#Gravity/Earth's Core
8 messages in this thread
Can anyone offer some possibilities of how gravity would act on abjects if they
were inside a huge "doughnut" shaped "tunnel" that was located in the center of
the earth?
This "doughnut" would be located around the earth's core.
Any thoughtful responses would be appreciated.
This was also posted in the student section. (I think by mistake. 🙂 )
Joe Haynes
Hi, Joe–
Welcome to the forum/section!
If one ignores the effect of the absence of mass in the tunnel, the gravity
would be a mild attraction toward the Earth's center. If the torus is
concentric with the Earth and of inner radius "r", then the gravity for someone
standing on that inner radius would be that of a denser-than-iron asteroid of
radius "r".
If the torus removes mass approaching that "asteroid"'s mass, one can no longer
ignore its effects; figure the effect a toroidal asteroid would have on objects
boring inside it and subtract those vectors from the imaginary asteroid's field
vectors. I am not minded to integrate to find such a field pattern; your best
place for such details would have been in physics section.
–Doug
Thanks. I'll print your reply and try to "decipher it". 🙂
Hi, Joe–
The thing to remember is that Earth's gravitational effect drops as one
approaches the center.
Imagine a hollow spherical shell of uniform composition (well, the composition
can vary with radius, but not asymmetrically). Its outer boundary is a sphere,
and its inner boundary is a smaller sphere. If you are outside, it will pull
on you depending on its mass and distance. If you are inside, it has no net
gravitational effect on you; the pull from nearby matter on one side of you is
balanced by the pull of more matter farther away on the other side. You are
weightless as far as the shell has it.
Inside the earth, everything farther away from the earth's center than you are
constitutes such a shell, and might as well not be there as far as gravity is
concerned. Only the matter closer the center has a net effect on you (hence my
imaginary asteroid of radius "r", where "r" is your distance from the earth's
center). If you are at the center, there is no matter closer to it than you
are, so there is no net gravity. No reason to choose any direction as "up" or
"down" (left and right are still there, since they are defined by your body,
not gravity) except maybe you want to think of "up" as the direction from your
feet to your head, which will change as you move about. A little bit away
from the center, there is gravity, and an "up" independent of your body, but
not a very important gravity.
–Doug
A person standing in the center of the Earth would be absolutely weightless.
Gravity is proportional to the amount of mass an object has. Just as if someone
walks by you in the hallway you are attracted to each other by gravity(of
course too minute to tell). –> Basically, everything that has mass has
gravity. <–
You're pulled down on the Earth because the mass of every rock and piece of
dirt is under your feet. Since all of the mass of the entire Earth is under
your feet your being pulled down. So if the Earth was even more massive, you
would be even heavier.
Now to the point, if your in the center of the Earth, you have the mass of
(for simplicity), let's say 1/2 of the mass of the Earth earth pulling down,
but the other half of the mass is pulling you up. The same for the sides,
there's an equal amount of mass to your left as there is to your right.
Therefore in the center of the Earth you would be weightless. You are being
pulled with equal force on all sides.
I think your question was what if the "donut" went "around" the center of the
core? In that case, you would be pulled towards the core but you would be
EXTREMELY light. Sinse your not in the center but just outside it, you will
have more mass to one side so you would be pulled slightly towards the side
with more mass.
I hope that makes sense. If you don't understand, leave me a message. I love
talking about this subject, (as you can probably tell).
James
Thanks for the input. It would seem to be logical that the mass on each side of
the "tunnel" would "pull" in all directions. I suppose if someone were inside
this "tunnel" they would not be an "up" or a "down". You would be totally
confused, much like being in weightless space. I suppose you could sense
"sides" but not a top or a bottom?
Joe Haynes
> Thanks for the input. It would seem to be logical that the mass on each side
of > the "tunnel" would "pull" in all directions. I suppose if someone were
inside this > "tunnel" they would not be an "up" or a "down". You would be
totally confused, > much like being in weightless space. I suppose you could
sense "sides" but not > a top or a bottom?
>
>
Exactly. However I don't think you would be able to sense "sides" either. There
would be no up, down, left, right, or anything. Like you said, it would be like
floating in space…
James
Joe,
>>I suppose if someone were inside this "tunnel" they would not be an "up" or a
"down". You would be totally confused, much like being in weightless space. I
suppose you could sense "sides" but not a top or a bottom?
Remember that there is still the entire mass of the earth on the other side of
the center and it will act on you until you reach the exact center. The pull
will get weaker as you get closer to the center of the earth, but there will
still be an up and down until then.
Jim