Final answer:
Katherine Johnson calculated the trajectory for John Glenn's safe re-entry into Earth's atmosphere during the Mercury-Atlas 6 mission, contributing significantly to NASA's spaceflight operations and the Space Race.
Step-by-step explanation:
The problem that Katherine Johnson, a mathematician and physicist, solved regarding the re-entry of John Glenn's capsule during the Mercury-Atlas 6 mission was a complex calculation involving orbital mechanics. Katherine was tasked with confirming the accuracy of the computer-generated numbers for the capsule's trajectory upon re-entry to ensure Glenn's safe return to Earth. Her critical contributions were a part of NASA's spaceflight operations and a significant event during the Space Race between the United States and the Soviet Union.