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Gravitational potential energy is the energy an object has due to its position above Earth, energy due to its height. We know this energy exists because it takes effort to lift an object up to a height and also because when we release an object, it falls, gaining kinetic energy.
This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of the system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity.