In describing the total mechanical energy of a system, a negative value is interpreted as meaning that the system is bound; that is to say, the total kinetic energy of all the particles (which is non-negative) has a smaller magnitude than the total potential energy of the fields between them. So there is not enough kinetic energy for members of the system to separate to limitless distances.
An example is the total mechanical energy for a satellite in, say, a circular orbit around a planet. If the masses of satellite and planet are m and M>>m, respectively, and the radius of the orbit is R, then the kinetic energy of the satellite is
(1/2)·m·(v^2) = GmM/2R ,
while the gravitational potential energy of the field is
Thus, the total mechanical energy for the system is
(We are treating the mass of the planet as effectively infinite here for simplicity. We really should use "reduced mass" for the system.)
A similar result is found for other sorts of systems bound by forces which can be described by potential functions.
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