You needed to calculate trajectories — the specific paths that a spacecraft would follow from the surface of the Earth to the orbit you wanted it to reach, accounting for the physics of propulsion and gravity and atmospheric resistance and the specific performance characteristics of the launch vehicle you were using.

You needed to calculate reentry — the conditions a spacecraft would encounter when it came back through the atmosphere, the heating and deceleration that could destroy a vehicle that was not designed correctly, the mathematical models that would allow engineers to design vehicles capable of surviving the return.

You needed to calculate orbital mechanics — the way objects moved in orbit, the way you transferred from one orbit to another, the way you rendezvoused with another vehicle in space, the way you navigated across the vast distances between planets.

And if you were thinking beyond Earth orbit — if you were thinking about Mars and Venus and the trajectories that would carry spacecraft to those worlds — you needed to calculate interplanetary mechanics.