Euler's three-body problem
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In physics and astronomy, Euler's three-body problem, named after Leonhard Euler, is to solve for the motion of a test mass that is free to move in the presence of the gravitational field of a primary and secondary mass which are fixed in space. This problem is the simplest three-body problem that retains physical significance. Euler discussed it in memoirs published in 1760.
The problem is analytically solvable but requires the evaluation of elliptic integrals. Numerical methods may be used, such as Runge-Kutta, to solve the resulting ordinary differential equations approximately and to gain some feel for the physics.
