Not that much, I'd say. By 1969 science fiction in print, film, and on television was highly developed and working from a firmly established foundation, and in many ways the Apollo 11 mission lagged behind a science fiction environment that had moved on from space stories. Unfortunately it's a little more complicated than that. Particularly in film and television certain developments coincide more or less with the Apollo program, but there doesn't seem to be any good reason to think that the Apollo program specifically had very much to do with it directly.

The 1950s were the tail end of what's sometimes called the Golden Age of science fiction. This is the high point of "hard" science fiction, the period when science fiction magazines and films were dominated by stories featuring logical, scientific (often highly strained, but there nonetheless) premises, and often written by actual scientists like Asimov or Clarke. The atomic bomb drew attention to science fiction, which previously had been the stuff of serials and pulp novels for children, and a growing intellectualism in science fiction, along with its rapidly increasing popularity, is a defining feature of the Atomic Age. For the first time serious writers like Bradbury could produce science fiction that really investigated difficult moral and intellectual questions, and science fiction films changed from being light-hearted to grappling with themes of anxiety, fear, and self-doubt. This is the period of science fiction stories like Heinlein's Starship Troopers and Bradbury's The Martian Chronicles. In film this is the time of Forbidden Planet, The Thing From Another World, and the Japanese movie Godzilla, films that deal with the oppressive fear and anxiety of an atomic, Cold War world.

But what about space travel? In point of fact by the early 1950s space travel was already so well established a feature of science fiction that many science fiction writers were already rebelling against the popular perceptions of spaceflight. For example, Clarke, in many of his stories from the late 40s and early 50s, explicitly challenged the idea of rocketmen travelling to distant worlds, pointing out that space travel is extremely slow and is limited by Newtonian physics. Other authors, like Bradbury or Heinlein, didn't really worry about the realities of space travel. The Martian Chronicles and The Illustrated Man, from 1950 and 1951 respectively, feature rockets travelling through space, but they're just a plot device that Bradbury really doesn't care about otherwise. The big height of stories about travelling to the moon and entering space was during the height of the Golden Age, a decade before the 1950s. This is when Clarke wrote The Sentinel, and even earlier in the 1930s you had the image of the "space ranger." Film and television in the 1950s often featured astronauts or fighter pilots, the military rock stars of the Atomic Age, as heroes, but by this period the space program was a (nascent) reality, not an imagined theory of the far future as it had been a decade ago. And there were, arguably, more interesting questions to explore than humanity's inevitable expansion into the stars. So while science fiction returned to the screen in 1950 after a period of four years or so of complete absence with Destination Moon (adapted from a Heinlein story), more typically 1950s science fiction used space travel as a backdrop. In film a typical example is The Quatermass Experiment, which depicts the fear that perhaps human beings ought to make sure that they understand what they're dealing with before opening up space, lest they repeat the mistake of the atomic weapon. In literature you have stuff like Bradbury's story The Long Rain, James Blish's A Case of Conscience, and Clarke's masterpiece Childhood's End. In all these stories space travel is a possibility that's so commonplace and obvious as not to need any further comment at all, but all three stories are really about the idea that perhaps there are philosophical and ethical questions that can't be solved by the application of nuclear power or rocketships.

That's all nice, but it doesn't answer the question about the late 1960s. On the one hand, the 1960s saw the trend of science fiction's entry into the mainstream continue. Television, for a long time the province of science fiction for children, saw The Twilight Zone and The Outer Limits. But both programs were more plugged into the stuff of the late 1950s than the space travel stories of the late 40s. Most Twilight Zone episodes, for example, don't even interact with space at all, but are about the minds of the (tormented) heroes. Perhaps the best episode of The Outer Limits, and certainly my favorite, is Soldier, based on Harlan Ellison's 1957 story The Soldier From Tomorrow. In a lot of ways it's very much like something you'd read from Bradbury, although Ellison's disgusted attitude towards war is very noticeable given that the episode came out in 1964 and Ellison was a very vocal critic of the Vietnam War well before the war was generally known to the American public. This leads to a couple features of 1960s science fiction. First, the space program was by then in full swing, and was a phenomenon which you could watch on TV. No longer the stuff of fiction, space travel rapidly became kind of blase for many authors. Second, the convergence of these factors continued to accelerate the visibility of science fiction, so that science fiction in print finally made the jump from magazines and publishers specifically tailored to science fiction writers to mainstream publishing. In 1947 the first "real" science fiction story (Heinlein's The Green Hills of Earth) was published in a mainstream American publication, the Saturday Evening Post, and by the end of the 1960s you could find science fiction on the shelves of reputable bookstores and in the pages of mainstream magazines. Third, and perhaps most importantly, the 1960s marked the turn away from the "hard" science fiction of the Golden Age and the beginning of the New Wave. 1/2