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How do astronauts use math in their jobs?

What are some reasons astronauts need to study mathematics?

Imagine you're on a spaceship in orbit around the moon. You have a fuel leak and are running out of power. When do you fire the ship's thrusters, and for how long and in what direction, in order to be able to return to Earth safely?

Obviously, this is not a question that astronauts usually face (except maybe on Apollo 13) but hopefully it illustrates the way in which math (in this case, calculus, algebra, etc.) and science (in this case, the physics of orbits), which has math at its heart, relates to everything that goes on in a space flight mission. All the science and engineering that goes into designing, building and flying spacecraft is based on math - without math, there would be no way to predict beforehand how the spacecraft would react to different conditions and how it would move in its orbit.

I imagine that astronauts probably don't directly use much more than simple math when on a flight - important calculations are done by computers - but to have some idea of what a spacecraft is doing and how it is operating, without placing complete blind faith in the people who built it, requires a knowledge of math.

Also, in addition to flying and maneuvering a spacecraft, astronauts are often involved in conducting scientific experements aboard the spacecraft, which would involve math in other ways too.

February 2002, Dave Rothstein (more by Dave Rothstein) (Like this Answer)

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