The Cherokee Mathematician Who Helped Design America’s Space Age – While Much Of Her Work Remained Secret
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.