Moon landing: NASA invented new mathematics to land on the Moon in 1969 | Science | News

succeeded in its Moon landing mission 50 years ago tomorrow on July 20, 1969. The historic Apollo 11 mission saw astronauts Neil Armstrong, Buzz Aldrin and Michael Collins fly to the Moon and back. But the mission would not have been a success without the tireless work of the 400,000 people in the Apollo programme. And one of them, Stanley Schmidt, provided NASA with the crucial number-crunching needed for Apollo 11 to launch, land and return.

Dr Schmidt was an electrical engineer at NASA’s Ames Research Center from 1946 to 1961, whose work was invaluable to the Moon landing. 

The engineer played a critical role in creating the calculations needed to navigate a spacecraft to the Moon. 

In the 1960s, the onboard Apollo computers were simply not powerful enough to handle the complex manoeuvres of a lunar landing. 

But as head of NASA’s Ames Dynamic Analysis Branch, he cracked the mathematics behind the conundrum. 


Moon landing: Apollo 11 Saturn V launch in 1969

Moon landing: NASA had to invent new equations to navigate spacecraft to the Moon (Image: NASA)

Moon landing: Stanley Schmidt at NASA

Moon landing: Stanley Schmidt was instrumental in safely landing Apollo 11 on the Moon (Image: NASA)

Now, ahead of the 50th Apollo 11 anniversary this weekend, his son Greg Schmidt has shared the incredible story. 

He said: “My father had been assigned the problem of navigating to the Moon and, as he told it to me, it was a very difficult problem. 

“They didn’t have a mathematical solution to it. 

“It involved taking a number of different sources of information and combining them in an optimal way to get the best estimate of where your spacecraft is at any time, how fast you’re going and other variables, too.” 


Inspired by his father’s life and work, Mr Schmidt followed in his footsteps and is now the director of NASA’s Solar System Exploration Research Virtual Institute at Ames. 

I’m immensely proud of what my father did

Greg Schmidt, NASA Ames Research Center

He explained how his father had a eureka moment during one of his lectures at Ames, allowing him to solve the navigation issue. 

Based on prior work done by mathematician Rudy Kalman, Dr Schmidt connected the dots to develop brand new equations for NASA. 

He said: “My dad invited Rudy Kalman to give a lecture at Ames, and when he did, dad had an epiphany. 


“Kalman had written a paper about a theoretical ‘linear’ solution to estimating a vehicle’s location and speed. 

“The problem was that this was a fundamentally ‘nonlinear’ problem; that’s like the difference in complexity between floating down a lazy river and going over a waterfall, where your motion becomes chaotic and unpredictable. 

“My dad then developed the equations for how to solve this nonlinear problem – a major extension of Kalman’s work.” 

The mathematical equations are now known as the Schmidt-Kalman filter and allowed Apollo-era computers to blitz through vast amounts of data in real-time. 

Moon landing timeline: Apollo 11 on the Moon

Moon landing timeline: Detailed look back at the Apollo 11 Moon landing (Image: GETTY)

Moon landing: Apollo 11 landing on the Moon

Moon landing: Apollo 11 landed on the Moon on July 20, 1969 (Image: NASA)

The method helped put the first human astronaut on the Moon and was extensively used in fields such as air traffic management. 

Greg Schmidt said: “I’m immensely proud of what my father did. 

“Before he passed away, I remember being at the hospital talking with him about his work.

“He was barely even able to talk, but recounted all the equations as clearly as if it were 50 years earlier. He was a truly amazing man.”

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