Aspies For Freedom

We covered this in Physics a few weeks ago.

I've just had a quick look through my room, but I can't find my notes or textbook, so here's the Wikipedia article on it, it makes for a pretty interesting read.

The Earth is actually (approximately) an oblate spheroid (i.e., squashed at the poles - which are actually the closest points to the centre of the Earth, even closer than the deepest ocean or the deepest holes we've dug).

Roughly speaking, the magazine is correct. Gravity will be ~0 at the centre of the Earth.

Regards,

James

Be sure to get the money up front.

I would say that gravity would be close to zero, cause the gravity from one side would counterbalance that from the other side, but i have a hard time figuring that the mass of the earth is distributed exactly evenly.

Allthough the gravity would be zero you would still be crushed by the pressure generated by the above zero gravity places around you.
It would probably feel like being at the bottom of the ocean times millions.

Reviving an old topic. I remember seeing some pictures in New Scientist of a cross section of the earth, showing the gravitational and magnetic fields, and it's actually full of eddies and inconsistencies, probably due to the motion of the magma and rock below, the gravitational mass of a mountain is actually pretty weedy compared to a glob of denser magma thousands of miles in diameter

Some of the magnetic inconsistencies are pretty severe too (and getting worse) which lends them to think we might be approaching a polar reversal.

On the original topic, there must be a point somewhere in the aproximate center point of the Earth, where the mass of the surrounding material in full 360 degrees balances out the equation so the effective gravity becomes zero (Sort of an anti-gravity effect). That point would probably move about over time too.

Going down physically into the earth would be quite good - your physical weight would drop, and your be squashed thinner and thinner; Could be the latest diet fad "Take a trip to the center of the earth, and feel good about your self image, payment up front"  :lol:

You would be crushed all right, but not just by the rest of the earth pressing in-  The earth's center is very very hot.  Its composed of liquid iron.  The pressure generated by all that heat pushes out as hard as the rest of the earth pushes in.

In fact in stars the force of gases inside pushing out can sometimes overwhelm the force of gravity pushing in...  when that happens, you get a nova or supernova.

If the force of gravity wins out in the end, you get a dwarf star, or a quasar, or even a black hole.

Oh, and the magnetic fields probably wouldn't make too much of a difference.



Anyhow, the earth's cetner of gravity is probably quite near the physical center.  Let me explain:

In the earth's core, the pressuse generated inside pushes against the pressuse cause by gravitation.  The equilibrium of forces causes it to assume a shape as close to a sphere as possible, like a spherical balloon, in which the air pressure inside balances the air pressure outside, as well as the spring action of the stretched rubber.

Anyway, this works well enough that the earth is smoother for it's size than a bowling ball.  It may not be perfectly spherical, but its pretty darn close.

Yes and no.  Gravity would indeed pull in all directions with approximately equal force, so there would be an appearance of microgravity as if you were in orbit.  In fact, at the center of the Earth one could be considered to be in a stable orbit about the center of mass.  Orbital velocity just happens to be zero at that altitude.

That said, the curvature of spacetime (in a relativistic frame) and the density of gravitons (in a quantum mechanical frame) would be far too great to say that there is zero gravity.  There would be zero apparent gravity, but actual gravity would be significant.

When I woke up this morning I was thinking about this for some reason. Since most of my thoughts had already been expressed I thought about it in a different and rather simplistic way.

If you walk around the equator you eventually end up back where you started because gravity curves you around it. So at the centre of gravity the equator is that small that for what ever movement you make gravity would curve you round to where you began so therefore you can't move out of the centre of gravity.

Anyway the implications of this would be that any slight part of you that wasn't in the exact centre of gravity would begin to orbit around the part that was in the centre in a very twisted manner. Infact it is most likely you would be compressed into the centre and become very spherical in shape.

The part of you exactly in the centre wouldn't be able to move because of the point in the last post.

Also does anybody know how much time slows at the centre of the earth?

Time is a construct measured by the amount of entropy there is in a system. The speed at which things work at a fundemental level. A change in this gives the apperance of a change in the speed of time.
Under this definition there would be a change in the speed of time in your example of the father and son, relative to the other. To the father time appeared to have slowed down and to the son, sped up even though it appears they both experienced the same amount of time from a third person point of view.

Time is relative so there is no fixed speed of time.

Maybe I should rephrase my question.
Does anyone know the apparant change in the speed of time at the centre of the earth relative to somebody stood on the earths surface?

(sorry if any of this is wrong. I used to be a whizz at this when I was 12 but have slowly forgotten alot of it)

Yes thats right but to the person percieving it, it is reality to them isn't it? To them nothing ever happened in a different way. As far as the perception of reality is conserned everybody is correct yet also incorrect from somebody elses viewpoint, its all relative.

You are right about the -273 C. Because temperature is how much extra energy something has (i.e. beyond its mass). At absolute 0 something has no extra energy so nothing can happen. Suspended animation would occur.

The gravity at the center of the Earth would be ERROR: CANNOT DIVIDE BY 0.

But, seriously, the formula for the force of gravity has the square of the distance from the gravitational center of the object in the denominator, and thus it would be undefined at distance 0. In which case, you 'd have to add up the gravity from the particles individually, or just say you're .000000000001 meters from the center of the earth, in which case the gravity would be about a trillion trillion trillion times stronger than at sea level.

(Sorry, not exact because I used the computer's calculator because I don't feel like fetching my TI-83 and looking up Earth's mass.)

Well, about the dividing by zero thing...
remember that this is physics, not math. If this were math, then it would be undefined, or, as I sometimes refer to such things in math, "the universe explodes". Now, we all know that there is an atom of iron in the exact gravitational center of the earth, as well as every star in the universe, and we've only blown up once (or not at all, depending on who you believe). Physics is about what Physically happens.

I would say that there is some sort of metastable L point, where you're stable until something else pushes you, when you fall very slowly to the nearest edge of the chamber. Gravity is pulling equally in every direction, or at least in each of the 3 (x, y, z) dimensions, so it has no net effect on you.

following the "bowling ball" analogy (doesn't that one need the assumption of gravity in the analogy itself? That's kinda self-referential, like "I'm right because I say I'm always right"), you'd be at the bottom of the hole.

so yeah, "corediving" would work if the earth didn't rotate. Since it does, you'd be smashed against a wall from the coriolis forces. If you did it on the rotational poles (assuming the gravitational center lines up with them), you'd probably get away with it. However, you'd better aim well. If you touched a side at the speeds you'd get at the center, your entire arm would vaporise. Nothing left but some CO2, and maybe a bit of water vapour. This vapourisation would rob you of enough energy you'd fall several hundred meters short of the surface on the other side. In fact, the amount of momentum a human body can safely absorb is so little that if you did make it without touching anything, you'd have a window of about a thousandth of a percent where you'd be able to survive the impact. Use of a freakish padded ceiling system starting a few kilometers below ground would probably bring it down an order of magnitude, but it's still outrageous.

If there wasn't a vacuum, you'd probably either hit the free-fall velocity "ceiling" where air resistance equals weight. Either that, or you'd burn, and maybe a few bits of charcoal would stabilise on the walls of the core. If you didn't burn, you'd the the worst case of "the bends" in medical history from the pressure differential.

If there was a vacuum, have fun jumping in your space suit.




Now that was fun...

Darmani person:
the formulae for gravitational attraction assume point masses at the center of gravity. If you were to physically be where the model described, at d=.000001 meters, you'd be a micrometer from the core of a small black hole. Plenty of reason to be at an exceptionally high acceleration due to gravity... at 0, you'd be inside the black hole, and of course that's one of those crazy "divide by zero" moments.

interestingly enough, "center of gravity" takes a slightly different meaning here... hard to explain, but necessary to understand. Sorry guys... maybe someone better at defining stuff can take over on this one...

perhaps it would make sense to divide the earth into eigths, on opposite ends of each vector axis, and assume a point mass at the center of gravity of each. It's still crude, but a lot easier to work with than doing each individual particle. We can keep it to 3 1D vectors now, for (just to make a few directions up) sunwise, orbital tangental, and polar directions (since we have to make this things that are independant of earth, but the sun's still there).

Now, assuming that this is the center of gravity of the earth (which is the point of the excercise), then we can assume that the acceleration due to gravity (weight) is the same in every direction. The eigths might have slightly different masses, but then they're slightly different distances away in such a manner that they exert the same gravitational attraction on the object at the center (again, because that is the point of this excercise).

If I wanted to work it out in full, and could use all the stuff I needed to write calculations, I would. In short, each eigth has a mass of 1/8 of the earth's mass. You'd have to use stupidly advanced stuff to figure out how far they are from the center of the earth.

In short, we can call the gravitational force from the sunwise eigth x1, and the force from the antisunwise eigth x2.
We know that they are equal in magnitude (forth paragraph of this post).
We know that they are opposite in direction
It doesn't take much physics to tell you that two equal, opposite forces mean that nothing happens at all in that dimension.

Therefore, the sum of the Force (sunwise) = 0
and thus, Acceleration (sunwise) = 0
same goes for every direction.

So, all acceleration stays at zero. It stays right there.