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Thread: Gravity in a hollow sphere?

  1. #1 Gravity in a hollow sphere? 
    Forum Cosmic Wizard icewendigo's Avatar
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    If you had an earth sized hollow spherical structure, that wasnt rotating), how would gravity effect a person?

    On the outside my guess is there would be much much less gravity but what little there was would attract you towards the center and you could walk and bounce on the outter surface.

    But what about someone walking on the inside surface, would they be attracked to the surface itslef because the mass of the surface is much closer to the person, or would the person be attracted to the center and would drift towards the center of the gigantic sphere without the possibility of walking (staying) on the inner surface?


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  3. #2 Re: Gravity in a hollow sphere? 
    Quagma SpeedFreek's Avatar
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    Quote Originally Posted by icewendigo
    If you had an earth sized hollow spherical structure, that wasnt rotating), how would gravity effect a person?

    On the outside my guess is there would be much much less gravity but what little there was would attract you towards the center and you could walk and bounce on the outter surface.

    But what about someone walking on the inside surface, would they be attracked to the surface itslef because the mass of the surface is much closer to the person, or would the person be attracted to the center and would drift towards the center of the gigantic sphere without the possibility of walking (staying) on the inner surface?
    Strangely enough, there is no gravity on the inside of a hollow sphere!

    http://hyperphysics.phy-astr.gsu.edu...sphshell2.html


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  4. #3  
    Forum Cosmic Wizard icewendigo's Avatar
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    Strangely enough, there is no gravity on the inside of a hollow sphere!
    That is suprizing to me.

    What about the structure itself? Are the various part of the building materials that compose the sphere experiencing the gravity of the entire structure or does the distribution of matter create an environment that is pretty close to a micro gravity space station from the perpective of each section composing the sphere?
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    To a particle on the exterior, the hollow sphere's whole mass acts as if it were concentrated at the center. So, standing on the surface, you wouldn't know the difference between the hollow sphere and a solid sphere of equal mass. As you penetrate the skin though, each layer that is outside the point under consideration does not contribute to gravity, so the weight goes from mg on the surface to zero inside the shell.
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    For a layman such as myself this is a rather odd and counter-intuitive notion. It would make a great starting point for a science fiction story about a non-rotating space colony where all the inhabitants live in a glass enclosed biosphere on the outside of a thick nickle-iron sphere. The author could then create a story about the poor creatures fated to take care of all the plumbing and electrical gear on the underside of the sphere. He could even call them Morlocks, and he could call the happy people living the good life in the biospere above the surface something like Eloi. Hmmm... this sounds familiar.

    Fortunately, science fiction doesn't have to pay too much attention to the practical problems associated with this unusual approach.

    One thing I'm curious about is: If a particle is not dead center in the sphere, would it have a tendancy to drift to the nearest "wall"? Or would the forces acting on the particle cancel out no matter where inside the sphere the particle is located?

    Chris
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  7. #6  
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    Quote Originally Posted by CSMYTH3025

    One thing I'm curious about is: If a particle is not dead center in the sphere, would it have a tendancy to drift to the nearest "wall"? Or would the forces acting on the particle cancel out no matter where inside the sphere the particle is located?

    Chris
    The forces cancel out no matter where inside the shell the particle is located.

    As you head towards one side you get further from the other, of course, but consider that you are getting further and further away from a larger area of the shell as you get closer and closer to a smaller area! The gravity of the mass in the larger area of the shell exactly balances the gravity of the mass in the smaller area.
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  8. #7  
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    (Double post)
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  9. #8  
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    "As you head towards one side you get further from the other, of course, but consider that you are getting further and further away from a larger area of the shell as you get closer and closer to a smaller area! The gravity of the mass in the larger area of the shell exactly balances the gravity of the mass in the smaller area."
    Thanks that made it easier to understand.

    What would happen if about a third of the inner volume was filled with salty sea water(injected in the center), and about two thirds was filled with air? Lets say the outter shell was some sort of greenhouse glass that's somehow able to let more sun heat penetrate than can escsape (to a void a freezing water scenario).

    Would water scater all over the place or would it form various spherical lakes floating around or a large mass in the center(unless theres a tidal effect from a planet)? Could you swim in that water and jump out and float in the air on your way to the outer shell?

    If you swim under water would you know where s up and down (center of bubble lake vs edge) and would you float by default in a direction or would it just depend on where you push the water to in your swim motion?


    (Ducks brought for a day in that environment would probably wonder what the hells going on, flying in the air in any direction and landing on floating water pools)
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    What would happen if about a third of the inner volume was filled with salty sea water(injected in the center), and about two thirds was filled with air?
    That is a hell of a lot of water, it would have a huge gravity and so form a big sphere (when it wasn't bouncing off the sides), but the water pressure in the centre would become so great that it probably would produce heat or maybe solidify (?). I wonder whether it would actually be continually boiling.
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    It wouldn't boil, since boilding isn't due to just temperature, but it might get hot.

    Anyway, water will form spheres in zero-G, even in small amounts, due to surface tension. Larger amounts will still produce spheres, but they'll wobble quite a bit if disturbed. Still larger amounts will make the wobbles small compared to the size of the water, so it'll look more like a smooth sphere (Earth is like this).

    The glass around the water, no matter how massive it is, won't keep the water centered, so the giant sphere will move around until it touches the glass, at which point, surface tension will pull it onto the glass, and then you'll have all the water on one side and all the air on the other (I don't know the exact geometry though). People on the outside of the glass would be able to feel the gravity moving around.
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    I don't think the water would stick to one side as its own gravity (which would be not much less than earth's) would keep it spherical, so it might bounce off in an elastic collision.
    If the ball of water had bounced off a few sides it might have some spin (so be a spheroid) or it might continue to have wave effects across its surface.
    Also, the air in the shell would condense towards the water planet, giving it an atmosphere, the humidity might be high due to compressive heat, so clouds would cover the blob of water, making it appear white.
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    Surface tension is pretty powerful with water, so I doubt the collision would be fully elastic. Also, there'd be no force to overcome surface tension and move it away from the point of contact, assuming the collision was slow enough not to cause massive waves. I don't know what a stable geometry would be though.
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    the surface tension would tend to pull the water into a large hollow sphere covering the whole inner surface. gravity from the water's previous shape may act against this but in this shape there would be essentially no gravity as there was when there was no water.
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    Quote Originally Posted by icewendigo
    What would happen if about a third of the inner volume was filled with salty sea water(injected in the center), and about two thirds was filled with air? Lets say the outter shell was some sort of greenhouse glass that's somehow able to let more sun heat penetrate than can escsape (to a void a freezing water scenario).

    Would water scater all over the place or would it form various spherical lakes floating around or a large mass in the center(unless theres a tidal effect from a planet)? Could you swim in that water and jump out and float in the air on your way to the outer shell?

    If you swim under water would you know where s up and down (center of bubble lake vs edge) and would you float by default in a direction or would it just depend on where you push the water to in your swim motion?


    (Ducks brought for a day in that environment would probably wonder what the hells going on, flying in the air in any direction and landing on floating water pools)
    A mass of water would form a sphere, but not necessarily in the center of the hollow sphere, since it is not affected by the gravity of the hollow sphere. So it would probably drift around until it collided.
    Someone or something thing in the air space between would be attracted to the water sphere, just as if the hollow sphere didn't exist. They couldn't jump out and float in the air. They would fall back into the water. They would tend to float on the water surface, since the water pressure would be greater toward the center.

    Also, if there is a mass of water inside the hollow sphere, which is not centered, then someone on the surface would feel more or less heavy depending on how close they were to the water ball.
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  16. #15  
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    " then someone on the surface would feel more or less heavy depending on how close they were to the water ball"
    Would the outer glass sphere itself be attracted to a large inner ball of water (ex: completely full 1/3 volume vs thin hollow sphere) or would it be immune by the same reverse effect that causes someone inside not to be attracted to the sphere itsef(small near area vs large far area)?


    "couldn't jump out and float in the air."
    Indeed if the sphere is large and the water within massive I can imagine falling back in the water, but a smaller structure like a huge space station might potentially not have enough water mass to offset a fast swimmer jumping out like a dolphin a flying fish or something.

    "the surface tension would tend to pull the water into a large hollow sphere covering the whole inner surface. gravity from the water's previous shape may act against this but in this shape there would be essentially no gravity as there was when there was no water."
    So if that was the outcome, you would get a 360 degree swimming pool inside along the surface and air in the center, and if that were the case then you could swim as fast as you could and jump out of the periferic pool water layer and float across the sphere in zero-G through the air until you landed/dived back in water at the other end? Yeeehaaw
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    the surface tension would tend to pull the water into a large hollow sphere covering the whole inner surface. gravity from the water's previous shape may act against this but in this shape there would be essentially no gravity as there was when there was no water.
    That would be an unstable equilibrium, the only stable one would be a big ball of water the size of mars.
    Also, 2/3 earth's volume of air is a lot of air... it would gravitate to the water mars, the air pressure would get so high as to form liquid air probably which would dissolve with the water, but above this the air pressure would make it unlivable, so you couldn't swim in the water, or breath.
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  18. #17  
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    The volume of air doesn't have any direct effect on its pressure. The gravity of the water ball should be less than that of the gravity of a ball of rock (I think), so the differential in the air pressure between the glass and the water shoudln't be all that great.

    I'm not sure that the water surrounding the air would be unstable, but I don't really know for sure.
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    It is a lot of air, about 700,000,000 billion tonnes worth. Like venus it would likely have a runaway greenhouse effect and have huge pressure from that weight.
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    The glass would cause a massive greenhouse effect, as would the water vapor. The air would disperse fairly evenly though. (Weight is meaningless without gravity.)

    The gravity of the water sphere (assuming it remained a separate sphere) wouldn't be so huge (less than that of Mars) as to create a huge pressure in the air at the surface of the sphere.
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    Surface gravity would be 1.2m/s/s, so similar to the moon.
    Earth has about 5 million billion tonnes of air, so here we would have about 140 times more air in 12% the gravity, which should cause about 16 times more pressure, or 16 atmospheres.
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  22. #21  
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    Where are you getting the amount of air from? 140 times more volume doesn't necessarily mean 140 times more mass or pressure. A basic calculation would use the ideal gas law, which for 140 times mass and 140 times volume would cancel out and give the same pressure.
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    The amount of air is 2/3 the earth's volume, presumably at one atmosphere.

    140 times the mass of air as earth has, with only 12% the weight would be 16 times the pressure right?
    The air pressure comes from the weight of air above. There will be a lot more mass of air above, but less force from gravity... still gives more pressure.

    16 atmospheres is physically survivable, but you'd need a scuba tank to be able to breath. I have a feeling it would be pretty hot at sea level though.

    What a strange thought to ponder... it would be like a hazey water moon I guess.
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  24. #23  
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    Quote Originally Posted by TGlad
    The amount of air is 2/3 the earth's volume, presumably at one atmosphere.

    140 times the mass of air as earth has, with only 12% the weight would be 16 times the pressure right?
    The air pressure comes from the weight of air above. There will be a lot more mass of air above, but less force from gravity... still gives more pressure.

    16 atmospheres is physically survivable, but you'd need a scuba tank to be able to breath. I have a feeling it would be pretty hot at sea level though.

    What a strange thought to ponder... it would be like a hazey water moon I guess.
    Emphasis mine. If you put 1 atm's worth of gas in (pressure wise), then its at one atmosphere, at least on average. Gravity will distort that, but it won't raise it all the way to 16. The thing is, it's a lot more gas, but it's spread over a lot more volume.
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    Gravity will pull most of the air towards the planet of water... I'm talking about 16 atmospheres at sea level, i.e. if you were swimming on the blob.
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    That's what I'm saying. Gravity won't pull most of it in. Only some of it. There's a reason the moon is nearly airless. The calculation of the actual pressure at the surface is not as simple as multiplying the amount and gravity.
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    Obviously gravity will actually pull ALL of the air towards the planet by definition... but I think you're right... or maybe not, not sure, oh well
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  28. #27  
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    Err, no. Gravity will pull on all the air, but air expands and spreads out. Even with Earth gravity, it spreads upward for at least 75 miles. With the glass, there'd be an upper limit to it. With moon gravity, the difference in pressure between the surface of the glass and the surface of the water won't be that great.

    On Earth, the pressure at a particular altitude is equal to the weight of the air column above it. Without the glass, and ignoring the gas escaping due to too low of gravity and a couple of other details, the increase in pressure from that much more air would be related to the change in height of the column multiplied the change in gravity. (Which works out to about 2.5 times the pressure.)

    With the glass, there's pressure beyond just the weight of the column though, but that wouldn't increase the pressure all the way to 16 atmospheres.
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