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This is the math that made Katherine Johnson — one of NASA’s “Hidden Figures” — a legend

Johnson, who died Monday at age 101, did groundbreaking work in helping return astronauts safely to Earth.

By Brian Resnick@B_resnickbrian@vox.com Updated Feb 24, 2020

NASA mathematician Katherine Johnson received the Presidential Medal of Freedom from President Barack Obama in 2015. Nicholas Kamm/AFP via Getty Images

Katherine Johnson, who died Monday at age 101, was a pioneer in many ways: She was an early employee of NASA (and even worked at the agency that predated it), and an African American woman working in a field hugely dominated by white men. She was also a pioneer in that her work helped put humans in space, and returned them safely home to Earth.

Before rising to pop-culture fame with the book and movie Hidden Figures, before being awarded the Presidential Medal of Freedom, Johnson created and calculated some extremely important equations to make America’s adventures in spaceflight successful. As Bill Barry, NASA’s chief historian, told the Washington Post in an obituary: “If we go back to the moon, or to Mars, we’ll be using her math.”

Here’s what she did, and why she’ll be remembered for a long time.
NASA gave Johnson landing zones. She figured out how to get spacecraft there.

In the 1960s, NASA had figured out how to launch a human being aboard a rocket into space. That was an extremely impressive feat. But equally hard was getting that human to land safely back on Earth.

One of the trickiest bits: the spacecraft couldn’t just land anywhere. Were an astronaut to touch down in a desolate corner of the ocean, without any land in sight, it could presumably take days to be rescued (if rescued at all).

This means that Johnson needed to calculate the entire trajectory of the flight — where it started, how fast it went, and where it would land. The missions to send humans to space and back had to be precise and choreographed. Johnson’s math enabled that choreography.

She best explained her job in her own words: “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,” Johnson said in a 2008 NASA interview. “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.’ That was my forte.”

And so, she calculated the trajectory for Alan Shepard’s historic 1961 flight that put the first American in space, and landed him in the Atlantic Ocean.

But greater challenges were to come. Shepard visited space, but he was not put into orbit around the Earth. He went up, and came down. Flying, essentially, in a simple parabolic arc.

Orbit — having the spacecraft encircle the Earth — is harder.

Katherine Johnson at NASA’s Langley Research Center in 1980. NASA/Donaldson Collection/Getty Images

In orbit, not only is the spacecraft moving at 17,000 mph, the Earth below is also moving, rotating on its axis.

Here, Johnson’s challenge was the same. She had to take a landing zone for an orbiting spacecraft, and calculate backwards: figuring out the math for how the spacecraft would arrive there.

She did this work to prepare for Astronaut John Glenn’s historic 1962 mission when he became the first American to orbit the globe.

This work meant juggling a lot of different variables: where the rocket took off, where it entered obit, how quickly it was moving in orbit, the rotation of the Earth beneath it, the angle at which it ought to reenter the Earth, and the location of the splashdown.

In figuring it out, she became the first woman to ever co-author a research paper at NASA. Entitled “Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position,” the paper — with co-author Ted Skopinski — basically explains where an orbiting spacecraft should fire its reentry rockets to land on a particular portion of the Earth.

Famously, before Glenn took off on his first orbital spaceflight, he requested Johnson double-check all the orbital math of the mission by hand — being slightly distrustful of the new-fangled electronic computers that NASA had installed to do the work.

Glenn’s flight, and the math making it happen, was the subject of the 2016 film Hidden Figures, in which Johnson, as well as other African American women working at NASA, are given the spotlight amid a workforce that’s largely white and male.

But Johnson’s work didn’t stop there. She worked on the Apollo program, which brought humans to the moon for the first time: Her calculations were critical in getting the lunar lander to meet back up with the command module in orbit around the moon. She later worked on the space shuttle program, as well as satellites, before retiring in 1986. Today, there’s a computational research facility at NASA’s Langley campus named after her.
Johnson’s celebrity came late in life, but it’s also important

Her mathematics is an important legacy. But so is the legacy of her recent celebrity. For too long, Johnson’s contributions to the space program were unknown by the public. The story of America’s success in the space race has largely been told through the stories of the men at NASA. But Johnson was there, too. And it’s important to remember that.

The public needs more diverse role models in science. “When you think about what a scientist means, you probably think of an Einstein figure — a man in a lab or at a chalkboard with fuzzy, unkempt hair,” as my Vox colleague Julia Belluz has written. “When you think of a scientist’s voice, you might conjure Neil deGrasse Tyson or Carl Sagan. With these voices and images so pervasive in our culture, it’s easier to associate ‘scientist’ with ‘man’ — and in particular, ‘white man.’”

Women scientists like Vera Rubin, Nettie Stevens, Henrietta Leavitt, Rosalind Franklin, Johnson and so many others ought to be just as famous. Today, too many women — and minorities — still feel unwelcome in many corners of science. Johnson’s legacy shows them they have every right to be there.

Katherine Johnson, ‘hidden figure’ at NASA during 1960s space race, dies at 101

When Katherine Johnson began working at the National Advisory Committee for Aeronautics in 1953, she was classified as “subprofessional,” not far outranking a secretary or janitor.

© Provided by Thomson Reuters, LLC 2.

THE WOMEN BEHIND THE MISSION: NASA research mathematician Katherine Johnson wrote the calculations for the Apollo 11 trajectory to the moon. She was one of just a few African-American women hired to work as "human computers" to check and verify engineer calculations at the National Advisory Committee for Aeronautics (NACA), the agency that preceded NASA. Johnson was a key contributor to several space milestones. She wrote the trajectory for Alan Shepherd's flight in 1961, the first by an American in space, and the verification of calculations for John Glenn's 1962 orbit, the first by an American. She was awarded the Presidential Medal of Freedom in 2015 and her life story was turned into the 2016 film "Hidden Figures." NASA/Handout via REUTERS

Hers was a labor not of scheduling or cleaning but rather of mathematics: using a slide rule or mechanical calculator in complex calculations to check the work of her superiors — engineers who, unlike her, were white and male.

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.

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.


NASA mathematician portrayed in 'Hidden Figures' breaks down how she helped astronauts


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.

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.

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.

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.

“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.

“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.

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.

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.’ ”



© NASA NASA research mathematician Katherine Johnson is photographed at her desk at NASA Langley Research Center with a globe, or "Celestial Training Device," in 1962.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.”

harrison.smith@washpost.com

Read more:

‘Hidden’ no more: Katherine Johnson, a black NASA pioneer, finds acclaim at 98

The stars of ‘Hidden Figures’ are now immortalized on street sign

The ‘Hidden Figures’ stars on how working at NASA in the 1960s is a little like Hollywood
© NASA An undated photo of Mrs. Johnson at NASA.

‘Human computer’ Katherine Johnson dies at 101

She was the inspiration for the movie Hidden Figures and calculated the flight paths for NASA’s early missionsBy Justine Calma@justcalma Feb 24, 2020

Photo credit should read MARK RALSTON/AFP via Getty Images

NASA mathematician Katherine Johnson, whose calculations helped get the first Americans to space and back safely, died today at the age of 101. Among her many accomplishments, she completed the trajectory analysis for Alan Shepard’s 1961 suborbital flight, which was the first time the US sent a human into space.

HER WORK PROPELLED MANY OF AMERICA’S BREAKTHROUGHS IN SPACE EXPLORATION

Johnson’s work over 33 years propelled many of America’s breakthroughs in space exploration, including Neil Armstrong’s “giant leap for mankind” on the Moon. But the contributions she made weren’t recognized until decades later. Johnson was made to work in a segregated wing with other black women mathematicians when she started at NASA predecessor The National Advisory Committee for Aeronautics (NACA) in 1953. Yet, her work was so integral to NASA’s early missions that John Glenn asked her to double-check computer calculations for his flight before becoming the first US astronaut to orbit Earth in 1962.

“Ms. Johnson helped our nation enlarge the frontiers of space even as she made huge strides that also opened doors for women and people of color,” NASA administrator Jim Bridenstine said in a statement. “Her dedication and skill as a mathematician helped put humans on the Moon and before that made it possible for our astronauts to take the first steps in space that we now follow on a journey to Mars.”

Johnson’s groundbreaking contributions were recognized in 2015 when she received the Presidential Medal of Freedom, the highest honor bestowed on civilians, from President Barack Obama. The bestselling-book-turned-Oscar-nominated-movie Hidden Figures brought Johnson’s legacy to the big screen in 2016, in which she was portrayed by Taraji P. Henson. NASA also named a building in her honor in 2017.

In an interview, she was asked what she’d tell young engineers working in the building that bears her name. “Do your best, but like it,” Johnson said. “If you don’t like it, shame on you.”

“I like work. I like the stars and the stories we were telling and it was a joy to contribute to the literature that was going to be coming out. But little did I think it would go this far,” Johnson said in the 2017 interview.

“If you think your job is pressure-packed, [Johnson’s] meant that forgetting to carry the ‘1’ might send somebody floating off into the solar system,” Obama said when Johnson received the Presidential Medal of Freedom. “Katherine was a pioneer who broke the boundaries of race and gender, showing generations of young people that everyone can excel in math and science and reach for the stars,” he said.