Gravity: Thoughts on Earth's Center Point

[Phalid]

Allow me to preface the following with an apology if the question I ask sseem a bit off.

While reading Coming Of Age In The Milky Way by Timothy Ferris I came across a line in which he states:

"Earths gravitational force extends from its center point"

My understanding of gravity is that it is nothing more than curved space-time. The mass of objects warp the space-time and that warping is what produces the attractive force. Why would the Earth's gravitational force extend from its center point. How can the center of the Earth warp space-time unless space-time exists within the Earth at its center? Wouldn't the outer edges of Earth's surface be the source of the space-time warping since that is the area which comes in "contact" with space-time?

 

[Harut82]

Allow me to preface the following with an apology if the question I ask sseem a bit off.

While reading Coming Of Age In The Milky Way by Timothy Ferris I came across a line in which he states:

"Earths gravitational force extends from its center point"

My understanding of gravity is that it is nothing more than curved space-time. The mass of objects warp the space-time and that warping is what produces the attractive force. Why would the Earth's gravitational force extend from its center point. How can the center of the Earth warp space-time unless space-time exists within the Earth at its center? Wouldn't the outer edges of Earth's surface be the source of the space-time warping since that is the area which comes in "contact" with space-time?

No. Space-time is everywhere and everything. Gravity curves the fabric of the universe and everything in it. When gravity "curves" space-time it does so in a higher dimension. Our 3 dimensional perception of the univierse doesn't change.

 

[Ray Eston Smith Jr]

Each little piece of the Earth contributes to the total curvature at any given point. The curvature at a given point is proportional to the the gravitational force at that point. At points in the interior of the Earth, the gravitational force is proportional to the total mass below that point times the distance to the center. So the gravity (and curvature) gradually decrease as you burrow down toward the center. At the exact center of the Earth, the gravitational force (and curvature) is zero (all the mass is pulling equally outward, cancelling to zero.)

By the way, if the Earth was a hollow shell, with all its mass concentrated in the shell, there would be no gravity (from Earth) in the interior. At a given interior point, there would be a pull from a small part of the nearby shell which would be exactly counteracted by the pull in the opposite direction from the larger but more distant part of the shell.

 

[Ray Eston Smith Jr]

I mis-stated something in my previous post. I said gravitational force is proportional to distance from the center. It's actually inversely proportional. So if there was just a spec of mass at the very center, and if you could get very very close to that spec, you would experience very high gravity (and space-time) curvature. The same would apply to any spec of mass anywhere in the Earth. If you could get right next to an electron, you could experience extremely large gravitational curvature (within that tiny radius). But maybe quantum mechanics keeps small things far enough apart (via the uncertainty principle) to prevent huge gravitational forces.

Another thought: The gravational curvature of space-time within the Earth is not smooth on a small scale. It's very bumpy - very large close to particles, very small in between. But on a large scale it looks like a smoothly varying curvature.

 

[JesseM]

I mis-stated something in my previous post. I said gravitational force is proportional to distance from the center. It's actually inversely proportional. So if there was just a spec of mass at the very center, and if you could get very very close to that spec, you would experience very high gravity (and space-time) curvature.

I don't think that's correct--in Newtonian terms, as you get closer to the center, the only gravity you feel is from the sphere of matter that's at a radius closer to the center than your current radius, while all the matter at a greater radius than you can be treated as a hollow sphere and as you pointed out when you're inside a hollow sphere its gravity cancels out. So, if you're only 1 kilometer from the center, the gravity you'd feel is the same as what you'd feel standing on the surface of a sphere of radius 1 kilometer (and the same mass as is contained in the 1 km radius from the center of the Earth) which was isolated in deep space, which is going to be a lot weaker than the gravity you feel on the Earth's surface.