On another forum has appeared the ol' "drop a ball down a tunnel that passes through the Earth's centre" discussion. Someone has naively calculated the speed of the object at a ridiculous number - a fraction of the speed of light! I'm pretty sure their error is that they are not taking into account the drop off in g as your distance from Earth's centre decreases. (i.e. they don't realize it, but they're actually calculating the speed of a ball falling towards an Earth-mass black hole with zero radius). So, what is the velocity of the ball as it passes through the centre of the Earth (ignoring all the usual factors: vacuum, Earth's rotation, etc.)? Thx.