« on: 08/05/2010 11:40:12 »
Wouldn’t the gravity from the mass of the doughnut and the gravity from the spin both be acting in the same direction if you were standing on the ‘hole’ (inner) surface of the doughnut but cancel out if you were standing on the outer surface. This is the opposite to the effect that would exist if the doughnut was not spinning – ie the gravity near the hole would be less due to the pull of the mass of the doughnut from the other side of the hole. As Geezer said “you would be a bit lighter on your feet when you were on the inside”. If you could make Planet Doughnut spin at just the right speed then presumably you could get equal gravity at all points on the surface.
Just a thought ... If the centrifugal force of a spinning planet affects the net pull of gravity, does that mean that if the planet Earth stopped spinning we would all get heavier?
I don't think it would. I agree with Nick - sorry I agree with Geezer. I think the centre of mass would be at the centre of the hole of the torus and any calculation can proceed as if there is a single force acting on your centre of mass and that of the torus/planet.
Standing on the inside surface of a non-spinning torus would, I believe, be impossible. Although the ground would be beneath your feet - the aggregate force would be towards the centre of mass; ie straight up in the air. I guess at this point I disagree with Geezer too.
I am unsure that I could work out the balance when spinning or even if it is possible - the force from gravity varies inversely with the square of the radius; however the force from rotation vary linearly with radius. Two points of equality (ie inside and out) would be doable - but I think anything more is not possible.
Great question by the way