“That’s one small step for man, one giant leap for mankind,” they heard him say as he dropped from the ladder of his spacecraft to make the first human footprint on the lunar surface.

But from the moment he said it, and for 37 years since, debate has raged over whether the Nasa astronaut might have fluffed his lines.

Mr Armstrong has long insisted that he meant to say “one small step for a man . . .” — which would have been a more meaningful and grammatically correct version, free of tautology. But even the astronaut himself could not be sure.

“Damn, I really did it. I blew the first words on the Moon, didn’t I?” he is reported to have asked officials later, amid uncertainty as to whether he had blown the moment or simply been drowned out by static interference as his words were relayed 250,000 miles back to Earth.

Now, after almost four decades, the spaceman has been vindicated. Using high-tech sound analysis techniques, an Australian computer expert has rediscovered the missing “a” in Mr Armstrong’s famous quote. Peter Shann Ford ran the Nasa recording through sound-editing software and clearly picked up an acoustic wave from the word “a”, finding that Mr Armstrong spoke it at a rate of 35 milliseconds — ten times too fast for it to be audible.

Mr Ford’s findings have been presented to Nasa officials in Washington and to a relieved Mr Armstrong, who issued a statement saying: “I find the technology interesting and useful. I also find his conclusion persuasive.”

Mr Armstrong and Buzz Aldrin, who stepped out seconds after him, landed the Apollo 11 Lunar Excursion Module on the Moon on July 20, 1969. In the tense six hours and forty minutes between touching down and stepping out, Mr Armstrong wrote what he knew would become arguably the most memorable words in history. But Nasa was bombarded with inquiries and the recordings were hastily reviewed.

The space agency backed Mr Armstrong’s claim that there should have been an “a”, but they agreed that, on official documents, the “a” should be placed in brackets because no one could be sure he said it.

In his official biography, First Man, Mr Armstrong tells the author James Hansen: “It doesn’t sound like there was time for the word to be there. On the other hand, I didn’t intentionally make an inane statement . . . certainly the ‘a’ was intended, because that’s the only way the statement makes any sense.”

Professor Hansen said: “Neil’s not got much of an ego, he’s a very modest man, but I think this really means something to him to have the proof.”

Officials at Nasa have met Mr Ford to discuss his findings. They have now instructed their own analysts to run in-house tests.

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