Newton’s three-body problem explained - Fabio Pacucci

Mathematical equations can predict the motions of two gravitating masses. But when a third or more are introduced, our analytical tools fall short.

It is impossible to write down all the terms of a general formula that can accurately describe the motion of three or more gravitating objects. The problem is in knowing how many unknown variables an n-body system contains.

Thanks to Isaac Newton, we can write a set of equations to describe the gravitational force that acts between bodies.

But, when we try to find a general solution for the unknown variables in these equations, we are faced with a mathematical limitation.

For every unknown, there must be one equation that describes it. A two-body system is solvable because its gravitational attraction influences the paths they take in such a way that a simple mathematical formula can describe it. But three or more orbiting objects leaves us with more variables than equations that can describe them.