Simpler equations can be applied to this system by defining the reduced mass.
The Laplace-Runge-Lenz vector is a constant of motion, and thus conserved, for this system. A more complex system is "restricted" to base its solutions on this system. Simpler equations can be applied to this system by defining the reduced mass. A special case of this system where the central force follows an inverse-square law is known as the Kepler problem. In the Kepler case, this generally solvable system's solutions are either hyperbolic, parabolic, or (*) elliptic, in the latter case being closed orbits. For 10 points, name this system from classical and celestial mechanics that includes the Earth-Moon system and binary stars.
The Laplace-Runge-Lenz vector is a constant of motion, and thus conserved, for this system.
two-body problem [or obvious equivalents, such as two bodies under the influence of gravity]