Would the Apollo missions have been possible without a computer? Did AGC make things a lot easier, or was it absolutely essential?
I think it was Buzz Aldrin who said that they were "essentially passengers" and the Apollo Flight was being flown by the computer most of the time.
From the Apollo 13 film, and watching many Apollo missions footage on youtube, it would seem that under an accident-free mission, the astronauts only managed the main engines (basically when to turn on and off the main engines), manually flew the Command and Service (C&S) modules when docking to the Lunar Excursion Module (LEM), Manually flown the touchdown of the LEM, and finally, the initial stages of reentry.
They seem to be flipping switches a lot more than joystick-banging.... It's the same thing you do if you're operating a computer...
Thus, it seems the computer is in control most of the time. If that's not enough, the astronauts also depended on the computer's calculations to help them fly the machine.
Unmanned Surveyor space probes which preceded the Apollo moon missions made the entire flight to a soft landing on the moon under computer control.
It is absolutely essential. A lot of things could go wrong in a manned space flight. It would certainly be wise to reduce pilot error by reducing the workload of the pilot (Even jet airliners are flown by the computer most of the time!)
NASA simply did it for national pride, vanity, morale, etc. For the Cold War....
If it weren't for this pride contest with the USSR, or simply the pride of sending people to space, robotic probes could have done the job way more efficiently even for the purpose of delivering moon rocks to Earth. Lots of money that could be saved for bigger space projects later on. Sigh....