Almost any calculus text that deals with gravity can provide the proof, which I have long since forgotten. I remember that it involves a simple integration.
Chuckle, I was quite chuffed with myself! (Note to self: Must try harder, must try harder, must try harder, repeat to fade...)


what i'm wondering is what is the force that will a planet will effeact an object that has it center in the center of the planet
Sounds like zero to me, by Newton's Law of Gravitation:
F=Gmm'/r^2