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NASA needs to use only 15 decimal places, or 3.141592653589793.
The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles.
We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off.
It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches.
Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
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Susan Gomez, manager of the International Space Station Guidance Navigation and Control (GNC) subsystem for NASA, said that calculations involving pi use 15 digits for GNC code and 16 for the Space Integrated Global Positioning System/Inertial Navigation System (SIGI). SIGI is the program that controls and stabilizes spacecraft during missions.
Peter Mohr, a physicist who works for the Fundamental Constants Data Center at the National Institute for Standards and Technology, which is involved in calculating and disseminating the accepted CODATA values, says that the institute uses 32 significant digits of pi in their computations.
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Why are they working in Pi? instead of Phi?
originally posted by: Treespeaker
Why are they working in Pi? instead of Phi?
NASA needs to use only 15 decimal places, or 3.141592653589793.