In everyday calculations not requiring much precision, 3.14159 is sufficient for getting answers that are ‘close enough’.
But when you’re dealing with astronomical numbers measured in parsecs or light years, then those extra added digits become quite relevant to your equations.....................
You rarely, effectively never, know any of he quantities in an astronomical calculation to more than about 10 decimal places. π was likely one of the physical constants used to calculate the astronomical quantity. I cannot use a constant to calculate the value of a variable, and then turn around and use the result to calculate pi.
Google says that π is known to 105 trillion decimal places, far more than would be useful for any practical physical problem.
That’s rational enough for me. I’ve accepted it, and moved on.
I say we raise a generation of Indian kids on base 12 mathematics, and let them figure it out.