Let's talk about an important consequence. If the work performed were not path independent, a circular path could be conceived which would dissipate energy, but on the contrary, because gravity is a conservative force, any path which ends in the same initial position must necessary result in no change in potential energy state. This means that for an isolated gravitational system, the total energy must be be the same everywhere. And because or an initial state has both kinetic and potential energy, this total energy value gives the total of the kinetic energy plus the potential energy for all other possible states, regardless of the path between states, as long as only gravitational force is involved.
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