[Campion]

That's a non-answer. We're talking about celestial bodies moving at known velocities. You schedule course corrections and the like in the future -- even if "the future" is only 20 minutes away, that blows any 1 1/2 second comms lag out of the water.

And, except on Apollo 13 where they had to do some seat-of-the-pants because systems had failed, you program the relevant commands into the onboard computer, which was very simple but enough to do the job, and it takes care of timing burns and attitude correctly. And that's all you need.

The actual computations were done by top-of-the-line IBM mainframes on the ground; the onboard computers were only responsible for physically executing the burns.

[cgbg]

Those onboard computers could not “physically execute” anything—they were props for the dupes.