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What about a meteor coming towards earth from far off in space. Is potential energy inherent in its system? Obviously it can be accelerated towards any planet. Is it's potential energy something which has stuck with it from its origin (wherever that may be), and may be expended on any planet? If that is the case, seeing that some planets have potential to accelerate it more powerfully than others, what balances the system?
Any two objects have potential energy between them. Even a distant meteor and the Earth. If you ignore the interaction of all other forces, any object will lose potential energy and accelerate toward the Earth.
I am not sure I understand your question. The meteor doesn't have potential energy by itself (think if the meteor was the only object in the Universe). It is only the positioning of the meteor with the Earth that has potential energy.
If there is another object that affects the meteor besides the Earth, you need to include the three objects in the system. But no single object has (gravitational) potential energy.
The question about potential energy at its origin is not relevant. If two objects with mass poofed into existance with some distance between them, they (that is the system) would start out with potential energy and would accelerate towards each other. The Big Bang theory implies there was no distance between objects when the universe started, but a whole lot of energy. The inital energy can be seen as being converted into the potential energy that exists now.
Are you interested in going into the mathematics?