May 19, 2024

# The science behind the ‘three body problem’ – so you can have an opinion too

At first glance, the Netflix series “3 Body Issue” deals with a classic sci-fi theme: humanity’s encounter with an extraterrestrial civilization. But with a new twist: The Trisolarians come from a planet that orbits not just one sun, but three suns. As a result, the planet’s orbit is constantly changing – sometimes deadly cold, sometimes intense heat. Only in the few “stable periods” that exist can this form of life continue to evolve. Could something like this really exist? So what exactly is this “three-body problem”?

## What is the three-body problem?

It is the mathematical formula for the question of how three celestial bodies whose gravitational pull affects each other move. The equations themselves are very simple, consisting of Newton’s law of motion of three bodies.

## What does it mean?

Around 1660, Isaac Newton realized that an object exerted by a force accelerates in the direction of that force. He realized that the force of attraction between two bodies is proportional to their mass and inversely proportional to the distance between them.

Reciprocal interaction: Block 1 “pulls” Blocks 2 and 3, Block 2 on Blocks 1 and 3, and Block 3 on Blocks 1 and 2. Two masses that get close enough together fall toward each other, so to speak, and then circle around another common center. This can be solved analytically and described by a formula. With three objects, one mass always disrupts the paths of the other objects. The system is behaving “chaotically”.

## Does this mean he does what he wants?

no. Even a chaotic system behaves “deterministically.” This means that if you know the initial conditions, i.e. the location and speed of each block, you can calculate how the system will evolve further. However, the result of calculations in chaotic systems depends largely on the initial conditions.

## So chaos is not chaos?

This depends on how you understand the term. In the 1980s in particular, chaos theory investigated the commonalities between chaotic systems, whose behavior strongly depends on initial conditions. To put it bluntly, these are often dynamic systems (their state changes over time) with nonlinear interactions between their individual components. The main result of chaos research was that such systems, although unpredictable, exhibited some regular behavior – completely independent of specific physics. For example, in phase space they have the so-called Strange attractions Which in turn Fractal dimensions You have – but here it gets very mathematical.

## So you can calculate the orbits in the three-body problem?

Yes, but you can only solve equations numerically, not analytically. However, numerical solutions are never completely accurate because they come from calculations with specific, finitely long numbers. So there are always small rounding errors. This is usually not that bad – but in chaotic systems it can lead to completely wrong solutions.

The author of the Trisolaris trilogy, Cixin Liu, explained in an interview that he had been fascinated by this paradox for a long time: There is a system of three equations that at first glance seems not particularly complicated, but we cannot solve it. He wondered: If humanity cannot solve such a simple problem, how can it imagine that it can solve the more complex problems it faces?

## Are there star systems with three suns and one planet?

Yes there is. The Alpha Centauri system, which is about 4.3 light-years away, contains three stars and at least one planet: Alpha Centauri A, Alpha Centauri B, and the star Proxima Centauri, 0.2 light-years away, in addition to the star. The star system HD 131399, in which a large gas planet can be found. In the two examples mentioned, the two suns are relatively close to each other, which is why they are completely stable. Only when we have a system of three objects of similar mass that are relatively close to each other is their motion chaotic.

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## Could there be life in such a system?

Based on what we know, this is highly unlikely. However, very unlikely cases also occur – if you repeat the experiment often enough. However, there is no scientific consensus on the question of the number of planets in the universe on which life could exist in principle. Although there is a formula for estimating this figure – the so-called Drake’s formula. However, the individual factors in this formula can only be approximately estimated.

Almost done!