They probably just ran through computations with a slide rule or log tables. I seriously doubt they planned or specified the trajectories. The old 7090s and 1108s cranked out piles of computations related to trajectories. Maybe they just looked for anomalies in that output. We would have heard about them long before now if the matter was more significant than that.
"Coder", when used as slang for a programmer, is one of my pet peeves. Sorry to trigger one of yours.