Two-body problem

The mathematical problem of predicting the motion of two bodies interacting through mutual gravity. In Newtonian mechanics, it reduces exactly to the motion of one effective particle in a central force.

Center-of-mass frame: A reference frame in which the system’s total momentum is zero and its center of mass is at rest. Separating center-of-mass motion removes the system’s uniform drift.
Newton's law of universal gravitation: The law stating that any two masses attract with force proportional to their product and inversely proportional to distance squared. This is the force law that defines the classical gravitational problem.
Binary star: A star system in which two stars orbit their common center of mass. A well-separated binary can closely approximate two mutually gravitating point masses.
Three-body problem: The problem of predicting the motion of three mutually gravitating bodies. Adding one gravitating body generally removes the two-body problem’s exact conic solution.
Reduced mass: The effective inertial mass, equal to the product of two masses divided by their sum. It replaces both bodies’ inertias in the equivalent one-particle equation.
Newton's laws of motion: Three classical principles relating motion to forces, inertia, and action-reaction pairs. They turn mutual gravitational forces into equations for both bodies’ motion.
Visual binary: A binary star whose two components can be resolved separately by observation. Its measured orbit can reveal stellar masses through the two-body solution.
N-body problem: The problem of predicting the motion of any number of mutually interacting bodies. It generalizes the two-body model to systems with many gravitational sources.
Central force: A force directed along the line connecting a particle to a fixed center, with magnitude depending only on distance. Newtonian gravity is central, so angular momentum is conserved.
Conservation of angular momentum: The constancy of angular momentum in a system with no net external torque. Central gravity exerts no torque, confining motion to a plane.

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