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The three-body enigma -

In physics, the three-body problem comes into existence when three celestial objects (like stars or planets) orbit each other and become unpredictable. While their initial positions can be known, their future motions become an erratic dance of forces that defies exact mathematical prediction.

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Simplicity of two-body systems -

In contrast to the chaotic nature of three-body systems, two-body systems (such as binary stars orbiting each other) are orderly and predictable. Their periodic orbits allow scientists to calculate their precise movements from the past and future.

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Chaos -

Introducing a third body to a gravitational system throws the delicate balance into disarray. Instead of stable, repeating orbits, the interactions lead to unpredictable and complex trajectories that resemble chaotic paths, tangled in space.

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Spaghetti -

Unlike the neat ellipses of two-body orbits that appear almost like a venn diagram, three-body trajectories create wild patterns comparable to tangled spaghetti. There is massive complexity and instability in such systems.

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Centuries-old -

The three-body problem traces its roots back to the ‘Principia,’ a book published by Isaac Newton in 1687 to explain the universal laws of gravity. While Newton accurately described two-body interactions, he struggled to account for the complexities introduced by a third body.

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Study of gravity -

In his book, Newton also recorded the mathematics of how the planets move in elliptical orbits around the sun. He also noted that Jupiter’s gravity had an effect on Saturn’s orbit.

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Moon mystery -

Newton’s studies extended to the Earth’s moon and its erratic orbit, which caused him significant frustration. He famously referred to the difficulty of predicting its variations as a literal headache.

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Failed calculations - But Newton was never really able to mathematically solve the three-body problem, and it remained a mystery for nearly 200 years after his publication.

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Pioneering chaos theory -

In 1889, French mathematician and physicist Henri Poincaré earned accolades for his groundbreaking essay on the three-body problem. His work laid the foundation for chaos theory, a field of physics that rose to dominance over the decades.

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Chaos theory -

Chaos theory essentially explores how small uncertainties in a system’s initial conditions (such as a planet’s mass or velocity) can cause it to become massively unpredictable in the future.

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The ripple effect of uncertainty -

Chaos theory reveals that such minor inaccuracies can exponentially magnify over time. This theory applies to any three-body system, since future trajectories or orbits will remain fundamentally unpredictable beyond a certain point.

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The wrong turn analogy -

The unpredictability of three-body systems can be compared to taking a wrong turn while traveling from A to B. If a person takes a wrong turn close to the end of their journey, they’re closer to their destination than if they had taken a misstep at the beginning.

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Practical importance -

Solving the three-body problem could revolutionize our understanding of how stars and planets (including Earth) move. It would allow scientists to chart their precise long-term movements, which could have profound implications for our planet’s future.

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Climate consequences -

Even slight alterations in Earth’s orbit could drastically impact the planet’s climate. By understanding and predicting these movements, scientists can attain more knowledge on what the human race might be up against.

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Exceptions to the unsolvable problem -

Despite its reputation as unsolvable, the three-body problem has specific exceptions. In certain scenarios, such as when the three bodies move in a figure-eight path, stable solutions can emerge, but these depend on very specific conditions.

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Restricted three-body problems -

One way in which researchers try to find solutions is with “restricted” three-body problems, where two large bodies dominate (like the sun and Earth) and a smaller object (such as the moon) exerts minimal influence. This approach simplifies calculations and reveals valuable insights.

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When three stars interact -

Three-star systems, like the one featured in Netflix’s ‘3 Body Problem,’ add further complexity to the three-body challenge. Their intense gravitational pull with each other creates unpredictable orbital chaos.

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Role of computers -

Modern computers are able to simulate three-body systems with far greater efficiency than manual calculations. But these simulations are not exact, since they only provide approximate orbital paths for celestial bodies.

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Space exploration -

Solving the three-body problem would also be vital to space travel. By modeling interactions among celestial bodies and spacecraft, scientists can identify potential trajectories for missions and create libraries of viable pathways through space.

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Real-world examples - Three-body systems exist in the real universe, such as triple-star systems (e.g. Alpha Centauri) and even moons that are caught between the gravitational pulls of their planets and the sun.

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Lagrange points -

The three-body problem introduced the concept of Lagrange points, where the gravitational forces between three bodies create pockets of stability as they move around each other. Theoretically, scientists would be able to place satellites in these points in order to further study orbital mechanics.

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Connection to n-body problems -

The three-body problem is a gateway to understanding n-body problems, where more than three objects interact gravitationally. The “n” can be substituted for any number, and these systems are even more chaotic.

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Testing general relativity -

The three-body problem has also been used to test Einstein’s theory of general relativity, which is a refinement of Newton’s universal laws of gravity. By observing systems in triple-star arrangements, scientists can study gravitational effects in intense conditions.

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Black holes - Scientists have also theorized that the three-body problem could extend to more extreme celestial bodies, such as black holes. If three black holes with similar masses were to orbit each other, the gravitational effects could be devastating.

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Planet formation -

The chaotic nature of three-body systems could hypothetically provide clues about how planets form. When early solar systems develop, the interactions in clouds of gas and dust often resemble three-body problems, which influence which bodies survive or are ejected.

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Literary and artistic works -

Beyond science, the three-body problem has inspired countless literary and artistic interpretations. Its themes of chaos, uncertainty, and celestial beauty resonate with creators, as exemplified in novels like Liu Cixin’s ‘The Three-Body Problem’ (2006), which was adapted into the Netflix show.

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The promise of future breakthroughs -

While the three-body problem remains unsolved, advancements in computation and mathematical theory continue to bring us closer to understanding its intricacies. Each discovery reveals new possibilities for science and exploration.

Image credit: NASA/JPL-Caltech

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A testament to human curiosity -

The three-body problem exemplifies humanity’s relentless pursuit of knowledge. Despite its challenges, the quest to solve this puzzle has endured thanks to the world’s curiosity and determination to unravel the mysteries of the cosmos.

Sources: (Business Insider) (Live Science) (Britannica)

See also: Mistakes made by some of the most well-known scientists

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