Exactly what the title says. I wonder if gravitational potential energy close to the Earth is something intrinsic in the object that can be measured or is it completely dependent upon where we consider our 0 level to be. For example if we lifted an object a distance h above the ground and set it on a table, would we be able to measure the potential energy without pushing that object off the table? Obviously if we did that we could measure the final velocity of that object assuming we could apply the conservation of mechanical energy but is there any way we can directly measure the gravitational potential energy of an object? I ask this question because unless I am mistaken, in this type of situation we are free to choose where we set y = 0 and therefore we could give an object a desired potential energy simply by changing what we consider to be ground level. Am I over-thinking this problem or over thinking it?