Mathematicians uncover 12,000 new solutions to ‘elusive’ 3-body problem – Times of India

Mathematicians uncover 12,000 new solutions to ‘elusive’ 3-body problem – Times of India
  • PublishedSeptember 20, 2023


NEW DELHI: In the world of physics and mathematics, the three-body problem has long been a tricky puzzle, illustrating the intricate complexity of the natural world. When dealing with two objects orbiting each other, say a lone planet orbiting a star, the mathematics behind it can be elegantly summarized in just a few equations.
However, when a third body is introduced into the mix, the math becomes tough. The gravitational interactions between all three objects make calculating a stable orbit a daunting task.
An international team of mathematicians claimed to have unearthed a remarkable 12,000 new solutions to this formidable problem, significantly expanding upon the few hundred known scenarios.
Their findings have been made available as a preprint on the arXiv database, although they have yet to undergo the rigorous peer-review process.
Isaac Newton laid down his foundational law of motion over 300 years ago, and scientists have grappled with the three-body problem ever since.
Unlike the simple and predictable orbit of Earth around the Sun, the orbits in the three-body problem can resemble intricate and convoluted patterns, resembling pretzels and scribbles.
These newly discovered solutions are no exception, as three hypothetical celestial bodies start from a state of rest and, under the influence of gravity, are drawn into intricate spirals toward one another.
They subsequently pass each other, moving further apart, until gravity’s attraction reignites, causing them to converge once again. This mesmerizing twirl repeats indefinitely.
Lead study author Ivan Hristov, a mathematician at Sofia University in Bulgaria, utilized a supercomputer to uncover these orbits.
Hristov believes that even more solutions could be found with more advanced technology, possibly up to five times as many.
Three-body systems are common in the universe, with numerous star systems featuring multiple planets or even multiple stars orbiting one another.
In theory, these newfound solutions could prove invaluable to astronomers seeking to decipher the cosmos. However, their utility hinges on their stability, i.e., whether the orbital patterns can persist over time without disintegrating or ejecting one of the celestial bodies into space.
Hristov acknowledges the importance of studying stability to assess their astronomical significance.
Juhan Frank, an astronomer at Louisiana State University not involved in the research, expresses scepticism regarding the stability of these orbits.
He believes they are “probably never realized in nature” and tend to disintegrate into a binary system with an escaping third body, typically the least massive of the three.
Nonetheless, irrespective of their ultimate applicability, these newly discovered solutions are a mathematical marvel.
“Whether stable or unstable, they are of great theoretical interest,” Hristov noted.


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