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Let´s say I stand on a gigantic ring-shaped spaceship which is located somewhere in space where no other force affect it (like the ring thing in Halo). I am standing on the inside of the ring and the ring is not rotating. Would I than fall into the middle of the ring due to the fact that gravity would pull me towards its center of mass? Because the ring does not rotate there should not be a centripetal-force so the only force would be gravity. Is my reasoning there correct?

Physics
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First of all, gravity is an extremely weak force. No spaceship would attract you enough. But since you're imagining a fictional scenario, even then you would not fall towards the center. The force of gravity does not act from the center of mass only; it acts due to all the mass particles of the spaceship. Every particle on the spaceship is attracting you. There's nothing special here about the center of mass. Only in the case of a sphere you can consider that you're being attracted towards the center(see Shell Theorem). That is only because for a sphere you find that the force between you and the sphere is exactly equal to the force between you and its center. If you view from above the spaceship, its gravity would pull you into itself and make you land on its surface. But as long as you're on the surface of the ring, you'll remain there and nothing will happen. Interesting question, though. You made this up while watching a film?
@Mani_Jha --"" is correct First of all, gravity is an extremely weak force. No spaceship would attract you enough. But since you're imagining a fictional scenario, even then you would not fall towards the center. The force of gravity does not act from the center of mass only; it acts due to all the mass particles of the spaceship. Every particle on the spaceship is attracting you. There's nothing special here about the center of mass. Only in the case of a sphere you can consider that you're being attracted towards the center(see Shell Theorem). That is only because for a sphere you find that the force between you and the sphere is exactly equal to the force between you and its center. If you view from above the spaceship, its gravity would pull you into itself and make you land on its surface. But as long as you're on the surface of the ring, you'll remain there and nothing will happen.
F=GMm/r^2 G is the same wherever u go u were concentrating on Mand m no matter how big the orbit is, it cannot nully the reducing effect caused by 6.67*10^-11 AND DUE TO r^2 it might also be useful to note that a bigger ring just means a bigger radius (just like us and the earth)

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Even though gravity is weak it would still be the one and only force which would act on me and because it is in space (with no air) their would be no friction ether so eventually I should get pulled somewhere. I mean this kind of structure: http://www.co-optimus.com/images/upload/image/2009/halo-ring.jpg So if I would be exactly in the middle of that ring than I guess I would just float their but if I would stand somewhere on the inside than the rest of the ring - opposite to me - would attract me and thus pulling me towards the middle right?. Or do at any point at the ring the forces that attract me to the ground and the forces that would pull me away from the ground cancel?
As long as you're standing on the boundary of the ring, there's a normal force acting on you. What makes you think that you'll be attracted to the 'middle'? Remember that gravitational force acts due to every mass particle of the ring. And in the case of that halo, there is no mass at the centre to attract you.
when u stand on the ring u cannot exerted any force because of ur weight so first of all in order for u to stand on the ring and be in contact with it(u can do this only using ur muscular force) and hence to receive a normal force equal to the force that u exert to be able to attached to it this is tremendously difficult to do without accelerating the entire system(you+ring) now who cares abt the effect (very litte to the negativew power) the action by the ring's surface will push u so will ur reaction push the ring so it is near impossible for you to stand on the ring or atleast have contact with it without moving the ring and as for the graviational force,let us assume the ring to be made up of several minute particles so only effective graviational force wud be contributed by the portion of the ring where you are attached to(as grav.force is inversely proportional to r^2 distance ===r) and u have to now accept the beautiful fact that by action-reaction forces,when the ring attracts you ,u r attracting it by the same amount so consider all these points introduce ur imagined values for the ring's mass and man and consider all these forces
I see all your points. So I guess could "stand" on it but when I start walking I would push the the whole thing away from the me and we would fly apart. Originally I was thinking that that the whole ring would attract me and not just he part where I am closest. So I guess that would only have a serious effect if the mass is really high and if the circumference is very small.

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