
One of the oldest problems in mathematics and physics is that of the three bodies: how will three objects mutually attracted by their gravity move in the future, given their current positions and speeds?
(their initial conditions are 18 values, consistent for each of the bodies in: its 3 position coordinates and the three components of their velocity).
Isaac Newton was the first to raise the problem.
It was later shown that it was unsolvable - in general it is impossible to find a formula that exactly predicts the orbits of the three bodies.
In general, the problem of the three bodies (and the problem of n-bodies, for n > 3) cannot be solved by the quadrature method or integrals of motion (or first integrals) . As the French mathematician showed Henri PoincarΓ© , there is no formula that governs it.
However, researchers have found interesting solutions for some specific cases. The study of the problem of three bodies has allowed them to discover new and fascinating mathematical principles.
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