They are old men now. That much is obvious from the tight camera shots. Nonetheless, it is hard to fathom: has it been 38 years since the first of them set foot on lunar soil?

“In the Shadow of the Moon,” a documentary that premieres this week in New York and Los Angeles, tells the story of the Apollo program and the race to reach the moon, as President John F. Kennedy declared in 1962, “before this decade is out.” And so, on July 20, 1969, we did.

Note the “we.” It is from one of the most powerful, lump-in-the-throat moments of this exceptional film. Michael Collins, who orbited the moon during the Apollo 11 mission while Neil A. Armstrong and Edwin E. Aldrin Jr. took their lunar module down to the surface, said that after the flight, on the around-the-world tour that NASA sent them on, “Wherever we went, people, instead of saying, ‘Well, you Americans did it!’ — everywhere, they said, ‘We did it! We, humankind, we, the human race, we, people, did it!’ ”

His voice breaks slightly in the telling, and he says: “I thought that was a wonderful thing. Ephemeral, but wonderful.”