I understand the maths in the core positioning/trajectories is Newtonian based (Laws of Motion) so relatively straightforward.
Some of the time/position sensitive critical calculations will probably acknowledge relativity for the precision
The weekend before the Apollo 11 astronauts went into quarantine was the 4th July. Armstrong and Collins took their families away to the beach or camping, while Buzz Aldrin kept his family home so he could strip apart and mend their dishwasher.
And during Apollo 13 Jim Lovell managed to calculate course corrections using a pen, paper and his wristwatch, using the Sun as a guide. Incredible that something so precise can be done without a computer, just like sailing ships did.