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In 1958, after NACA was reformulated into the National Aeronautics and Space Administration (NASA), Johnson was among the people charged with determining how to get a human into space and back. The following year she remarried, to decorated Navy and Army officer James A. Johnson.
For Johnson, calculating space flight came down to the basics of geometry: "The early trajectory was a parabola, and it was easy to predict where it would be at any point," she said. "Early on, when they said they wanted the capsule to come down at a certain place, they were trying to compute when it should start. I said, 'Let me do it. You tell me when you want it and where you want it to land, and I'll do it backwards and tell you when to take off .' " As a result, the task of plotting the path for Alan Shepard's 1961 journey to space, the first in American history, fell on her shoulders.
The next challenge was to send a man in orbit around Earth. This involved far more difficult calculations, to account for the gravitational pulls of celestial bodies, and by then NASA had begun using electronic computers. Yet, the job wasn't considered complete until Johnson was summoned to check the work of the machines, providing the go-ahead to propel John Glenn into successful orbit in 1962.
While the work of electronic computers took on increased importance at NASA, Johnson remained highly valuable for her unwavering accuracy. She performed calculations for the historic 1969 Apollo 11 trip to the moon, and the following year, when Apollo 13 experienced a malfunction in space, her contributions to contingency procedures helped ensure its safe return.
Johnson continued to serve as a key asset for NASA, helping to develop its Space Shuttle program and Earth Resources Satellite, until her retirement in 1986.