I have a number of queries about the shell theorem, specifically the external case, which states that the gravitational pull of a spherically symmetric body always acts at the centre of the sphere.
Isn't the case for outside the shell easily proven using the fact that forces always 'act' on the centre of mass of a body (shown by applying Newton's second law). And using Newton's third law to state that an equal and opposite force is applied on the test object, (in the direction of the centre of mass)? Is this line of reasoning flawed; does it even apply (that gravity pulls towards the C.O.M of an object)?
A rigorous proof is given on wikipedia: http://en.wikipedia.org/wiki/Shell_theorem#Outside_a_shell
Also, I have reason to doubt my 'proof' because they claim that the shell theorem shows the converse of a more general form of Newton's laws which appears to have a terms proportional to $r$. However, my statement should apply to any force. I'm not sure why this is.