Her title, poached by the technology that would soon make the services of many of her colleagues obsolete, was “computer.”

Mrs. Johnson, who died Feb. 24 at 101, went on to develop equations that helped the NACA and its successor, NASA, send astronauts into orbit and, later, to the moon. In 26 signed reports for the space agency, and in many more papers that bore others’ signatures on her work, she codified mathematical principles that remain at the core of human space travel.

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She was not the first black woman to work as a NASA mathematician, nor the first to write a research report for the agency, but Mrs. Johnson was eventually recognized as a pathbreaker for women and African Americans in the newly created field of spaceflight.

Like most backstage members of the space program, Mrs. Johnson was overshadowed in the popular imagination by the life-risking astronauts whose flights she calculated, and to a lesser extent by the department heads under whom she served.

She did not command mainstream attention until President Barack Obama awarded her the Presidential Medal of Freedom — the country’s highest civilian honor — in 2015. The next year, her research was celebrated in the best-selling book “Hidden Figures” by Margot Lee Shetterly and the Oscar-nominated film adaptation starring Taraji P. Henson, Octavia Spencer and Janelle Monáe.

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Mrs. Johnson was “critical to the success of the early U.S. space programs,” Bill Barry, NASA’s chief historian, said in a 2017 interview for this obituary. “She had a singular intellect, curiosity and skill set in mathematics that allowed her to make many contributions, each of which might be considered worthy of a single lifetime.”

A math prodigy from West Virginia who said she “counted ­everything” as a child — “the steps to the road, the steps up to church, the number of dishes and silverware I washed” — Mrs. Johnson worked as a schoolteacher before being hired as a computer at the NACA’s flight research division, based at Langley Research Center in Hampton, Va.

The agency was established in 1915 and began enlisting white women to work as computers 20 years later. Black computers, assigned mainly to segregated facilities, were first hired during the labor shortage of World War II. Mrs. Johnson was one of about 100 computers, roughly one-third of whom were black, when she joined the NACA.

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The movie “Hidden Figures” took occasional liberties with fact to emphasize the indignities of segregation. Mrs. Johnson, played by Henson, is forced to run half a mile to reach the “colored” bathroom. In reality, Mrs. Johnson said, she used the bathroom closest to her desk.

“I did not feel much discrimination, but then that’s me,” she recalled in a 1992 NASA oral history. When she detected hints of racism, such as when a white colleague stood up to leave as soon as she sat down, she said, she tried not to respond. “I don’t wear my feelings on my shoulder. So I got along fine.”

Mrs. Johnson had a bachelor’s degree in mathematics and spent her early career studying data from plane crashes, helping devise air safety standards at a time when the agency’s central concern was aviation. Then, in October 1957, the launch of the Soviet satellite Sputnik thrust the space race into full tilt.

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Mrs. Johnson and dozens of colleagues wrote a 600-page technical report titled “Notes on Space Technology” outlining the mathematical underpinnings of spaceflight, from rocket propulsion to orbital mechanics and heat protection.

One of rocket science’s most vexing challenges, they soon realized, was calculating flight trajectories to ensure that astronauts returned safely to Earth, splashing down in the ocean reasonably close to a Navy vessel waiting to pluck them from the water.

For astronauts such as Alan B. Shepard Jr., who became the first American in space when Freedom 7 launched on May 5, 1961, the math was relatively straightforward. Shepard’s craft rose and fell, like a champagne cork, without entering orbit.

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Calculating the trajectory for an orbital flight, such as the one to be undertaken by Marine pilot John Glenn in 1962, was “orders of magnitude more complicated,” said Shetterly, the “Hidden Figures” author.

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“I said, ‘Let me do it,’ ” Mrs. Johnson recalled in a 2008 NASA interview. “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.”

Mrs. Johnson’s findings, outlined in a 1960 paper she wrote with engineer Ted Skopinski, enabled engineers to determine exactly when to launch a spacecraft and when to begin its reentry. The paper, “Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position,” marked the first time a woman wrote a technical report in NASA’s elite flight ­research division.

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“You could work your teeth out, but you didn’t get your name on the report,” she said in the 1992 oral history, crediting her breakthrough to what she described as an assertive personality. When a superior said that she could not accompany male colleagues to a briefing related to her work, Mrs. Johnson asked, “Is there a law that says I can’t go?” Her boss relented.

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Mrs. Johnson’s handwritten calculations were said to have been more trusted than those performed by mainframe computers. A short time before Glenn launched into space, he asked engineers to “get the girl to check the numbers.”

“All the women were called ‘the girls,’ ” said Barry, “and everyone knew exactly which girl he was talking about.” Mrs. Johnson, who was then 43, spent a day and a half checking the trajectory calculations made by the IBM computer before giving the go-ahead to Glenn, who became the first American astronaut to orbit the Earth.

In a subsequent report, Mrs. Johnson took her calculations one step further, working with several colleagues to determine how a spacecraft could move in and out of a planetary body’s orbit. Her formulas were crucial to the success of the Apollo lunar program and are still in use today, Barry said. “If we go back to the moon, or to Mars, we’ll be using her math.”

Modest beginnings

Katherine Coleman was born in White Sulphur Springs, W.Va., then a town of about 800, on Aug. 26, 1918. Her mother was a former teacher. She credited her proclivity for mathematics to her father, a farmer who had worked in the lumber industry and could quickly calculate the number of boards a tree could produce.

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By 10, Katherine had finished all the coursework offered at her town’s two-room schoolhouse. Joined by her mother and her three older siblings, she moved to Institute, a suburb of the state capital, to attend the laboratory school of West Virginia State College while her father remained at home to support the family.

Mrs. Johnson went on to study at West Virginia State, a historically black college, with plans to major in French and English and become a teacher. A mathematics professor — W.W. Schiefflin Claytor, widely reported to be the third African American to receive a doctorate in math — persuaded her to change fields.

Mrs. Johnson later recalled his saying: “You’d make a good research mathematician, and I’m going to see that you’re prepared.” She had never heard of the position before. “I said, ‘Where will I get a job?’ And he said, ‘That will be your problem.’ ”

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After graduating in 1937, at 18, she taught at a segregated elementary school in Marion, Va., a town near the North Carolina border.

Three years later, she was one of three black students selected to integrate West Virginia University’s graduate programs. She dropped out of her master’s in mathematics program after one semester to start a family with her husband, James Goble, a chemistry teacher. She later returned to teaching, in West Virginia, before a brother-in-law suggested she apply for a computer position at Langley.

Goble died of cancer in 1956, and three years later Mrs. Johnson married James Johnson, an Army artillery officer. He died in 2019.

Mrs. Johnson’s death was confirmed by lawyer and family representative Donyale Y.H. Reavis, who said she died at home in Newport News, Va., but did not cite a specific cause.

Survivors include two daughters from her first marriage, Joylette Hylick of Mount Laurel, N.J., and Katherine Moore of Greensboro, N.C.; six grandchildren; and 11 great-grandchildren. Her daughter Constance Garcia died in 2010.

Mrs. Johnson was invited to move to Houston in the mid-1960s to help establish what is now the Lyndon B. Johnson Space Center, but she declined the offer to maintain her family’s ties to the Hampton community, Shetterly said.

At Langley, where she retired in 1986, she performed calculations that determined the precise moment at which the Apollo lunar lander could leave the moon’s surface to return to the command module, which remained in orbit high above. She also contributed to NASA’s space shuttle and Earth satellite programs.

After the release of “Hidden Figures,” Mrs. Johnson played down the importance of her role in the early years of the space program. “There’s nothing to it — I was just doing my job,” she told The Washington Post in 2017.

“They needed information, and I had it, and it didn’t matter that I found it,” she added. “At the time, it was just a question and an answer.”