There would be no net gravitational force at the center of the Earth (due to the Earth alone), if the Earth were perfectly spherical and made up "shells" of material of uniform density.
In fact, the "real" Earth is pretty close to those "ideal" requirements.
You can use the "related link" below, to confirm these details.
Of course, actually reaching the Earth's center is impossible with present technology. We haven't even drilled very far down yet.
Molten lava could disintegrate you long before you ever reached the center.
In fact, the center of the Earth is reckoned to be at about the same temperature as the surface of the Sun!
Also, there are huge pressures inside the Earth.
Imagine a hole that is drilled straight through the center of the earth from one side to the other. This hole is big enough to jump into. I jump in *crazy thing to do*; at that point I am falling.
As I approach the center of the earth, the question is, do the gravitational forces increase, or do they cancel.
If gravity increases, than I have the potential of exceeding my muscular-skeletal capacity to sustain me. (Try to forget the molten core for just a few minutes.)
If gravity cancels, than I have the potential of hanging around for quite sometime.
Through observation, we know that as an object goes further from the Earth, it feels less of Earth's gravity. If it goes far enough away from the Earth, it will not be affected by Earth's gravity. As objects get closer to Earth, gravity increases. But in all of those observations, the mass of the whole planet has always been to one side of the object that is being attracted. For example, when a plane is in flight, the mass of the whole planet is pulling the plane downward.
I do not know of any observational models that clearly demonstrate the concept of a larger mass (one with appreciable gravity) surrounding a smaller mass (one with negligible gravity). I would suggest, however, that since mass is directly proportional to gravitational attraction, and, at the center of the earth all of the mass is outward, toward the surface in all directions, that if I were in the center of the earth, I would be attracted outward, evenly in all directions. It would feel as if I were in a non gravity environment.
Hypothesis: In the center of the earth, gravitation forces, acting evenly outward in all directions, create a limited spherical zone where gravity is canceled.
So I believe the first answer is right.
Questions not figured into this hypothesis include: In the canceled gravity zone would I become aware of the effects of the Moon's gravity, or the gravity of the Sun?
NOTE on celestial body gravity. Their effects would be there, but about on the same order that astronauts feel when they are in orbit. Not enough for human senses to really pick up. While in orbit, you technically experience microgravity, not zero gravity.
Take the example of drilling a hole all the way through the Earth (ignoring the molten outer core and other problems).
You would indeed encounter effectively zero gravity at the center of the Earth.
I say effectively, because people are not points - so there would be microgravity effects that are felt most at your extremities.
An object dropped into that theoretical hole drilled through the Earth would accelerate towards the center of the Earth.
At the center of the Earth its speed would reach its maximum.
The object would continue to move, but would start getting slowed by the increasing net gravity pulling it back towards the center.
The object should just reach the surface on the other side of the Earth, ignoring frictional forces and other complications. Then it would start to fall again.
But even barring lava, I doubt you'd survive in a hole drilled through. And this is because the air pressure would crush you. The net effective force of gravity at the center is zero, but that air column will have a lot of pressure, most of that air is not at the center, is encountering the effects of gravity and is crushing you.
A second note on a person not being a point: If your center of mass was positioned exactly on the center of mass for the Earth, you would actually encounter a slight gravitational force PULLING you apart. I suspect it would be negligible and no more noticeable than the Sun's pull. If someone wants to do the integral calculus for a human shape in a sphere we could figure out the effective gravitational pull.
Yes, Mecca is "centre" of Earth. It is scientifically proved.
It is not scientifically proven yet, but the Muslims believe that Mecca should be the centre of the Earth!
Another Answer: The centre of the Earth is a very hot place and is under very high pressure. You wouldn't like to be there. It is about 4000 miles below the surface.