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  • Writer's pictureDale DeBakcsy

Trajectories: Katherine Johnson’s Orbital Mathematics

Before NASA, there was NACA, an oddball collection of aeronautics nerds using black box data and wind tunnel analysis to figure out as much as they could about the science of flight. Calculations, done almost entirely by hand, were the coursing lifeblood of the organisation. Those calculations were handled by a small army of women who were ‘checked out’ and ‘returned’ to the mathematical pool as needed by the male scientists. And in a room separate even from those women was the place where the African American calculators were kept, segregated because of their race, and given brute force computational tasks because of their gender.


All the externals spoke against sustained success for any non-white female mathematician and yet, from within that segregated room there came one person, Katherine Coleman Goble Johnson (1918–2020), who refused to be domineered by tradition and who, as a result, over thirty-three years at NACA and NASA, made fundamental contributions to the Mercury and Apollo missions, the space shuttle, the mathematics of space flight, astronaut emergency navigation systems, satellite tracking techniques, and plans for a future Mars mission.


She was a maestro of trajectories, NASA’s go-to mathematician for developing the equations of the country’s first ventures into space and, as could be expected, she showed genius from the start. Her parents cared about education more than anything, and her father was willing to work in one city while the rest of the family lived in another just to ensure that she had access to a high school. He only got to see them once a month when school was in session, but thought the sacrifice was worth it, especially as Katherine continually leapt with great bounds over and beyond her classmates.


She entered school at the second grade, bypassing kindergarten and first grade entirely and then her teachers found her still so advanced that they skipped her over fifth grade as well, with the result that she entered high school at the age of 10. She chewed through the standard mathematics courses handily and so her teachers developed a college-level course which had her as its only student. She attended West Virginia State, a historically African American school, and benefited from the intense and personal mentorship of her professors there. Professor John Matthews, a fluent speaker of seven languages and head of the Romance Languages department, inspired her to study French and English, while Professor James Evans, who took her into his family as an adopted daughter of sorts, pushed her to continue expanding her substantial mathematical skills, with the result that she double majored in French and mathematics, getting her degrees at the age of 19.


Had she been a male, she would have been swooped up into the field of research mathematics that Evans encouraged her to pursue, but as an African American female in the late 1930s, teaching was more or less her only option, taking what jobs she could as they arose to keep herself out of the grinding maw of the Great Depression. For fifteen years she carried on like this. For two years she attended graduate school but had to leave before obtaining her degree when her husband, who she’d married just after graduating West Virginia State, started succumbing to brain cancer. She dropped her studies to find more work as a teacher to provide money for his care and for the raising of their three daughters.


Photo by NASA


For most women struggling to feed their family during the Depression, that, or something still more tragic, would have been the end of it, but fortune granted Johnson a break. She heard about jobs for women with mathematical abilities at NACA. Not glorious jobs – primarily grinding out routine calculations that the aeronautic researchers and engineers couldn’t be bothered with, but real and steady work at the heart of a new frontier. Johnson joined the pool of calculatorial ladies in 1953, and was assigned her spot in the ‘colored room’ to wait until she was needed.


Classified as a ‘subprofessional’ on account of her gender, she used slide rules and instinct to churn her way through masses of wind tunnel data. Johnson was so deft mathematically, however, that she was soon snatched up by the Flight Research Division, who decided to keep her rather than returning her to the lady calculator closet. She argued for, and won, a place at division meetings, a thing unheard of at the institution, but one that was generally accepted because her deep knowledge of the subject was too useful to have at hand to refuse.


When, in 1958, NACA became NASA and the entire organisation had to shift its focus to compete with the Soviet Union in space, they found themselves in the embarrassing situation of having no basic text laying out the mathematics of space flight, and Johnson was put on a secret team to create it. That work turned out to be one of NASA’s core manuals during the institution’s Golden Age. Johnson was then let loose on trajectory calculations. When a new mission was being planned, a representative would come to Johnson and ask for the trajectory equations that would result in the desired touchdown location and time, and she developed them, creating the trajectories that lifted Alan Shepherd and John Glenn into space, and which handled the immense task of getting the Apollo program to the moon, the lander to the surface, and the crew back to Earth.


Photo by NASA

In an interview with Wini Warren, she related:


Everything was so new. The whole idea of going into space was new and daring. There were no textbooks, so we had to write them. We wrote the first textbook by hand, starting from scratch. People would call us and ask, ‘What makes you think this or that is possible?’ and we would try to tell them. We created the equations needed to track a vehicle in space. I was lucky that I was working with the division that worked out all the original trajectories, because I guess that’s what I’m remembered for.


She worked days and nights, pulling sixteen-hour shifts with her colleague Al Hammer in order to develop fail-safe routines that astronauts could use to navigate by the stars if their link with the ground was severed or the computers failed, and in 1970, when Apollo 13’s systems were damaged and it was feared the crew wouldn’t make it back, it was Hammer and Johnson who were summoned to track the flight and advise the white-knuckled administration.


While working on these problems for NASA, Johnson wrote her first scientific paper in 1960, ‘Determination of Azimuth Angle at Burnout for Placing a Satellite over a Selected Earth Position’ which, upon its publication in 1960 represented the first time NASA had ever allowed a woman to attach her name to the work she did in a public document. It was instrumental in the planning of the Mercury missions, and would be followed by twenty more technical papers over her thirty-three-year career. After Apollo, she worked on finding better procedures for object tracking, work which required sifting through tracking station data from all over the world and which helped make possible our satellite-clustered sky of today.


She worked on the space shuttle, the projected Mars program, and on methods of using satellites to map the mineral resources of the planet. Her projects read like a Greatest Hits album of humanity’s efforts in space, from its slide-rule and wind-tunnel origins to its dreams of interplanetary exploration and satellite proliferation. She started in a segregated office trying to earn enough to keep her husband well and her family thriving. She ended by mathematically mapping the expansion of humanity from its modest home planet. ‘I had a wonderful, wonderful career at NASA. I don’t imagine everyone can say that, but it’s true in my case. I have always loved the idea of going into space – I still do.’


Photo by NASA


Katherine Johnson passed away in a retirement home on 24 February 2020, at the age of 101.


FURTHER READING: The publication of Hidden Figures by Margot Lee Shetterly in 2016, and subsequent 2019 film, lifted Katherine Johnson to a level of well-deserved scientific superstardom that paved the way for the publication of her autobiography, My Remarkable Journey: A Memoir in 2021. Before 2016, your best source for her life and work was contained in Wini Warren’s Black Women Scientists in the United States (1999), which is a key text for anybody interested in the history of gender and race in the sciences and features easily a hundred biographies of success torn from the mouth of systemic discrimination.


If you'd like to read more about women mathematicians like this one, check out my History of Women in Mathematics, launching in October 2023 from Pen and Sword Books!

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