How Many Digits of Pi Does NASA Use? (kottke.org)

An anonymous reader quotes an article on Kottke.org: Mathematicians have calculated pi out to more than 13 trillion decimal places, a calculation that took 208 days. NASA's Marc Rayman explains that in order to send out probes and slingshot them accurately throughout the solar system, NASA needs to use only 15 decimal places. Rayman explains, "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."

Comments

Planck length

[Sqreater]

How many digits would it take of PI to bring the error down to the Planck length? Anything smaller in any measure of distance would be meaningless.

Re:All physical constants are known much less accu

[slashping]

The Rydberg constant is known to 14 decimal places, but I don't think it's very relevant for NASA calculations. https://en.wikipedia.org/wiki/...