Newton's Philosophiae Naturalis Principia Mathematica (published 1687) contains a mathematical (geometric actually) proof that the gravitational attraction between the Earth an a man standing on the surface of the Earth is the same as it would be if all of the mass of the Earth were at its center. There's another proof that if the man is standing at the bottom of a one-mile hole, and the Earth is assumed to be a perfect sphere, then the attraction is the same as if the Earth's radius were one mile less than it actually is (i.e., the attraction between the man and the shell of mass higher in altitude than the man is exactly zero because the attraction from the various points in the one-mile-thick shell exactly cancel out).
That is that kind of thing I mean: proofs and calculations, not "why wouldn't it?"
Hey thank you for your reply. I learned several interesting examples from your first paragraph in the comment.
I do think your last sentence here was unnecessary though:
”That is that kind of thing I mean: proofs and calculations, not "why wouldn't it?"”
When I said “why wouldn’t it” I was asking out of genuine curiosity. There really wasn’t any need to criticize that part. It came off as maybe more hostile than I think you intended.
Again I most certainly appreciate you taking the time to type up the rest of your comment though because I did learn quite a bit from those examples you posted so I am indeed sincerely grateful for that.
Both the constant G for gravitation and g for the acceleration for gravity on earth.
I am not a physicist so I may be getting something wrong