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Gravity at the centre is zero, and varies with 1/r. See Newtons Shell Theorem
Was it not St Aquinas who answered as to what god was doing before he created heaven and Earth that he was creating a special hell for those who persisted in asking silly questions.
Was it not St Aquinas
so if the ball was placed at the centre it would float then? but if mass exerts gravity wouldn't the mass of the room walls exert a gravitational force and attract the ball to the wall as every bit of matter attracts every other bit of matter.?
or continue at a constant velocity until it reached the edge of the chamber and bounced off.
Geezer - nope; I think Rosy has it right. Presuming symmetry (which we shouldn't, but we will); within a spherical shell the net attraction at all points within the shell is zero. Even though objects exterior to the shell are attracted to the point of the centre of mass - those interior to the shell feel no gravitational attraction in any direction at any point. It is counter-intuitive, but the maths works in two distinct ways as discovered by Newton and by Gauss.
I would just like to point out that gravity increases with distance. So gravity is strongest at the poles (Earth has an oval shape), i.e you would actually weigh more if you were at the poles.
is gravity at the centre of the earth the same as it is on the surface?in other words if you was to drill a hole through to the centre of the earth and measure the Gravitational forces in steps along the way would it be the same as itis on the surface of the planet or proportional to the mass passed along the way or is gravity infinite?
As a sidenote, I suspect this is the result Geezer had in mind further up-thread, but the fact that I completely misread the original question seems to have thrown him off...