After graduating in three and a half years, Northcutt was hired in 1965 by TRW, an aerospace contractor with NASA, as a computress for the new Apollo program. She was soon promoted to engineer stationed in the Mission Control's Mission Planning and Analysis room. She was the first female engineer to work as part of NASA's Mission Control. Northcutt and her team designed the return-to-Earth trajectory that the Apollo 8 crew took from the moon back to Earth. She made key insights that identified mistakes in the plan before they were executed. If there was any delay in swinging around the moon resulting in using up more fuel than planned it was up to Northcutt and her team to make on-the-spot calculations and changes to the plan to ensure the astronauts' safe return. Apollo 8 was the second crewed Apollo spacecraft and became the first crewed mission to ever leave Earth orbit. It successfully reached the Earth's moon, orbited it and then returned to Earth safely on December 27, 1968.