Having worked through some of these types of calculations myself doing my physics degree, once you remove the atmosphere from a scenario, the maths becomes surprisingly simple. Though doesn’t make the precision any less impressive.
This is why I can’t abide the whole “there’s no way we went to the moon when the 1969 lunar module had less compute power than a modern calculator” argument. What do those people think the computer is actually doing? It’s not rendering a video game in 4k resolution or running some crazy simulation. It’s literally just taking measurements from the navigation instruments and then multiplying numbers together, you don’t need big computers for that. NASA staff used to do loads of these calculations by hand.
Going to the moon has always been a challenge in engineering and material sciences, not a computational challenge.