It's a very common misconception that the Apollo guidance system wasn't as powerful and was simpler than a modern pocket calculator. Nothing in this world is further from the truth. It was a horrendously complex feat of electro-mechanical/digital bespoke engineering designed to guide a spacecraft through three-dimensional space based principally on simple inertia.
One of the best documentaries around is a series called, simply, "Moon Machines". They're all on YouTube and are so well worth the watch. The set in particular you should see is titled "The Navigation Computer" (Zuke969):
http://www.youtube.com/watch?v=pjVxhIQ14Qc
Watch all parts, you'll be left with an impression somewhat different to that which we're asked to swallow.
My old man was part of the endeavour too. He was a top IBM engineer back in the 50's, 60's and 70's. Here's myself and my younger brother Steven sitting on the console of an IBM System/360 Model 40 during that time (April 1967) at an overseas posting. I can't remember what part of the project he officially played, but it was an exciting time nonetheless.
