Density and buoyancy prove that gravity exists. 
How so? The theory of gravity has never been proven, you'll be the first!
*truth is relative*
*notbatman is a big fat meanie*
... this is the point where I can't respond any more. ...
You've justified the heliocentric model in your mind based on images of puppets hanging from wires the government showed you when you were six. You can't even consider a flat Earth model with a close small Sun for the purposes of evaluating Eratosthenes experiment. This is the point where I tell you to go rope yourself.