Space Sunday: the mathematician of NASA

Tribute to Katherine Johnson. Credit: Breen, San Diego Union-Tribune

So often, when we think of the early years of US space flight, we think of steely-eyed, square-jawed test pilots supported in their missions by male, bespectacled and white-shirted scientists and flight controllers, their breast pockets lined with pens of various colours, all with similar haircuts and staring earnestly at computer screens, headsets allowing them to talk in clipped, precise terms with one another in acronym-laden sentences.

While both were very much the public persona for NASA, even becoming something of a cliché in television and film, they were only in fact the tip of the iceberg of the multitude of talents that formed NASA and made its missions possible. In particular, the image of the “nerds” of mission control has tended to very much overshadow the role played by many women in getting America both into orbit and to the Moon.

One of the foremost of these women was Creola Katherine Coleman, better known as Katherine Johnson, who sadly passed away on February 24th, 2020 at the age of 101. As a mathematician who spent 35 years working for NASA and its precursor, her calculations of orbital mechanics were critical to the success of the first US flights into space during the Mercury programme, and her work also encompassed the Apollo programme and the space shuttle.

Katherine Johnson, circa 1960. Credit NASA

Katherine Johnson was born on August 26, 1918, in White Sulphur Springs, West Virginia, the youngest of four children born to Joylette Coleman, a teacher, and her husband Joshua Coleman, a lumberman, farmer, and handyman. She showed a natural ability with mathematics from an early age. However, as her home county of Greenbrier did not offer public schooling for African-American students past the eighth grade (13-14 years of age), her parents enrolled her, at the age of 10, at the high school on the campus of West Virginia State College.

Following her graduation at 14, she attended West Virginia State, where she took every course in mathematics offered by the college and studied under chemist and mathematician Angie Turner King, and William Schieffelin Claytor, the third African-American to receive a Ph.D. in mathematics In fact, Claytor was so impressed with Johnson, he added new courses just for Katherine. Graduating summa cum laude in 1937 at the age of 18 and with degrees in mathematics and French, Johnson took on a teaching job at a black public school in Marion, Virginia.

She returned to studying mathematics after marrying her first husband, James Goble in 1939, becoming the first African-American woman to attend graduate school at West Virginia University.

Johnson’s association with aerospace commenced in 1953 when she joined the National Advisory Committee for Aeronautics (NACA), joining the Guidance and Navigation Department at the Langley Memorial Aeronautical Laboratory, Virginia. Here, she initially worked in a team of women supervised by mathematician Dorothy Vaughan, carrying out a range of mathematical analyses of aircraft flight dynamics, wind handling and more. She was then reassigned to the Guidance and Control Division of Langley’s Flight Research Division.

At first she [Johnson] worked in a pool of women performing maths calculations. Katherine has referred to the women in the pool as virtual “computers who wore skirts”. Their main job was to read the data from the black boxes of planes and carry out other precise mathematical tasks. Then one day, Katherine (and a colleague) were temporarily assigned to help the all-male flight research team. Katherine’s knowledge of analytic geometry helped make quick allies of male bosses and colleagues to the extent that, “they forgot to return me to the pool”. While the racial and gender barriers were always there, Katherine says she ignored them. Katherine was assertive, asking to be included in editorial meetings (where no women had gone before). She simply told people she had done the work and that she belonged.

– Oral history archive at by the US National Visionary Leadership Project

Katherine G. Johnson Computational Research Facility, Langley Research Centre, Virginia, inaugurated in 2019 and named in honour of Katherine Johnson. Credit: NASA

With the formation of NASA, Johnson worked as an aerospace technologist, moving to the agency’s Spacecraft Controls Branch, a department in which she continued to work through until her retirement from the agency in 1986. Her first major project was calculating the launch window and flight trajectory for Freedom 7, the sub-orbital flight that made Alan Shepard the first American in space on May 5th, 1961. In particular, her trajectory calculations – manually produced – ensured the recovery teams were on hand when Shepherd splashed down. In addition, to her calculation for flights, Johnson plotted backup navigation charts for the astronauts in case of electronic failures aboard their craft.

Such was her reputation and prowess, Johnson was key to ensuring NASA could transition from human computers to electronic computers. In this role, when John Glenn was preparing to make NASA’s first orbital flight around the Earth, he refused to fly unless and until Johnson had personally verified all of the electronic flight calculations for the mission. Despite the greater complexity in orbital flight calculations, Johnson did so by comparing the electronically-produced calculations  with her own manual calculations that she produced over the course of a day and a half – a feat that passed almost unnoticed in the pages of history.

In this respect, Johnson – although living in a state where segregation on the basis of colour was still very real (despite NASA’s somewhat more relaxed view of things) – would later state that she found sexism in the workplace the bigger problem (Glenn, for example, called for her to review the data relating to his flight simply as “the girl”).

We needed to be assertive as women in those days – assertive and aggressive – and the degree to which we had to be that way depended on where you were. I had to be. In the early days of NASA women were not allowed to put their names on the reports – no woman in my division had had her name on a report. I was working with Ted Skopinski and he wanted to leave and go to Houston … but Henry Pearson, our supervisor – he was not a fan of women – kept pushing him to finish the report we were working on. Finally, Ted told him, “Katherine should finish the report, she’s done most of the work anyway.” So Ted left Pearson with no choice; I finished the report and my name went on it, and that was the first time a woman in our division had her name on something.

– Katherine Johnson quoted in Black Women Scientists in the United States, 1999.

President Barack Obama awards the Presidential Medal of Freedom to Katherine Johnson in 2015. Credit: UPI

As NASA shifted gears to achieve President Kennedy’s goal of “landing a man on the Moon and returning him safely to the Earth”, Johnson threw herself into the task of making sure it could happen. She would arrive at the office early in the morning, work through until late in the afternoon, then go home to look after her three daughters – born to her late first husband, and living with her and her second husband, James Johnson – then returning to NASA after the children were in bed, maintaining a schedule of 14- to 16-hour days.

These hours enabled her to carry out a critical role in calculating Apollo 11’s flight to the Moon and back and – most crucially of all – she calculated the exact time that the lunar module ascent stage needed to lift-off from the lunar surface in order to successfully rendezvous with the Command and Service Module, a feat she would come to regard as her proudest accomplishment.

During this time, she also embarked on co-authoring a series of papers specifically for the Apollo programme (as part of some 26 science and mathematics papers she wrote while at the agency). These were intended to guide mission teams and astronauts alike through scenarios in which various computer systems on the spacecraft might fail. One of these papers, produced in 1967 with Al Hamer, detailed alternative methods of celestial navigation in the event of a failure with Apollo’s on-board navigation systems, and was pulled into use in the Apollo13 rescue in April 1970.

Everybody [in the Apollo programme] was concerned about them getting there. We were concerned about them getting back.

– Katherine Johnson, 2010, discussing her co-authored approach to one-star navigation,
tested by Jim Lovell during Apollo 8 (1968), and which formed a part of the Apollo 13 recovery efforts (1970)

Following Apollo, Johnson moved to the space shuttle programme, again playing a key role in preparations for the 1981 first flight of the original space-capable orbiter vehicle, Columbia, and worked on orbital requirements for the Earth Resources Technology Satellite (ERTS) project, which would later be renamed Landsat. Additionally, in leading up to her retirement in 1986, she turned her mind to plans for missions to Mars.

Following her official retirement, Johnson spent her later years encouraging students to enter the fields of science, technology, engineering, and mathematics (STEM), talking about her work at NASA and remaining a strong advocate of human space flight. In 2015, she was awarded the Presidential Medal of Freedom by President Barack Obama, while in 2016 her work, and that of her fellow African-American women at NASA was charted in the 2016 biographical movie Hidden Figures. In that same year NASA dedicated a purpose-built unit, the Katherine G. Johnson Computational Research Facility at the Langley Research Centre, in her honour. A second facility, also in Virginia, was renamed in her honour in 2019. The is responsible for developing and verifying software crucial to NASA missions. Both are fitting tributes to one of NASA’s pathfinders.

Katherine Johnson at 97. Credit: unknown

I found what I was looking for at Langley. This was what a research mathematician did. I went to work every day for 33 years happy. Never did I get up and say, “I don’t want to go to work.”

– Katherine Johnson, commenting on her time at NASA

Katherine Johnson died at a retirement home in Newport News on February 24, 2020, at age 101, she is survived by her three daughters, six grandchildren and 11 great-grandchildren. Her legacy is one that has carried humans into space and to the Moon, and paved the way for modern human space flight.