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Moon is about a lunar miner named Sam Bell who is the sole worker on a lunar base. It is Sam's job to mine a valuable lunar element called Helium-3, which he seals in capsules and ships back to Earth. While mining he experiences a visual hallucination of a young teenaged girl, which startles him and causes him to crash his rover. Sam is awakened by his only companion on the base, an artificially intelligent computer program named GERTY, who tells Sam that he suffered from an accident and that he needs to rest. Sam remembers nothing of the accident and instead of resting in bed, he overhears GERTY speaking to workers from Lunar Industries. They discuss plans for sending a rescue team, and the men tell GERTY not to let Sam outside until after the team arrives. Sam devises a plan that gives him a reason to escape. While outside, Sam finds the crashed rover and discovers himself still unconscious inside and revives him.

Together they brainstorm as to what was going on and each decide that they must be clones of each other. They get in an argument; they fight. Afterwards they confront GERTY and demand an answer. GERTY tells them that they are both clones, and that he woke a new clone because the old Sam was thought to be dead. Both Sam's then explore the ship, where they discover hundreds of sleeping clones and old videos of clones who had begun to deteriorate at the end of their three year term, and each would be incinerated in what they thought was an escape capsule.

Both Sams know that when the rescue team comes, they will both be killed. So they decide to leave old Sam, who is deteriorating at an advanced degree, and new Sam will don a mineral capsule and go back to Earth.

In the end, new Sam spreads word of the illegal activity that Lunar Industries is partaking in, and we learn that they are ruined.