The way the planets moved relative to each other.

The windows during which a launch from Earth could reach Mars or Venus with the minimum expenditure of fuel.

The specific trajectory shapes — the Hohmann transfer orbits, the gravity assists, the ballistic trajectories — that would allow a spacecraft with a given amount of propellant to travel between worlds.

These calculations were extraordinarily difficult.

They required advanced mathematics — differential equations, numerical methods, orbital mechanics, astrodynamics — at a level that very few engineers possessed.

They were also, at the time, genuinely new: the problems were being worked out for the first time by people who did not have textbooks to consult because nobody had written the textbooks yet.