Ok, so I read on SD once that if you jumped into a hole that went to the centre of the earth, you would oscillate until finally coming to rest.
Fair do’s, but this made me think of another question entirely:
If a supreme being managed to dig out a space in the centre of the earth for us to fit in, and we did so so that the exact centre was located somewhere in the middle of our body, would we collapse in on ourselves?
I have had two answers so far:
a) Yes, indeed we would, since gravity increases proportionally to the distance away from the centre of the earth, and thus, the gravity at the centre is powerfull enough to rip us apart.
b)No - all the forces would balance themselves out and nothing would happen.
My beliefs firmly sit in answer A), but if we were to collapse, where would our mass go? would it condense into something super-dense?
No, definitely not; gravity does not originate from the centre of the earth, it is just that the net effect of it averages out as if it does.
If you are placed in the hollow middle of a uniform spherical body massive enough to exert noticeable gravitational attraction, you will not feel any gravity at all, as the forces in each direction all cancel out.
Nope, the answer is b). Inside a hollow sphere, all cravitation cancels out, since at every point inside, there is exactly equal mass in all directions, and distance cancels out of the equation, hence zero gravitation.
If you are placed anywhere (it doesn’t just have to be at the centre) inside a massive (i.e. possesed of mass) hollow uniform spherical body you will find that the net gravitational force exerted by that body is zero.
Incidentally, this works for other forces too, not just gravitation. In the design of the Van de Graffe generator, it was discovered that the inside of the dome on top that was meant to collect charge, there is zero voltage, and this fact is used to more effectively “feed” the charge on to the dome, by running the conductor up through the inside of the dome, rather than attaching it to the outside.
I like to point out that if you have a hollow sphere filled with air the air itself has mass so there will still be a tiny gravitational pull toward the centre…
this probably explains why you dont have hollow planets in nature.
[/pointless nitpick]
Here is TSD. Imagine you find yourself somewhere inside a massive spherical body that has uniform density in every spherical shell. This means that all the stuff at any given distance from the center has the same density, although the density may vary with distance from the center. This includes a hollow sphere where the density is 0 inside the hollow part and also, to a reasonable approximation, the earth where the main variation is with depth (and the earth is not a sphere, but never mind). Then you feel all the gravitational force from the stuff deeper than you as though it were all concentrated at the center of the sphere, while all the gravitational force from the stuff less deep than you cancels exactly and you feel none at all. If the sphere should have uniform density throughout (which is not true of the earth), then you would find that the gravitational force on your (in other words your weight) would decrease linearly as you go deeper, becoming 0 at the center. The last would still be true of the earth but the decrease would not be linear. All this is easily proved using calculus.
So if, as the OP said, you were placed in a hollowed-out space at the center of the earth (assuming you could determine the center when the earth is not a true sphere), gravity from the earth would be equal in all directions.
But I’d think you could still tell what side the moon was on, because of the gravity pull from it. It’s enough to cause tides, so I’d think you would be able to notice it easily when everything else is cancelled out. But I’m pretty sure that the other planets & the sun are too far away for their gravity to affect you noticably.
Maybe someone with more Physics background could calculate this?
First off, you should know that the sun exerts a much stronger gravitational force on the Earth and its inhabitants than the moon does. Yes, it is further away but it is also MUCH more massive. And what does the Earth orbit around? The sun.
It’s a mistake to think you would feel the effects of the moon or sun because of tidal forces. Tides are caused by the difference in the moon’s/sun’s pull on nearer and further parts of the earth. You are not big enough to have a noticable tidal effect on your body. In other words, the moon’s pull on your head is not very different at all from the moon’s pull on your feet. The sun’s tidal effect on a person would be even smaller (because the sun is even further away, so the DIFFERENCE in its pulls would be less).
The sun and moon would each still exert a gravitational force on you. And again, the sun’s gravitational force on you is larger than the moon’s. You wouldn’t notice the sun’s pull, just like we don’t notice it now, because you and the Earth are in a freefall orbit around the sun (like astronauts in orbit around the Earth don’t “feel” the gravitational pull of Earth). I’m not sure if you would notice the moon’s pull, though it might have the same explanation since the Earth and moon actually both orbit about the center-of-mass of the Earth-moon system (located somewhere inside the Earth). In that case you wouldn’t feel the moon’s pull either.
True, and I should have mentioned this, since it makes my calculations irrelevant. We only feel gravity in the sense that we feel a normal force pushing back at us. A skydiver doesn’t “feel” gravity (though they do feel air resistance). They will, however, feel a significant and abrupt normal force if their parachute doesn’t open…
The connection to our scenario being, of course, that if you are hovering at the center of the Earth, there is no terra firma pushing back at you and thus you feel no force.
No, the mass on top is pressed down by gravity, which presses on the mass below–so even though the mass below is not as affected by gravity, there is still tremendous pressure from above.
No, that’s wrong. There need not be any great (or even significant) pressure exerted by the shell surrounding the gas inside. Assuming the crust could withstand the internal forces without shattering, the diameter of the shell need not change enough to exert a great amount of pressure. The volume inside will remain relatively stable. And yes, the gas would be gravitationally attracted to its own center, so there would, in fact, be a pressure gradient as a result of that.
I was thinking that the exercise was eburacum45’s “this probably explains why you dont have hollow planets in nature.”
The way I read it, eburacum45 had it that a hollow in the center of the Earth would have no pressure to collapse, except the tiny amount of gravity produced by the air in the chamber–and that would have prevented the formation of hollow planets.
