Here is a document that derives many things from scratch and answers the question about how far the Moon falls.
Recently, I’ve been trying to pretend that we know nothing about the universe, similar to people in the far distant past, and duplicating the way that they ‘found things out’. All this came about because of a Feynman lecture I was watching, where he showed how fast the moon was ‘falling’ to earth due to gravity. He used certain known values, like the diameter of the earth. I’m currently using the Internet to consolidate a bunch of deductions and how they were reached, leading up to a calculation of the moon’s velocity due to gravity. I’ll release it on baselines.com when I am done, but for now, all this led to looking at the tilt angle of the Earth. I was interested in how all the planets tilt, and it was incredible how fast the information is found with a simple search.
I thought I would paste the info in here if anyone else was interested.