Three-body problem

The three-body problem asks how three bodies move under their mutual gravitational attraction, given their initial positions and velocities. Unlike the two-body problem, it has no general closed-form solution.

Newton's law of universal gravitation: A law stating that every pair of masses attracts with force proportional to their masses and inversely proportional to distance squared. It supplies the pairwise forces that govern all three bodies.
Isaac Newton: English mathematician and physicist who formulated the laws of motion and universal gravitation. His mechanics established the framework in which the three-body problem was posed.
Two-body problem: The problem of predicting two bodies moving under their mutual gravitational attraction, solvable in closed form. Its exact solution shows the sharp contrast with three mutually interacting bodies.
Restricted three-body problem: A model in which two massive bodies move under gravity while a third body has negligible mass and does not affect them. It simplifies the general problem while retaining rich orbital behavior.
Newton's laws of motion: Three laws relating forces to changes in motion and describing inertial motion and action–reaction pairs. Combined with gravity, they yield the equations for each body's acceleration.
Pierre-Simon Laplace: French mathematician and astronomer who developed mathematical astronomy and analyzed planetary perturbations. His celestial-mechanics work advanced attempts to predict interacting planetary orbits.
Ordinary differential equation: A differential equation involving an unknown function of one independent variable and its derivatives. The bodies' positions evolve according to coupled ordinary differential equations.
Kepler's laws of planetary motion: Three laws describing elliptical orbits, equal areas swept in equal times, and the relation between orbital period and size. They describe ideal two-body motion, not the full mutual interaction of three bodies.
Lagrange points: Locations in a rotating two-primary system where gravitational and inertial effects allow a smaller body to remain in a fixed relative position. They are equilibrium configurations in the restricted three-body problem.
Joseph-Louis Lagrange: Italian-born mathematician and astronomer whose work shaped analytical mechanics and celestial mechanics. He found important special solutions, including configurations now associated with Lagrange points.

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