It's said that potential energy is "energy of position." If an object is sitting on a shelf five feet above the floor, its potential energy can be thought of as equal to the amount of energy that would be involved in it falling off the shelf and onto the floor.
Conservation says that energy is neither created nor destroyed, only transformed. Therefore, the potential energy of an object has to be absolute, a constant in some sense. But that makes me wonder. If a meteor is drifting through space, and it ends up caught in Earth's gravitational field (and is coming in at the right angle, etc,) it will fall to the surface of the Earth, converting potential energy into possibly a few megatons of kinetic energy.
On the other hand, if that exact same meteor were to meet the exact same fate, except the planet in question was Jupiter, which has much stronger gravity, the impact would therefore be much more intense. So how does that work? If the potential energy of the meteor in space is constant, how can it be determined?