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When your phone shows where you are, it relies on an accurate description of the shape of the Earth. That shape is not a perfect sphere, and it is not even a perfect squashed sphere. Working out its real form from satellite data was the life's work of a mathematician who grew up on a farm in rural Virginia. This post covers what Gladys West did, works through the measurement her data depended on, and ends with what students can learn from her career.
Who was Gladys West?
The Royal Academy of Engineering records that she was born in Dinwiddie County, Virginia, graduated from Virginia State University in 1952 and taught maths and science before being hired in 1956 at the Naval Proving Ground in Dahlgren, Virginia, where she was the second Black woman ever hired and one of only four Black employees. Nature's obituary adds that she earned her master's degree at Virginia State in 1955 and that segregation laws stopped her travelling with colleagues. The obituary, published in January 2026, reports that she died aged 95.
What did she work on?
Nature describes her early work on Project 29V in 1962: calculating the orbit of Pluto relative to Neptune, a job that took more than five billion calculations and nearly 100 hours of computer time, and which by 1964 showed Pluto's orbit was regular.
She then moved to satellite data. She was project manager for the radar altimetry project of Seasat, which NASA's Seasat record describes as measuring the distance between spacecraft and ocean surface to 10 cm before it failed on 10 October 1978, after 105 days in orbit. The Royal Academy says she cut her team's processing time in half and was recommended for a commendation in 1979.
Her own papers show the work. In Smoothing of Geos 3 satellite radar altimeter data (1979) she describes filtering altimeter data with Wiener and then Kalman smoothers. In Mean Earth ellipsoid determined from SEASAT 1 altimetric observations (1982) she fitted an ellipsoid to Seasat geoid heights and found an equatorial radius a = 6,378,134.9 m. In 1986 she wrote the 51-page Navy report on data processing for the Geosat altimeter.
The Royal Academy sums up the result: her models of the Earth's geoid "underpinned the mapping functions of GPS and the study of global mean sea level". She worked at Dahlgren for 42 years, retiring in 1998, and afterwards completed a PhD in public administration at Virginia Tech, according to IEEE. Much of the work was classified. As she later recalled, in words quoted in Nature's obituary, "We didn't know exactly where it was going because we worked for the military where everything is secret."
How can a satellite measure sea height to 10 cm? A worked example
A radar altimeter times a pulse down to the sea and back. The height is h = ct/2. NASA's Seasat orbit data give a height of 769 to 799 km; take h = 790 km and c = 2.998 × 10⁸ m/s.
Round-trip time. t = 2h/c = 2 × 7.90 × 10⁵ ÷ 2.998 × 10⁸ ≈ 5.27 × 10⁻³ s, about 5.3 ms.
Timing needed for 10 cm. Δt = 2Δh/c = 2 × 0.10 ÷ 2.998 × 10⁸ ≈ 6.7 × 10⁻¹⁰ s, two-thirds of a nanosecond.
Fractional precision. 0.10 m ÷ 790,000 m ≈ 1.3 × 10⁻⁷, about one part in eight million.
Her ellipsoid in context. The NASA Earth fact sheet gives an equatorial radius of 6,378.137 km. West's 1982 value differs by 6,378,137 − 6,378,134.9 = 2.1 m, or 3.3 parts in ten million.
One measurement is not a map. Turning huge numbers of them into an accurate model required, in the Royal Academy's words, complex algorithms "to account for variations in gravitational, tidal, and other forces that distort Earth's shape". That is where West's filtering and programming came in.
Common mistakes: forgetting the factor of 2 for a round trip, mixing km and m, and treating the ellipsoid and the geoid as the same surface.
If this kind of multi-step estimate is where you lose marks, Fermi's AI tutor can work out what you already know and build a plan for the session, so you practise the step you actually find hard.
How was she recognised?
IEEE notes that she was inducted into the Air Force Space and Missile Pioneers Hall of Fame and received the IEEE President's Award in 2024. In 2021 she became the first woman to win the Royal Academy of Engineering's Prince Philip Medal. Accepting it, she said: "I encourage young women to believe in yourself, find your passion, work hard and apply yourself, stay committed, find a mentor".
What can a student take from West's way of working?
Accuracy is a habit. Her results depended on checking millions of numbers, not one clever idea.
Learn the tools of the time. She programmed some of the largest computers then built.
Keep studying. She finished a PhD after retiring.
Work through barriers without waiting for credit. Recognition came decades later.
Our post on satellite problems in gravitation has more practice with orbits. Try it now: find how far the radar pulse travels in 1 nanosecond, and what height error that would cause.
