The Three-Body Problem

by | Nov 30, 2018


The “Three-Body Problem” is one of the oldest problems in physics, dating back to the 1680s, and concerns the movement of three bodies in space under mutual gravitational interaction. The “problem” is that there is no equation or rule which predicts how three interacting celestial bodies will move in relation to each other. Some orbits of three objects repeat, while others are thrown into chaos. Physicists and mathematicians have been searching for a solution to the three-body problem for about 300 years.

Instead of an analytical solution – such as having an equation –  physicists must test each specific scenario to determine the path and orbits of the bodies using brute force mathematical calculations. “Solutions” have been found for specific situations, but no universal analytical solution has been found to exist.

The “two-body problem” – referring to the path of movement of two bodies under gravitational influence – was solved during Newton’s time, meaning that the orbit of two objects held together by gravity can be predicted with complete accuracy.

The problem with predicting three bodies in orbit is that very tiny changes in the initial conditions can lead to huge differences over time. This is especially true where each of the bodies makes a material gravitational contribution to the system of the three bodies. On one hand, the three-body problem with respect to the Sun, Earth and Moon is slight given the very small gravitational effect of the Moon on the Earth as compared to the Sun. The planets of the solar system and their moons really operate like a bunch of two-body problems.

One simulation of three objects under mutual gravitational influence

For other situations, where there are stars orbiting each other (so-called binary stars) along with large planets, the three-body problem can be pronounced.

The Three-Body Problem is also the title of a fantastic science-fiction book by Cixin Liu.



  1. I LOVED that book.. So surprised ( and pleased) to see you write about it.


  2. Poincare’ won a big prize that was intended for the person who could prove the stability of the solar system. He proved that it cannot be proven. This led to the development of the calculus of manifolds, differential geometry, and other incredible things like fractional spatial dimensions… Beautiful stuff but pretty challenging technically.

  3. Proud to be a physics Friday clicker!

  4. The Three Body Problem would also be a good title for a murder mystery.

  5. This mirrors a similar problem in marriage, where when there are only two bodies, life proceeds along a predictable linear path (usually upward sloping). When you throw a third body into the mix the ability to analyze or predict your life trajectory completely breaks down and total chaos sets in.


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