The moon - or "luna," as it's called in Nadsat, the slang language Burgess invents in the film's source novel - has strong symbolic power in both the film and the novel. In Kubrick's film, before Alex and his gang savagely beat an intoxicated Tramp (Paul Farrell), the elderly vagrant states, “It’s a stinking world because there’s no law and order anymore." He continues, “There’s nowhere for an old man any longer,” since with “Men on the moon, and men circling around the Earth, there’s not no attention paid to Earthly law and order no more.”
Given that the novel was published only one year after the Soviets traveled into space and the film was released only a few years after the Americans landed on the moon, the space race was an obsession for many at the time. Kubrick even takes the opportunity to plug the soundtrack of his previous film, 2001: A Space Odyssey (1968), as Alex wanders his favorite record store.
But while space exploration and landing on the moon are signs of man's progress, the moon is also used as a symbol of the cyclical aspect of human life and the limits of civilization's power to mold human nature.
In the closing lines of Burgess' novel, Alex brings the story full circle, invoking both the celestial orb and the clockwork orange of the work’s ominous title. The maturing adolescent wonders if his unborn son will make the same mistakes he made in his youth. He goes on to realize that the cycle of things will continue on over and over: “When I had my son I would explain all that to him when he was starry enough to like understand. But then I knew he would not understand or would not want to understand at all and would do all the veshches I had done... and I would not be able to really stop him. And nor would he be able to stop his own son, brothers. And so it would itty on to like the end of the world, round and round and round, like some bolshy gigantic like chelloveck, like old Bog Himself (by courtesy of Korova Milkbar) turning and turning and turning a vonny grahzny orange in his gigantic rookers... Tomorrow is all like sweet flowers and the turning vonny earth and the stars and the old Luna up there and your old droog Alex all on his oddy knocky seeking like a mate. And all that cal. A terrible grahzny vonny world, really, O my brothers."
While the state seems all-powerful in its ability to turn oranges into clocks, shaping Alex into something purely mechanical and alienated from his own feelings, the cycle goes on, and new unmolded life will continue to enter the world.