Final answer:
The Apollo 13 crew performed a manual course correction by aligning their spacecraft to keep Earth in a specific window, using this visual reference for the trajectory adjustment.
Step-by-step explanation:
The Apollo 13 crew was forced to make a last adjustment to their trajectory without the aid of guidance computers due to a catastrophic failure aboard their spacecraft. This critical maneuver had to rely on manual adjustments using the Lunar Module's thrusters. The space crew ingeniously used a visual reference, aligning their spacecraft so that Earth remained in a specific window, which served as a rudimentary aiming point for the course correction.
This adjustment allowed them to safely re-enter Earth's atmosphere and return home, illustrating both the human capacity for problem-solving under pressure and the fundamental principles of orbital mechanics.