How many digits of pi does NASA use?

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.


Link

I thought this was interesting. I wonder if there are other calculations that actually need more digits.

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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a reply to: roadgravel

Why are they working in Pi? instead of Phi?

That's the interesting question.

And my take away from your post. Fascinating.

Thank for a neat post.

a reply to: Treespeaker

Why are they working in Pi? instead of Phi?

What makes you think "instead?"

You know, tool for the job. Like that.
Depending upon the function, pi is the tool. Depending on the function, phi is not.
Irrational numbers are not interchangeable.

originally posted by: Treespeaker
Why are they working in Pi? instead of Phi?

Why would they? Phi is of no use in calculating orbital trajectories.

I thought it was more like Pi to 15 decimals could calculate the radius of the universe within the distance of a hydrogen molecule.

originally posted by: FlyingFox
I thought it was more like Pi to 15 decimals could calculate the radius of the universe within the distance of a hydrogen molecule.

Without knowing the circumference of the universe, or its shape, pi wouldn't really help much.

except for the fact that the circumference of a circle is pi x diameter, the area is pi x radius squared

Normally these sort of limits are the result of having to be a standard number over many different computer systems and even small rounding errors can roll up enough to cause an error so there normally is a lot of bounds testings on the routines to ensure that when numbers get passed around they don't cause anything strange.

Probably in the 1960's that was all that was needed as the floating point units in those days were rather slow compared to now and the more detail you wanted the longer the calculation would take and for what NASA had planned then it was overkill.

a reply to: roadgravel

NASA needs to use only 15 decimal places, or 3.141592653589793.

This is funny, and all the responses as well...


There is a very simple reason that NASA, and everybody else as well would use a number like this...

In the programming languages used to write everything we use and take for granted is a data type known as a "Double" or "Double Precision"...it is always a value / format like the above when rendered as a "string". It can be extended to include an exponent (i.e. E+09) the exponent can be as large as 300+. Represented inside the computer this value may be as many as 128 bits, though typically 64 bits.

I'm curious as to which point continuing decimal places of pi leads to sub-quantum differences. If we are doing a math problem, is their a measurable (more than quantum) difference between the 1000th and 1001th point?