah Institute of Physics, and Nathan Leigh, a professor at Chile's La Universidad de Concepción, used mathematical equations to describe and predict the movements of planets in an unstable system.

"When we compared our predictions to computer-generated models of their actual movements, we found a high degree of accuracy," Stone said in a news release.

While their work -- published this week in the journal Nature -- doesn't solve Newton's three-body problem, the authors claim their statistical representation of an unstable three-body system will help scientists visualize the complicate processes involved in three-body systems.

"Take three black holes that are orbiting one another," Stone said. "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."

Moving forward, scientists hope to tweak their equations to explain the relationship between two bodies that have recently expelled the third body and formed a newly stable relationship.

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