They were using slide rules and very crude computers.
When Apollo 13 went wrong these same engineers figured out how to get them home from a failure they never anticipated nor even planned for. Their crippled craft was on a trajectory to take them around the moon and back toward earth. They had to calculate everything using the Lunar Excursion Module for thrust to get them on the correct reentry path. Get it wrong and you burn up in the atmosphere or be forever in orbit and dead. The astronauts had to use star shots to correctly orient their crippled craft for each engine burn. They got it right. They were brilliant and the engineers on the ground were brilliant. That was NASA's finest hour.
Yes, and many true prayers to the God of heaven,