Restricted three-body problem

A gravitational model of two massive bodies and a third, massless body that moves under their gravity without affecting their motion.

Circular restricted three-body problem: The restricted three-body problem with the two massive bodies on circular orbits about their common center of mass. Its rotating-frame equations make the standard equilibrium-point analysis tractable.
Three-body problem: The problem of predicting the motion of three mutually gravitating bodies. The restricted model simplifies this generally non-integrable gravitational problem.
Interplanetary Transport Network: A network of low-energy trajectories formed by invariant manifolds in the Sun–planet restricted three-body models. It turns the model's dynamical channels into routes between planetary regions.
General three-body problem: The gravitational motion of three bodies whose masses all influence one another. Unlike the restricted model, all three bodies exchange momentum and alter each other's trajectories.
Lagrange point: A location in a rotating two-body system where gravitational and centrifugal effects permit a third body to remain fixed relative to the primaries. These five equilibria organize motion in the circular model.
Newtonian gravitation: The classical theory in which masses attract through a force proportional to their product and inversely proportional to distance squared. It supplies the force law governing all three bodies in the model.
Genesis (spacecraft): A NASA mission that collected solar-wind particles and returned them to Earth in 2004. Its trajectory used dynamical structures associated with the Sun–Earth L1 region.
Elliptic restricted three-body problem: A restricted three-body model in which the two massive bodies follow elliptical rather than circular orbits. Its time-varying separation removes the circular model's autonomous rotating-frame structure.
Jacobi integral: A conserved quantity in the circular restricted three-body problem that combines the test body's kinetic and effective potential energies. It bounds accessible regions and identifies forbidden zones in configuration space.
Center of mass: The mass-weighted average position of a system, whose motion follows the system's net external force. The two primaries orbit their shared center of mass.

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