Introduction to chaos: How the 3-body problem complicates Newtonian physics.

Chinese science fiction writer Liu Cixin became very popular with his book series ‘Remembrance of the Earth’s Past’, also known as ‘The Three-Body Problem’; this is the name of the first book of the trilogy. The work, which was recently adapted into a TV series by Netflix, is one of the most talked about topics on the internet.

Despite the fame of the series, not all readers of the work and viewers of the series know that: The ‘three-body problem’ concerns a still unsolved question in Newtonian physics.

The title of the series refers to the Newtonian problem: The theory shows that a system of two-bodied celestial bodies can regulate their binary gravitational interactions without any problems. However, the entry of a third object into this ‘orbital waltz’ would create a much more unpredictable scenario.

“The three-body problem in astronomy is the problem of determining the motion of three celestial bodies that do not move under any influence other than mutual gravitational forces. A general solution to this problem (or the more general problem involving more than three bodies) is not possible because the motion of the bodies quickly becomes chaotic.

In fact, the ‘three-body problem’ is not completely unsolvable because scientists have already found some solutions to solve some gravitational questions regarding three or more celestial bodies. But, these solutions are only suitable for some specific systems; For example, by examining a three-body system with unique parameters, researchers were able to explain how this structure works.

Chaos and the three-body problem

Concept used in the literary work and the Netflix adaptation He explains that the gravitational dynamics between two celestial bodies can be explained, but physicists and astronomers have not yet solved the dynamics related to three or more objects..

For example, the situation between the Earth and the Moon or between the Earth and the Sun can be explained relatively simply by the laws proposed by scientists such as Johannes Kepler and Isaac Newton. The addition of a third celestial body, such as a second Moon close to our planet, would significantly affect orbital dynamics. It is not surprising that some thinkers describe this exquisite dynamic between two cosmic objects as a ‘dance or orbital waltz’.

As noted, science has already managed to solve the three-body problem in some types of systems. However, there is still no single solution to solve this problem. Experts in the field explain that chaos theory is closely linked to the three-body problem, adding a third body will cause chaos and unpredictability in gravitational dynamics; this can occur with even the smallest gravitational changes in a system.

French mathematician and physicist Jules Henri Poincaré was one of the thinkers who initiated the debate on what would later be known as chaos theory. To contain, Poincaré tried to solve the problem of the three bodies while he was still alive and, based on his observations, realized that it was an ‘unsolvable’ problem.

Isaac Newton’s theory of gravity is capable of fully explaining the gravitational interaction between two celestial bodies, but interrogating three bodies requires an equation that explains more about this strange dynamic.

In the case of two celestial bodies, Newton proposes that the system moves in an orbit based on the idea of ​​planetary motion proposed by Kepler; Kepler’s first law explains that every planet in the Solar System moves in a conical manner. When there are two celestial structures, these conical motions share the same focus, which is the center of mass of the two objects.

“Problem [dos três corpos] can be solved for some special cases; cases where the mass of an object, such as a spaceship, can be considered infinitely small; the Lagrange case where three bodies form an equilateral triangle; and Euler’s case, in which two bodies are at rest,” adds the encyclopedia Britannica.

If we add another celestial body to the binary system, chaos theory comes into play and scientists cannot understand the unpredictability of these orbital dynamics. Even with the most modern computational models and the work of the best mathematicians and physicists, we have been able to find an explanation for only some of these more complex systems.

The book series and the Netflix adaptation share the same scenario: Humanity faces an invasion of aliens who live in a solar system with three suns and where unforeseen problems permeate the region. Just like Liu Cixin’s work, modern scientists have still not been able to solve the three-body problem.

Do you believe this problem will be solved one day?

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