She worked temporarily as a high school teacher to help her husband financially get a law degree from Harvard. Hamilton later decided to continue school wanting to get a PhD in abstract mathematics, but was then offered a job at MIT to help create software for NASA that would help put humans on the Moon, a job that he accepted. One of Hamilton's greatest contributions to NASA was when he helped develop a program that helped the Apollo 8 spacecraft return to Earth. One day, Hamilton's daughter Lauren was tinkering with a flight simulator when she accidentally crashed the simulation by launching a prelaunch program called PO1 mid-flight. Hamilton saw this as a potential problem if someone initiated the launch program during the mission. He asked NASA for permission to build a program that would somehow prevent the simulator from launching the prelaunch program; Unfortunately, NASA believed that astronauts would never do such a thing. However, astronaut Jim Lovell initiated the program during the mission, erasing data that would have helped the spacecraft return to Earth. Hamilton and a few others began working on a solution, and after nine hours NASA was able to send a replacement set of data to the Apollo 8 computer to bring it back.