Super Miles

What about π when dealing with super duper trooper STARS in the universe?

Lets say we got this super duper trooper BIG STAR in the universe with 10000000000000000000000000000000000 miles in radius. How many decimals and how exactly would one demand π to be to determine its PERIMETER? 2πr

Lets say we gonna send a super satelite in motion around this super duper troper BIG STAR and the scientists wanted to calculate the exact round time

How important is really π?

The precision requirement of any calculation depends on the consequences that arise from the imprecision. So, if the orbit can be made stable by keeping it within 1% of nominal, than a value of PI given as 3.14 is fine. If the requirements of the mission require knowing the orbital distance to within 0.001%, than the value of PI should be used as 3.14159. However, since ALL computer computations invariable add imprecision (some number that are simple to represent as rational fractions (1/3) lose precision when represented in a computer because we can only save so many digits of the decimal representation (0.33333...)), it makes sense to make all computations as precise as possible, to reduce the effects of continual precision loss.

When working with computers (and, let's face it, computers are going to do all this calculation for us), ALL computations are faced with precision limitations. Most computers represent floating point numbers using a system that encodes the number in scientific notation, n * 10^m. (Actually, in a computer, depending on the system, it might also be n * 2^m.) The value of n can be represented using 32 or 64 bits. With 64 bits, we can be precise to 1 part in 1.8*10^19. Any value of PI that is more precise than that is useless in computation, because it can't be represented in the computer.