For a system to remain gravitationally bound, how must the total kinetic energy compare to gravitational potential energy?
Answer
Total kinetic energy must be less than the total gravitational potential energy.
The stability of any gravitationally bound system, whether a star cluster or a massive galaxy, depends on the balance between the energy of motion (kinetic energy) and the energy holding the structure together (gravitational potential energy). When the system is stable and bound over cosmic timescales, the binding energy must be greater than the energy driving dispersion. Specifically, the kinetic energy must be less than the potential energy. If the kinetic energy dominates, the system is considered unbound and will disperse into space.
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