The play, whose emotional punch depends upon its tracing the history of the space program leading up to the Apollo 11 mission, has a lot of explaining to do, placing the events in the context of the time.

Mr. Wilford, 85, has “sort of become the Virgil of the story,” Mr. Rogers said, because of “his ability to step back and paint the larger picture.”

In a phone interview from his home in Bellport, Long Island, that’s exactly what Mr. Wilford did, conjuring the excitement of the era, the rapid pace of scientific progress and the relative youth of the Apollo 11 astronauts — like him, then all in their 30s.

NASA’s arrival on the moon made good on John F. Kennedy’s vow that the United States would be there before the ’60s were done. But it was a turbulent decade. Mr. Wilford remembers 1968, when Martin Luther King Jr. and Robert F. Kennedy were assassinated, as “one of the worst years in my lifetime from the standpoint of the public, of being an American.”

That December, when the Apollo 8 astronauts triumphantly circumnavigated the moon, taking the famous photo of the Earth with the moon in the foreground, “It was the first hopeful thing that had happened all year,” Mr. Wilford said.

Mr. Rogers was only 14 months old the next summer when Apollo 11’s lunar module Eagle landed. His parents woke him from his crib to watch it on TV — his first memory, he says, unless he just heard the story enough times that he burnished it into recollection.