“Just looking at the damn MOON” means you don’t know when Passover falls until it’s too late. (Many Jewish holidays are traditionally celebrated on one day in Israel, but on two days outside Israel, on the assumption that it may take an extra day to get word from the Temple via pony express.)
And the math for predicting it ahead of time with 100% accuracy is a bitch. You’re working on a three-body problem, with precession, nutation, libration, and other fun facts that have to be taken into account – and that assumes that you’re using Kepler and Newton to start from. In fact, one of the jobs IBM’s second computer, SSEC, was given was to calculate new lunar tables, which were later used for the Apollo mission. (The first applications of most early computers, from Babbage on, were to calculate printed tables of mathematical and scientific data. It never occurred to people then that someday computers would be so cheap and accessible that the tables wouldn’t be needed anymore.) You see, as a problem in pure calculus, Newton’s law of gravity has never been completely solved, except for a simplified universe with only two objects in it, both of them perfect, infinitely rigid spheres of uniform density.
Today the problem could be solved, and, perhaps, someday, all Christians will get together on a new arrangement. But for most of history, approximations were the only available choice.