When I was a kid my parents bought me a book called "practical astronomy with your calculator" that went over all the workings and formulae for calculating eclipses, moon phases, locations of the planets and heaps more. If you want to get into it I highly recommend this book or something similar.
There are certain aspects of it that look more complicated than they are because you are seeing it as a representation on a flat map. It makes a lot more sense when you see it on a globe with all the pieces moving in 3d space.
It is complicated because there are tilts to the earths rotation and a tilt to the moon's orbit, but people thousands of years ago figured it out, so it's solvable.
Are you so deeply entrenched in modern technology that you cannot fathom that a human could comprehend and map future astronomical patterns?
Humans have been doing this since early records of humankind on earth. Loooooong before computers existed. Computers have only been around the last few decades.
Me too! Always wanted to get into, thinking it worthwhile to have a running solar system or celestial model on your own machine that you know how to operate etc. Just never really tried sadly!
Oh yea I’ve used it and from memory it’s awesome as you say. I was more talking about getting into the technical details of running a model and calculating various things of personal interest.
They discovered Neptune by math. They studied the orbit of Uranus and noticed anomalies in the mavity, so they postulated there must be another planet. Using math, calculated it's path, aimed their telescopes, and voila, Neptune.