If there was a room at the very centre of the earth, could you walk on the roof and walls?

Question

... or would you float in the centre?

Answer 1

gravity will be zero at the center of earth as it depends only on the matter inside the virtual sphere....hence we could not walk over walls...well just float as if we wer in space

Answer 2

Actually, I have reasoned out that you COULD walk on the walls, ceiling, etc.

Here is why:

Every mass has/generates gravity.  If you were in a room at the exact center of the Earth, is a special case.  The Earth on all sides of you would be generating gravity.

I would like to ignore the fact that the Earth bulges more in the center (equator), but in all fairness, I can't, so it leaves me with two different cases, but the results appear to be the same.

First, I will presume that the room is large enough (enough headroom) to actually walk, if possible.  Let us assume a room such as found in most houses or close to eight foot ceilings (commonly used, causing designers to design around that spec, but in practice the height is a little less.)

Ok, so if standing (push yourself away from the center of the room towards a wall...) more of your own mass is then on that side of the center point of the room.

Consequently, that part of the Earth's mass is closer to you.

Since gravity follows the inverse square law (meaning gravity decreases according to the distance between the two object's masses), the gravity of that part of the Earth will draw on you more than the part above your head, simply because you are closer to it.  This is why I said you could walk.  There will be (VERY SLIGHTLY) more gravity in the direction towards your feet, than upwards or outwards.  If you were to get down and crawl, movement should be even easier, as the mass above your head would be even further away.

Now the other case that complicates the answer, it the shape of the Earth.  It is not a perfect sphere.  The polar flattening exceeds the equatorial radius by more than the small difference within the room, when you kick off towards a wall.

However, if you try walking on the roof/ceiling, the equatorial pull will be more even  around you.  You will be closer to the North Pole than to the South, and since they are both flattened by the same amount, the pull would still be equal if you were in the dead-center of the room.  Since we defined the size of the room as a common human habitat-sized room, you will still get more pull from the mass under your feet, (even if it is the ceiling) than from the other directions.  The same will hold true for the floor being closer to the south polar mass of hte Earth.

Consequently, it would actually turn out that you could walk (very carefully) on any of the "walls",  the "floor", or the "ceiling".

Even if we start with a room just barely tall enough for you to stand up in, you could crouch down and walk, due to the same principles. (True, it would not be normal walking, but it would be theoretically possible, and I believe that is the intent of the question.)

I believe in theory, I am right.  What say the rest of you?

Answer 3

Float, like in a large spaceship ball with thick walls!

Answer 4

Hmm I guess its a valid question.  The idea of walking is a consequcne of friction and friction is a consequence of a force perpendicular to a surface.   As long as there some kind of weight present on the surface from your feet then you will be able to walk.  

Therefore,may be able to walk on all surfaces on the outside of your little box (room) (Your weight would be very very small, so you might actually bounce yourself away from the exterior of the room) , but inside of the room your weight would NOT be directed to the walls but it would be directed to the center of the room.  You will not be able to walk on your walls and ceilings, you would be pulled away from the walls and float in the center of the room.