Nine of them are still alive, and 30 years on author Andrew Smith set out to interview them all, curious to discover how they now feel about what they did then. The result is his absorbing book Moondust (Bloomsbury).
All nine of the moon walkers, he finds, were changed by the experience, and found frustrations in their lives afterwards. Buzz Aldrin, of Apollo 11, now active as a promoter of space exploration, was for years a depressive alcoholic. Al Bean, of Apollo 12, endlessly paints moon scenes - nothing else -trying to portray and preserve not just what he saw but how he felt.
Gene Cernan, of Apollo 17 - the last man on the moon - says: "It's kind of tough to find an encore."
Edgar Mitchell, of Apollo 14, sums up their common feeling. Out there he had what he calls his "epiphany" and wrote afterwards: "The view from space has shown me - as no other event in my life has - how limited a view man has of his own life and that of the planet."
It occurred to me as I read about these men - and the quality of Smith's writing is such that you do engage with them - that becoming a headteacher, in charge of a school, responsible for young lives and adult careers, is in its own way a life-changing rocket ride into a dangerous space. There are frustrations and there are casualties.
I chatted recently about all of this - the highs and lows of leading an urban comprehensive - with Sir Robert Dowling, honoured for the transformations he has wrought at George Dixon international school, which serves a diverse and demanding community in Birmingham. He was eloquent on the external pressures from government and critics, but about the burden of the core mission he was deadly serious.
"It's the enormity of the responsibility for the children that weighs on you," he says. "The knowledge that you are the only chance they have - trying to get them to see that they really can have the same opportunities as Prince Harry."
Sir Robert took on George Dixon in 1999, having already worked wonders at a Birmingham special school, and it's reasonable to assume that one of the keys to school improvement nationally lies in the willingness of able heads to move on to other challenges. The pressures of headship, though, are increasing - the Government threatens to close poor schools that aren't quickly turned round. Why, then, should a successful head take on another school if the demands are going to be greater than they were the first time around?
Kay Askew, the principal of the North Liverpool academy, an academy opening in September after the amalgamation of two community comprehensives, believes this is one reason behind the current dearth of headship applications. "When you've reached a career high, you're reluctant to leave it and take on a new challenge," she says.
Fortunately, there are still some, Kay Askew included, who do move on. Why, I wondered, did she take the plunge? Her answer offers a clue that might be picked up by governing bodies looking to appoint heads.
"It was when I met the children," she says. "I asked them what they wanted from a new head, and they came up with what seem like simple things - a football team, a choir - bits of school life that you normally take for granted. Then one of them asked, 'could we do a show?' and I was won over."
For heads and teachers who are pressured and looking into darkness, it's always a meeting with children that becomes the equivalent of astronaut Edgar Mitchell's epiphany moment.
"I'll tell you about my epiphany," said Sir Robert. "It was 5.30 in the evening, and I was chatting to a cleaner, when 30 or so kids came walking across the hall. I asked them where they had been, and they said they'd stayed behind for extra English and maths. They gathered round, some sat on the floor, and we just chatted about their hopes and aspirations. I thought to myself, 'by Jesus, we're getting something right! These kids are buying into the message!' "
Gerald Haigh is a former headteacher who writes widely about education