This is such an interesting peek into the engineering of these sort of systems with very constrained resources at the time. Like any random file you open contains little pragmatic design decisions like this https://github.com/chrislgarry/Apollo-11/blob/master/Comanch... # THE POSITION OF THE MOON IS STORED IN THE COMPUTER IN THE FORM OF # A NINTH DEGREE POLYNOMIAL APPROXIMATION WHICH IS VALID OVER A 15 # DAY INTERVAL…
Given the constant launch delays how could they justify hard coding a 15 day window like this?
Of course, the justification is that compute and memory were at an extreme premium on the spacecraft. Accurately predicting the position of the moon at arbitrary times requires more complicated calculations. You can dramatically optimize the calculation by fitting a polynomial approximation which is valid for the length of the mission. And there's no reason to waste resources fitting that polynomial in space when it could be done on the ground, using much more powerful machines.
The AGC is what tends to get the press. It's easy to forget that the Apollo program relied on a cutting-edge distributed hardware and software stack, most of which was in Mission Control at the Real Time Computing Center.