No person alive has been more closely associated, for so long, with America’s triumphs in the early days of the Space Race than John Glenn, and few Americans in history have served their country in as many high-profile, multifarious roles: First American to orbit the earth; decorated Marine Corps veteran (in both WWII and Korea); novice, eager politician; seasoned, savvy, multi-term United States senator; space shuttle crew member — across seven decades, Glenn has lived much of his personal and professional life in the public eye.

But it was during a remarkably brief, heady period in the late 1950s and early 1960s — the period brought to life by the rare and previously unpublished pictures in this photo gallery — when Glenn first entered the national consciousness and became, in a very real sense, the public face of the American space program.

[Read TIME's salute to John Glenn.]

“America was in something of the doldrums when Project Mercury began,” Glenn recalled in an interview with LIFE.com, painting a picture of the era during which he and his fellow astronauts — the Mercury 7 — helped light a fire in the nation’s belly. “Within the memory of an awful lot of people, we’d come through the Great Depression, World War Two, and the Korean War. We weathered the Depression, we won the Second World War — but then we fought to a stalemate in Korea. No one had a very good feeling about that, and quite a few people began questioning whether America’s greatness was a thing of the past. The space program really helped restore our confidence as a nation. It wasn’t designed to do that, of course. But looking back, I think what we accomplished as astronauts went a long way toward bringing people out of the doldrums of the late fifties and early sixties, and I’m proud to have had a hand in that.”

“Of course,” Glenn continues, “a crucial element of our program was competition with the Soviets. They were claiming technical superiority, and were taking thousands of kids from Third World countries, educating them in Russia, and sending them back to their homes as dedicated little commies. In their view, they were proving their technical superiority to us by the fact that their rockets were succeeding, and ours were, far too often, blowing up on the launch pad. We didn’t believe they were superior to us, technically — not by a long shot. So there was definitely that intense, Cold War mentality attached to much of what we did.”

And yet, while the Cold War was the larger, geopolitical framework in which the Space Race played itself out, Glenn makes clear that there was always another quieter — but no less intense — scientific, and even a metaphysical, force driving the advances of the late fifties and early sixties.

“All of us looked at Project Mercury as far more than just a job,” Glenn says. “You know, we already had jobs flying jets, we were all test pilots, and that was interesting enough, in its own way. But thinking of this other extraordinary leap forward, the space program, as just another job? No, it was never quite that simple. Human beings have been looking up at the sky for millennia, wondering what’s up there. And all at once, here we were, with the chance to actually go. It was something brand new, and hugely exciting.”

Here, in a gallery filled with intimate photographs by some of LIFE magazine’s finest photographers, the 90-year-old, still-straight-talking Ohio native shares his memories and insights on one of the most thrilling, inspiring, nerve-wracking eras in the nation’s history, and his own career as both pioneering astronaut and fledgling, earnest candidate for public office.

Fifty years after John Glenn’s historic Earth orbit, TIME presents its original March 2, 1962 issue. Get it here.