It’s one of the most immediately recognizable photographic sequences ever made: Ralph Morse’s dizzying pentaptych capturing the July 16, 1969, liftoff of Apollo 11. Here, in five narrow frames, we witness—and celebrate—a distillation of the creativity, the intellectual rigor, the engineering prowess and the fearlessness that defined the best of the Space Race. [See the complete LIFE special issue on the Apollo 11 triumph, ‘To the Moon and Back’] But for all of their emotional and historical heft, Morse’s pictures also call to mind, in almost anyone who encounters them, a straightforward and pressing question: How the hell did he do that? Morse, now 97 years old, recently spoke with LIFE.com, and briefly described how the sequence came about. “You have to realize,” he says, “that the rocket had to go through the camera, in a sense. It had to go through the camera’s field of view. It took me two years to get NASA to agree to let me make this shot. Now, RCA had the camera contract at Cape Canaveral at that time, and they had a steel box—with optical glass—attached to the launch platform. We negotiated a deal with them and I was able to put a Nikon, with maybe 30 or 40 feet of film, inside the box, looking out through the glass. The camera was wired into the launch countdown, and at around minus-four seconds the camera started shooting something like ten frames per second. “It was probably less than an hour after liftoff when we rode the elevator back up the launch tower and retrieved the camera and film from inside that steel box.” Finally: Below is a picture of Neil Armstrong’s wife, Jan, with sons Erik and Mark, watching the launch of Apollo 11—from the deck of a boat rented for them by LIFE magazine. The scene, as captured by LIFE’s Vernon Merritt III, is a quiet reminder that the mission to the moon was not only an epic public spectacle. It was also a deeply personal and private adventure, shared by the astronauts and those closest to them in ways, and with an intensity, that the rest of us can hardly imagine.