The author is Charles Fishman, and the subtitle is The Impossible Mission That Flew us to the Moon. Here is one excerpt:
It [NASA’s Mission Control] was the first real-time computing facility IBM had ever installed.
…the Apollo flight computer was the first anywhere to have responsibility for human lives.
That computer had 73 kilobytes of memory and had 0.000002 percent of the computing capacity of an iPhone. And don’t forget this:
At least while you were headed outbound, you’d have plenty of fuel to correct things. Coming home from the Moon is a lot less forgiving. The heat of reentry, the splashdown targeting into the ocean, and the g-forces piling up on the spaceship and the astronauts inside combine to create a very thin slice of air you need to slide your spaceship into. The command module had just 1 degree of latitude on reentry. Too shallow an angle, and your space capsule skips off the top of the atmosphere like a flat stone — out into space and a wide orbit around the Earth, from which there was no rescue. Too steep a cut into the atmosphere, and the speed, heat, and g-forces would combine to incinerate your space capsule. And unlike on the way out, on the way back there are no go-arounds.
Definitely recommended, gripping from start to finish. Overall the best history of how the space revolution and the computer revolution were interconnected.