Then I remembered that it's still accurate enough to be awesome and stopped worrying about it. :)
There weren't powerful enough computers to model full Eisenstein N-Bodies Systems until actually very recently (also its complete over kill for inner-solar system travel). Relativity is really complex math, and even modern computer clusters struggle to model very complex systems.
Yes we sent astronauts to the moon using KSP math.
I'm almost positive that we did not.
While patched conics would have been used very early on for rough mission analysis and design, we had a very good understanding of perturbation theory at the time. Wikipedia tells me that the restricted 3-body problem was also essentially solved in 1917. I've seen very detailed plots of the free return trajectories that the Apollo missions followed, too.
Using patched conics for the earth moon system would have resulted in an error on the scale of lunar escape velocity upon entering the sphere of influence of the Moon.
Free return trajectories can be calculated with patched conics. 3 Body problem was solved, but actually doing all the math involved dynamically was far to complex for mission computers.
You forget that at the time NASA was using IBM System/360's which were struggling to maintain 5 megaFLOPs
For one thing, I'm not convinced that your mental models of what a "mission computer" is and what a "mission computer" would be doing, or when, make sense from an engineering perspective. I'm also not convinced that you know what an orbital perturbation is, nor how they would be used to plan and fly a mission.
To take an example from aviation, we didn't have practical simulations of general viscous fluid flow in the 1960s, but it would be meaningless to say that we "used Bernoulli's principle" to fly across the Pacific.
The Apollo vehicles had an on-board IMU. A trajectory could thus be pre-planned and flown to using feedback control. That trajectory would certainly have been calculated ahead of time. Thus, while there would be no need to have "[done] the math involved dynamically," that by no means implies that patched conics were used while in flight, nor does it imply that they were in any meaningful way used for the final design of the missions' flight paths.
Further, on any deviation from the planned flight path, numerical integration methods would yield results that would be good enough for later correction, again, by using feedback control.
If you still need to believe that "KSP math" is how we got to the Moon, go ahead. You've certainly done nothing to convince anyone else, though.
http://forum.kerbalspaceprogram.com/threads/68502-WIP-Princi... https://github.com/mockingbirdnest/Principia
http://en.wikipedia.org/wiki/Orbital_station-keeping
But anyway, I still hope that Principia mod (the n-body simulation addon mentioned elsewhere in this thread) will get released. This will really bring KSP into Dwarf Fortress level of enjoyment. Also, you'd get to make some really weird-ass stuff:
http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamm...