Everything you describe is consistent with Newtonian mechanics.
Gravity is self-evident. Mathematics is the quantify it and accurately predict its effects, not confirm it.
There is no guesswork in Newtonian celestial motions until he reaches the perimeter of his knowledge, at which time he inserts a deity into his work to keep the solar system stable. His mathematics was incomplete, and he was unable to solve gravitational problems involving more than two bodies. His numbers suggested that the gravitational pull of other planets on the earth would have thrown the earth into the sun or into interstellar space, so, he added the hand of God to his work.
And it's remarkable to see you diminish the importance of that work as a drop of fact in what is "basically all pure gravitational guesswork." It's one of the greatest of human achievements. You do this with all science, but not effectively, since you can't make science's stellar success go away however much you ignore it.
Gravitational theory works well as is with the current state of knowledge. It worked well with just Newton's contribution centuries ago. My beliefs, which are dicta of science, are demonstrably correct. It's not necessary for you to agree.
None of these are stumbling blocks for me. They seem to be for you, however. They are impediments to your making progress in understanding science and recognizing it for what it is. And another example of false crisis, or claiming that something is a problem for an individual or for science without feeling any need to explain how it is a problem. I have no problems caused by scientific beliefs.
I have no blind beliefs. I have learned how to never believe anything more than the quality and quantity of the available evidence supports. It's a habit of thought one develops thinking critically, one never forgotten when evaluating evidence and arguments, like looking both ways before crossing. I assume that you would never cross the street blindly. If so, you have developed a habit that you never accidentally forget to use, just like NEVER believing ANYTHING blindly.
I'll assume that you are referring to what I discussed above, or else, Newton's interest in alchemy. The following is from his Principia:
- "The six primary Planets are revolv’d about the Sun, in circles concentric with the Sun, and with motions directed towards the same parts, and almost in the same plane… But it is not to be conceived that mere mechanical causes could give birth to so many regular motions… This most beautiful System of the Sun, Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful Being."
If you read Newton, you'll find that he doesn't invoke his deity until he runs out of science and mathematics. As ND Tyson notes writing about this phenomena in the writings of Ptolemy, Newton, and Huygens,
- "[T]he authors invoke divinity only when they reach the boundaries of their understanding. They appeal to a higher power only when staring into the ocean of their own ignorance. They call on God only from the lonely and precarious edge of incomprehension. Where they feel certain about their explanations, however, God gets hardly a mention."
That's when the occult enters the picture, when empiricism changes to faith, and when the useful part of his work changes to the useless part, when the parts that any atheist of sufficient intelligence might have written to the part that only a theist could have written.