Sorry to ask the long way, but trying to make the question clear so that I can get a clear answer.
Why does it make any physical sense for a body to have negative potential energy?
If a body A is at infinite distance from another body B, it has zero gravitational potential energy, but if it is at "zero" distance from another body B, it has negative infinite potential energy, and acquires infinite kinetic energy in the process of getting there.
Please don't tell me that the zero point of potential energy is arbitrary, and it could just as well have zero potential energy when it is at zero distance from another body B, and positive infinite potential energy when it is at infinite distance from the other body B. How can it have this? When body A is at infinite distance from the other body B, then it is not influenced by the other body B at all, it is as if the other body B does not exist at all, so then the potential energy in body A must be zero, as there is no gravitational field of the other body B to cause any potential energy in body A.
But then the question is if the potential energy contained in the body A is zero at infinite distance from the other body B, then how is it possible for this zero potential energy to be reduced further and get changed to kinetic energy as the body A accelerates towards the other body B, so that the potential energy becomes negative? As I see it, if the body A never had any potential energy to begin with, then this not present energy cannot change into kinetic energy, otherwise we would be creating kinetic energy out of nothing.
Why does it make any physical sense to say that the body is in "potential energy debt", ie the potential energy is reduced to negative when it was zero to begin with?