You are entitled to think I do not understand the shell theorem. Not only does it seem quite pointless for me to correct that misconception, you seem so invested in it I cannot see how I could do it in principle. Would a derivation serve? At any rate this is not my main point. I was referring to the following exchange:
You offered to "help" me with the math on something you had just discovered existed. Please, DO show me the math. It's a shame something that wasn't your main point has now become a focus, but, you brought it up, not me.
Firstly, notice that as best as i can tell what you wrote is in no way in contradiction to what I wrote. I claimed the acceleration of an object inside a hollow sphere was zero and you wrote: it's not, as you said, "no acceleration in a hollow sphere". I am still puzzled where you think the contradiction lie.
Because it's not "no acceleration on an object inside the sphere", it's "total acceleration is equal to zero". Very different things.
The shell theorem describes the vector field of force (the gravitational field) in any point inside or outside the hollow sphere due to the gravitational attraction of the hollow sphere. Can we agree upon this basic point?
YES. Now you are getting it.
Thus, the radius of this sphere matters insofar as it determines when an object is inside or outside the hollow sphere, however asides this trivial point the only thing that matters is the mass of the hollow sphere (see the wikipedia description or my description).
Please explain to me how the radius of a second body in gravitational computations that explicitly REQUIRE the radius of the objects in in question canbe trivial.
There is furthermore no "other" radius as you seem to suggest ("that's the radius you were missing, the second body") since the geometry of the other object does not matter insofar as the shell theorem is concerned, as long as it is either inside or outside the hollow sphere (if it is on the boundary the shell theorem still applies to the parts on either side of the boundary seperately).
Well, you were getting it. Read a paper on it rather than wikipedia.
So you are comparing yourself to a hungry lion?
No, I'm comparing you to someone that doesn't understand what's going on but should.
Actually I would say there was no gravity inside the shell (or at the center of the earth), not just that it "cancelled" out, however clearly the answer depends on what we mean by there "being gravity"
Again, there is not "no gravity". The total gravitational acceleration is zero.