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An orbit that remains within a bounded spatial region for all times for which the motion is defined. In an attractive inverse-distance central potential with zero potential energy at infinity, a noncolliding orbit is bound when its total mechanical energy is negative. That sign test depends on the potential and its energy origin; it is not a universal definition of bounded motion. A closed orbit repeats its position and velocity, whereas a general bound orbit can precess without closing.

A closed orbit returns to the same complete state and repeats its motion. For a nonconstant solution of an autonomous differential equation with unique solutions, $x(t+T)=x(t)$ for a positive period $T$ describes a periodic orbit. This usage excludes an equilibrium point, which is a stationary state rather than a moving cycle.

A harmonic oscillator has closed ellipses in its phase plane, because both position and velocity return after one oscillation. Returning to position alone is insufficient: a particle can pass the same point with a different velocity. A bound orbit also need not close; a precessing orbit can remain in a limited spatial region while changing its direction of closest approach. Specifying the complete state prevents a repeating projection from being mistaken for a repeating physical motion.