Gravitationally bound system ($\epsilon =\frac{1}{2}{v}^2-GM/r<0$)

A system whose mutual gravity confines its constituents rather than letting them separate indefinitely. In an isolated two-body problem, the relative specific orbital energy $\epsilon =v^2/2-G(M_1+M_2)/r$ is negative exactly for bound, noncollisional Kepler orbits; $\epsilon =0$ is the marginal escape case. External forces, collisions and time-dependent potentials require additional qualifications. The separation of a gravitationally bound system is determined by its equations of motion and need not follow the cosmological Hubble flow.