Physics / gravity question

[jwaterdawg]

There would be absolutely zero gravity anywhere inside the hollow sphere regardless of the thickness of the shell or your location inside the hollow. This assumes a spherical shell of material with a spherical hollow (think of a basketball).

If you are closer to one side it is true that the gravitational pull from mass on that side will be larger. However, there will be more total mass pulling you back from the other side. The net result is that there is zero net force anywhere inside the hollow.* **


* As an interesting side note, apparently Hitler and many of the higher up Nazis believed the earth was hollow and that they could escape capture by tunneling to the center of the earth. They believed they could live on the inner surface of the earth. Crazy stuff, I'm not making this up.

** This assumes a classical description of gravitational force (Newton's Universal Law of Gravity). Gravity is an inverse square force, meaning the force goes as 1/(r*r) where r is the distance between the objects. Since the surface element of a sphere goes as r*r, there is a balancing between the surface element and the inverse square force that results in zero gravitational force inside the hollow.

[Anna]

assuming the mass is liquid, then gravity would pull you until you were at the center of mass. Once there, gravity would be equal on all sides so you would stop moving through the liquid. Or at the very least move in small amounts as gravity tries to maintain balance on a non-spherical object.

But the effects on a human could be something else. AS the moon rotates around the earth, it has an effect on the human body. When it is "directly" overhead it pulls on our bodies and we are "taller", while when it is on the opposit side of the planet the gravity is cumulative and we are at our "shortest". While we are talking about miniscule amounts between the two the effects are none the less real. Even though we don't really feel this effect.

So in our sphere, with mass being equal on all sides, we would be being pulled in all directions which could stretch our bodies since we are not a solid form. Just like the moon does. This could be termed "bloated"

In the case of the earth and the moon and a man on the surface of the earth, there is a net force of sorts that allows the man's height to change depending on the location of the moon relative to the earth. The fact that it's a very weak net force accounts for the fact that we don't go hurtling off the face of the earth when the moon is overhead.

For an object inside a hollow sphere - like a small spherical room in the center of the earth - there is no net force, i.e. there is no "bloating." Say there's a clump of sand and put it in that room, the sand particles won't all go floating towards the nearest wall (as in getting bloated) because, again, there is no net force on each particle. In fact, absent any outside action, they'll stay perfectly still (Newton's 1st Law).

[Alex Franke]

The fact that it's a very weak net force accounts for the fact that we don't go hurtling off the face of the earth when the moon is overhead.

Then why on Earth do I have to hang on to a tree every time I see the moon? Oh, wait a minute -- we're talking physics here, not psychiatry...

Say there's a clump of sand and put it in that room, the sand particles won't all go floating towards the nearest wall (as in getting bloated) because, again, there is no net force on each particle.

Great example!

Here what I don't get, then: Take the example to one extreme and you end up with a spherical hollow shell the thickness of, say, a sheet of paper, with the clump of sand on the inside. None of the particles of the sand feel any net acceleration in any direction. Add another clump of sand and it should act the same way. Then keep adding clumps until the void is filled. At what point do the rules change and iron starts sinking to the middle and less dense matter starts floating to the top?

If it's when you start adding more particles, then it stands to reason that you'd feel the opposite of bloated if you're stuck in that little room at the center...

(...This stuff really confuses me -- I sure wish it weren't do darned interesting!)

[scorrpio]

Just a note on the 'bloat'. To feel bloated, different parts of your body would have to be pulled by different sections of the sphere. I.e. if you are oriented north-south, northern hemisphere would have to exert 1/2g on your head and no force on your legs, while southern would pull the legs and have no effect on head. This is not the case. North hemisphere will pull the whole of you, and south will pull the whole of you, cancelling each other out.

To go a bit further, to really represent forces acting upon you, you'd need to integrate. Imagine said sphere as constructed from many long pyramids, points inward. you find center of mass of each such pyramid, which will be fairly close to its 'bottom' (and therefore, close to the surface of said sphere) and calculate gravitational vector using your mass, mass of the pyramid, and your distance from its mass center - then you add those vectors up. Since mass centers will be about 3000 miles away from you, the dimensions of your body in calculating the difference in acting force will be totally negligible. Now, if you had two black holes placed on both sides of you, putting centers of enormous mass within a foot of you, then you'd feel the stretch.

Going back to said sphere - suppose the hollow is 1000 miles diameter. Again, considering this sphere as an assembly of many blunted pyramids, and integrating the gravity vectors, I'd say folloing will happen: it will be possible to be at equilibrium at the very center, but it'll be like balancing a razor on its edge. Gravity pull is inverse proportional to distance squared, meaning with mass distribution constant, a shift from center will send you falling towards the inner surface.

[jseklund]

This is interesting stuff. I'm sticking to my guns- given the mass of the sphere is not great enough to collapse itself, and the distance of the sphere is far enough to not collapse itself- you would be stuck in the center.

However, this is somewhat Newtonian- and to be quite honest I'm really only thinking in 2 dimensions to a large degree. How do we account for 3 dimensions and a curved universe? Also- what about the fact that we are thinking of a static sphere with no acceleration factored in?

Ok, too early in the morning. My brain is fried- done for the day j/k

[Alex Franke]

Just a note on the 'bloat'. To feel bloated, different parts of your body would have to be pulled by different sections of the sphere. I.e. if you are oriented north-south, northern hemisphere would have to exert 1/2g on your head and no force on your legs, while southern would pull the legs and have no effect on head. This is not the case. North hemisphere will pull the whole of you, and south will pull the whole of you, cancelling each other out.

This is exactly what I was missing. Well put.

And I guess as you put more and more matter into the middle of the sphere, then the gravity of that matter needs to be considered as well, which is why at the end of the day (so to speak) Earth has a hot, dense core.

My friend will be please to know that he was correct! Thanks for all the input -- this is the best woodworking forum ever!

[Anna]

This is exactly what I was missing. Well put.

And I guess as you put more and more matter into the middle of the sphere, then the gravity of that matter needs to be considered as well, which is why at the end of the day (so to speak) Earth has a hot, dense core.

My friend will be please to know that he was correct! Thanks for all the input -- this is the best woodworking forum ever!

Any two objects will have a gravitational attraction to each other - same value, opposite directions.

F = G.m1.m2/r^2 where G is the universal gravitational constant.

Inside a hollow sphere, the sphere itself does not exert any gravitational force.

But if you have two objects (say the same mass, m) inside the sphere, then the two objects will have a net grav force towards each other. The result of that particular net force is for the two objects to move towards each other (accelerate) until they're right up next to each other.

Add another object with mass m, and it's also attracted to the two objects now hanging around the inside of the sphere (the position of the two objects will be determined by their original positions). They'll all have this grav attraction again and clump together. And so on. It doesn't change the fact that the sphere itself still has no net force exerted on the objects.

For objects outside the sphere, however, the additional masses in the hollow sphere will have an effect on the gravitational pull, like you said.

I don't know, though, how that would lead to a conclusion that the Earth has to necessarily have a hot, dense core. It could just as well have been solid. The liquid core, however, creates all sorts of strange electromagnetic effects on the surface, and probably is responsible for the Earth's magnetic poles.

[Russianwolf]

Just a note on the 'bloat'. To feel bloated, different parts of your body would have to be pulled by different sections of the sphere. I.e. if you are oriented north-south, northern hemisphere would have to exert 1/2g on your head and no force on your legs, while southern would pull the legs and have no effect on head. This is not the case. North hemisphere will pull the whole of you, and south will pull the whole of you, cancelling each other out.

Ah, but since the head is 6 feet closer to the northern hemisphere is would exert .50000001 G on the head while .499999999 G on the feet and the vice versa for the Southern hemisphere.

See my point is that if we were talking about a solid spherical object at the center it would be as you guys are saying, but since the human body is neither solid, nor spherical it would be stretched due to the differences in the gravitational forces working on it. Even though these may be miniscule, they would none the less exist.

[Anna]

Just a note on the 'bloat'. To feel bloated, different parts of your body would have to be pulled by different sections of the sphere. I.e. if you are oriented north-south, northern hemisphere would have to exert 1/2g on your head and no force on your legs, while southern would pull the legs and have no effect on head. This is not the case. North hemisphere will pull the whole of you, and south will pull the whole of you, cancelling each other out.

The magnetic poles might not be a good example, especially considering the effects on a compass, e.g. there is a net magnetic pull. But I don't know. It is too early to think about these things.

I think I'll shut up now.

[Anna]

Ah, but since the head is 6 feet closer to the northern hemisphere is would exert .50000001 G on the head while .499999999 G on the feet and the vice versa for the Southern hemisphere.

See my point is that if we were talking about a solid spherical object at the center it would be as you guys are saying, but since the human body is neither solid, nor spherical it would be stretched due to the differences in the gravitational forces working on it. Even though these may be miniscule, they would none the less exist.

That's really not quite right. You can look at any object as a collection of many very very small points or particles. To find the net force exerted on that object, you add up the forces exerted on the many small points comprising it.

If you pick a random point on the body, and it doesn't have to be a spherical body, there is NO net force on that point. In fact, there is no net force on any other point of that body, at least not due to the sphere. Add them all up, and you still get zero. Not miniscule. It's zero.

As I mentioned in another post, the magnetic field is probably not the best analogy. A gravitational analogy to the north pole/south pole example is just an object on the ground as opposed to the same object on top of a mountain. The gravitational forces are going to be different because the distances are different.

But inside a hollow sphere, the gravitational force is still zero.

[Kristofor]

Ah, but since the head is 6 feet closer to the northern hemisphere is would exert .50000001 G on the head while .499999999 G on the feet and the vice versa for the Southern hemisphere.

See my point is that if we were talking about a solid spherical object at the center it would be as you guys are saying, but since the human body is neither solid, nor spherical it would be stretched due to the differences in the gravitational forces working on it. Even though these may be miniscule, they would none the less exist.

While your head is slightly closer to the north pole (your reason for going to .500000001G) this means that there is more shell mass south of your head and while it's slightly farther away these automagically cancel out.

The only gravitational force your head would be feeling would come from your body. With such small masses to work with you wouldn't feel much of a squish.

[scorrpio]

The magnetic poles might not be a good example, especially considering the effects on a compass, e.g. there is a net magnetic pull. But I don't know. It is too early to think about these things.

I think I'll shut up now.

I said nothing about magnetic. North-South is purely orientation reference here. Replace with up/down, left/right or this way/that way if you wish.

Note - it appears I am wrong on the 'fall to the side' count. It does appear that a hollow sphere does not produce any sort of gravity on objects inside it since regardless of position, the sum of all gravity vectors to all points of the sphere is 0. This means however, that you are not stuck in the center either. If you have any means of autonomous propulsion, you can move to any point inside a sphere. I.e. if you take off a shoe and hurl it in one direction, you'll go floating off the opposite way until you eventually reach a wall.

[Anna]

I said nothing about magnetic. North-South is purely orientation reference here. Replace with up/down, left/right or this way/that way if you wish.

Sorry. My bad. Reading comprehension problem.

[lrogers]

Any one who flies model helicopters tries to ignor gravity and it's effects! When we fight gravity, it usually wins.

[Kristofor]

Any one who flies model helicopters tries to ignor gravity and it's effects! When we fight gravity, it usually wins.

Without gravity the atmosphere would be awfully thin for giving your copters much bite. Plus you'd need to be able to reverse the rotation or blade angle if you ever wanted to come back down...

When your machines break on impact with the ground it's not gravity that's doing you in but inertia, and you'd have just as much of that in zero gravity. If you tried a full power landing you'd still crater