I'm trying to solve the three-body problem for earth, moon, and sun.
One of my favorite Apologetics Books, Show Me God, was written by Fred Heeren. He is not a scientist, but he writes engagingly, and gives a lot of food for thought. The second time through that book, I read that it was a “miracle” that the centrifugal force of the moon around the earth exactly matched the gravitational attraction between the two bodies. I thought when I read that, “No, the orbit would adjust itself so that that very thing happened!” Then I proceeded to put together the theory, not exactly in my field, and wrote a small program on a programmable calculator, the HP 33s, to find the radius. Everything worked except for one thing. Whenever I was able to think clearly enough about the problem, the magnitudes of the forces were almost exactly equal, erring by the miniscule difference due to use of a 12-digit calculator, but the direction of the force was pushing the moon away from the optimum orbit radius. Finally, I realized that I was ignoring the forces due to the sun! Kind of a duh-moment. When I calculated the maximum gravitational force on the moon by the sun, it was about twice the gravitational force of the earth on the moon. So, even though the force of the earth on the moon was pushing the moon away from the optimum orbit radius, the sum of earth and sun on the moon was pushing the moon toward the optimum orbit radius. This theory needs to be polished a lot, but if the calculations lead to the known orbit radius, it could greatly simplify the complex 3-body theory that has been used to solve it. I sent my results to Fred Heeren earlier, before I realized that I had forgotten the sun, despite living in Texas, and he answered and said that that particular miracle was the weakest, and was replaced in a later edition. He was very positive and I enjoyed hearing from him.