The three-body problem

The three-body problem consists of determining the positions and speeds of any three masses subject exclusively to their mutual gravitational attraction and starting with a given set of their positions and speeds.

Although there is an analytical solution for two bodies, this is not the case when the number of bodies is increased to three or more.

The three-body problem has been haunting mathematicians and physicists since Newton posed it over 300 years ago.

Great mathematicians the likes of Euler, Lagrange, and especially Poincaré have grappled with the problem, proposing some particular solutions and analyzing the stability of the trajectories, while noting that the problem is highly sensitive to small changes in the initial speeds or positions.

The chaotic nature of the problem implies not only that is there no closed solution, but also that computer-based simulations cannot provide any specific reliable predictions in the long-term.

This problem is crucial to many facets of astronomy, celestial mechanics, and aerospace engineering.

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