How many decimals of pi does NASA use?

This week we received from one of Facebook's subscribers the question of how many decimal places of the mathematical constant pi ( π ) are used by scientists and engineers of NASA in calculations.

Does JPL use 3.14 for pi? Or do you use more decimal places like this:
3,1415926535897932384626433832795028841971693993751058209749445
923078164062862089986280348253421170679821480865132823066470938
446095505822317253594081284811174502841027019385211055596446229
489549303819644288109756659334461284756482337867831652712019091
456485669234603486104543266482133936072602491412737245870066063
15588174881520920962829254091715364367892590360

We sent this question to the head and chief engineer of the Dawn mission, Marc Rayman. That's what he said.

“Thank you for your question! He was asked not the first time. In fact, such a question was asked many years ago by a sixth grader, a lover of science and astronautics, who was later fortunate enough to get a degree in physics and work on space exploration. His name is Mark Reiman.
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To begin with, I will answer directly. In the Jet Propulsion Laboratory (JPL) for the highest accuracy of calculations in interplanetary navigation, we use the value 3.141592653589793, that is, 15 decimal places. Let's see why no more decimal places. I think that in general there are no physically realistic calculations for which scientists needed to include more decimal places than here. Consider such examples.

1. The Voyager 1 spacecraft furthest from the Earth is at a distance of about 20 billion km . Imagine a circle with a radius of this size, that is, 40 billion km in diameter, for which we want to calculate the length using the formula 2 π R. A little more than 125 billion km is obtained. We do not need to focus on how accurate the circumference is (you can multiply yourself if you wish), we are interested in the measurement error due to rounding up to 15 characters. So, it turns out that the length with rounding up the constant to 15 characters is calculated with an error of less than 4 centimeters. Think about it. We have a length of 125 billion km, and the error is less than your little finger.

2. We can study the problem on the example of the Earth. The diameter at the equator is 12,756 km. Equator circumference 40,075 km. This distance will have to be overcome if you want to go on a world tour (not counting mountains, valleys and obstacles like buildings, parking lots, ocean waves, etc.). How wrong will your odometer be when using a rounded pi? He is wrong about the size of the molecule. Of course, there are different types of molecules that differ in size, but you get the idea. The size of the error is approximately 10,000 less than the thickness of the hair.

3. Let's take the largest object: the visible Universe. Its radius is about 46 billion light years. And now the question is: how many decimal digits pi should be used to calculate the circumference of the Universe with an error not exceeding the diameter of the hydrogen atom (the smallest atom)? Answer: you will need 39 or 40 decimal places. If you think about how huge the Universe is - truly bigger than we can even understand - and what a tiny hydrogen atom, then you will understand that for really accurate calculations many decimal digits of pi are not required. ”

Marc Reiman's articles can be read in the Dawn Journal magazine, where he talks about the mission of the Dawn research apparatus, which now explores the dwarf planet Ceres, on a monthly basis.

Note World Pi Day was celebrated on March 14 (3.14), but it is quite possible to celebrate it a second time on July 22, because 22/7 is even closer to the real value of pi than 3.14.

Note 2 . An irrational pi is an example of a source of random numbers. The randomness of decimal places is confirmed by all statistical and cryptographic tests. To the last day of Peter Stephen Wolfram launched the site Find Your Pi Day , which shows exactly where the pi is your birthday (or other number).