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She calculated the trajectory for Alan Shepard, the first American in space. Even after NASA began using electronic computers, John Glenn requested that she personally recheck the calculations made by the new electronic computers before his flight aboard Friendship 7 – the mission on which he became the first American to orbit the Earth. She continued to work at NASA until 1986, combining her math talent with electronic computer skills. Her calculations proved critical to the success of the Apollo Moon landing program and the start of the Space Shuttle program. //
https://youtu.be/E4j_LpKzcZQ //
A wonderful interview with Johnson where she gets to tell you her story. The interview is 22 minutes and well worth the time.