Gravity

[Cheif Operations Director]

If you have a perfect sphere with no other forces will the EXACT Center be 0 gravity

[Superfluous J]

Assuming the universe is only made up of you and it and you are of zero mass, yes.

More accurately, the sum of all gravity force vectors will be zero.

[peadar1987]

Yup.

And if you have a spherical cavity at the exact centre, the forces at any point inside that cavity will also be zero

[PB666]

1 hour ago, Cheif Operations Director said:

If you have a perfect sphere with no other forces will the EXACT Center be 0 gravity

Gravity in newtonian terms is an acceleration vector and can be dissociated into component vectors. It is caused by the warping of space time, the warping of space time is near its highest at the CoM.

The vectors are pointing in opposing direction if you were at the center of a sphere and we created 6 vectors A, B, C, D, E, F

representing both direction of a 3-axis basis R3 A and D representing X, B and E representing Y and C and F representing Z
A + D = Φ, B + E = Φ, C + F = Φ the zero vector. These vectors represent the field.

You should also note the zero vector in a r3 coordinate system simultaneous represents all direction, thus just because the net acceleration is zero does not imply that all vectors representing that field are also zero and  directionless.

Even if you were to hollow out the earth creating a shell with 1000 km of space at the center the composite vector would still be zero.

https://en.wikipedia.org/wiki/Shell_theorem

https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

 

[Cheif Operations Director]

So where would you go if you were being pulled on all sides

[insert_name]

6 minutes ago, Cheif Operations Director said:

So where would you go if you were being pulled on all sides

whatever direction you were going before

[Green Baron]

The closer you get to the center of a (otherwise homogeneous!) mass (a planet), the less your weight. The pull of the mass of the planet outside of your height cancels itself out (the shell theorem above).

5 minutes ago, Cheif Operations Director said:

So where would you go if you were being pulled on all sides

nowhere and everywhere :-) The pull of the mass outside cancels itself out. You are not being pulled nowhere.

 

But, of course, few gigapascal pressure and thousands of degrees temp. (nevermind if Celsius or Fahrenheit) will have their play with you :-)

[Superfluous J]

8 minutes ago, Cheif Operations Director said:

So where would you go if you were being pulled on all sides

You would not go anywhere, if all the forces are equal (which they would be in the exact center of a perfect uniform sphere, or in the hollowed out center, as stated above. Or you'd keep moving in the direction you were going, as @insert_name noted.

[Cheif Operations Director]

That's what I thought. Now the question is will the planet collapse into itself.

[PB666]

If you are at the center of the planet, compress you to a density of about 2, without much excitement, since the metal at the temperature and pressure would act like peanut butter being squeeze through a 30 guage needle and over the next few billion years your remains will slowly drift to the outer core. Since there is no net gravity at the center there is no differential gravity, but there is a slight favoritism of heavy metals (uranium, gold, lead, but in particular siderophilic heavy metals) and you are not one of these so your bulk would thermodynamically want to exclude from the center over time.

You should consider this however, the energy potential is -u/r, current you are at 6391 km (r) if you were at the center   4E14 kg m³/s²/0 is infinity. But we know that the barrier stops a few centimeters before when E is somewhere close to the speed of light squared (as anything inside that volume would be a black hole, the earth is not a point mass anyway). Your density, fully compressed is 2 and the stuff at the center of the Earth is 6~8, and although the full potential energy is not achieve because the earth is not a point mass, your ability to move your bodies volume of material from the center of the earth  is limited. Imagine that your weight is say 50 kg, you would have to move net of 150 kg of metal from the center of the Earth to the surface, so lets say the average gravity peaks at 3 million radius and goes down. In order to move that 150kg would require theoretically about 7 times as much specific energy as to launch into a circum solar orbit. This does not even consider the cost of excavating dirt stabilizing the walls of the tube. IOW, it would take more specific energy to just displace your weight to earths center than has ever been generated for any solid object (not counting the core of ²H-³H devices) by human.

[K^2]

Gravity at the center is zero, regardless of whether you're in Newtonian or GR Gravity framework. In fact, even if the planet is not spherical, there will be a point of zero gravity. It might not be dead-center for such an object, though. Now, gravity is zero, but stress isn't. The rest of the planet is still trying to collapse, and it's the mechanical stress in the planet's core that's resisting such a collapse. In planet or regular star, the stress resisting the collapse is going to be due to electrostatic forces. In a neutron star, due to nuclear forces.

[Nuke]

now what are the chances of that massive hollow object not collapsing and crushing you into a tiny little sphere of meat paste? 

[Superfluous J]

1 hour ago, Nuke said:

now what are the chances of that massive hollow object not collapsing and crushing you into a tiny little sphere of meat paste? 

Gotta be 3,720 to 1

[Shpaget]

2 hours ago, Nuke said:

now what are the chances of that massive hollow object not collapsing and crushing you into a tiny little sphere of meat paste? 

We haven't defined how massive it is.

If it's a steel shell 1 m thick it can easily be 100 m in diameter without collapsing.

Heck, in an otherwise perfectly empty universe, it can be any arbitrarily thin thickness and it won't collapse, assuming you achieve perfect structural uniformity and shape.

[Green Baron]

As @K^2 has pointed out there are always forces in equilibrium. One side is Gravity, the counterpart lies in the material, forces between the atoms/molecules, between the particles in the atom, between the particles that the particles consist off. And as gravity goes down (mass * acceleration, the acceleration sinks towards the center) pressure goes up from all the stuff higher up in the column and density increases corresponding with lower depth. Pressure of a planet's interior is expressed in gigapascal.

So as the mass of the whole planet increases the pressure in the center increases and the stuff goes through different phase transitions first, from the normal dense stuff we know at the surface through several states of crystalline stages (atoms packed denser together), some of them experimentally replicated and some hypothetical. At one point the matter gives in, protons are forced into the electrons and form neutrons and if even that is not enough then density can even become infinite. I hope a physicist excuses my simple wording :-)

What happens to a human body at the center of earth ? It'll be compressed to ~13gr/cm³, heated to 6000K and form a lasting amalgamation with the present mostly iron/nickel stuff in hypothetical phases there (not 100% clear what else, possible sink for missing sulphur to meet the observations of gravity and overall density). Maybe the water and carbon molecules pressed between free spaces of the core's iron/nickel molecules. If it is solid/crystalline or some sort of plasma can be debated. You won't mind anyway

But it'll probably stay there until the earth is swallowed by the sun should that case happen one day since there is probably no big disturbance at the center.

Edited January 9, 2018 by Green Baron

[Piatzin]

Confusion

Also, why the one-star rating lol

Edited January 9, 2018 by Earthlinger

[Green Baron]

6 minutes ago, Earthlinger said:

Confusion

Why ? :-)

[Piatzin]

16 minutes ago, Green Baron said:

Why ? :-)

Joke?

Edited January 9, 2018 by Earthlinger

[Green Baron]

Ha ?

[NSEP]

So if you where in a hole at the exact centre of gravity of a planet, would it feel like you are in Zero-G or would it feel like you have a black hole in your stumach?

[Matuchkin]

I just got mentally lost right now, thinking what it would be like to do this. Everything is pitch black, but you know that you are surrounded by thousands of kilometers of rock. Just floating there is creepy as hell. What would you hear? Just the rumbling of the Earth's mantle outside, or nothing at all? (Given that you are not affected by the pressure and heat)

[Green Baron]

Guys, as a warm up, just jump into an iron ore smelter

Edited January 11, 2018 by Green Baron

[Matuchkin]

1 hour ago, Green Baron said:

Guys, as a warm up, just jump into an iron ore smelter

Tried it, felt uncomfortable at first, but holy crap it heat you up real quick. Good way to get the blood flowing.

Edited January 11, 2018 by Matuchkin

[PB666]

2 hours ago, Matuchkin said:

I just got mentally lost right now, thinking what it would be like to do this. Everything is pitch black, but you know that you are surrounded by thousands of kilometers of rock. Just floating there is creepy as hell. What would you hear? Just the rumbling of the Earth's mantle outside, or nothing at all? (Given that you are not affected by the pressure and heat)

Seriously. Think major compression tension coming from all directions, in the matrix of the iron core you would not be moving, except inward under a massive crushing force.

The pressure on the last cubic material of core at the center of the Earth is 44,145,000,000,000,000,000,000,000 P. The compressibility of water 5.1×10⁻¹⁰ Pa⁻¹ which will decrease in a temperature dependent manner.

You ----Core----> Soup + carboard like boney material - crushed within moments, pressure cooked within minutes, displaced within hours or days, out of the core within billions of years. I would say that within an hour nothing of you would be recognized down to the DNA level, there would be nothing about that mass that could identify you except your initial mass and the amount of bone-mass that you had.

You would hear your body being disintegrated.

Edited January 11, 2018 by PB666

[Matuchkin]

4 hours ago, PB666 said:

Seriously. Think major compression tension coming from all directions, in the matrix of the iron core you would not be moving, except inward under a massive crushing force.

The pressure on the last cubic material of core at the center of the Earth is 44,145,000,000,000,000,000,000,000 P. The compressibility of water 5.1×10⁻¹⁰ Pa⁻¹ which will decrease in a temperature dependent manner.

You ----Core----> Soup + carboard like boney material - crushed within moments, pressure cooked within minutes, displaced within hours or days, out of the core within billions of years. I would say that within an hour nothing of you would be recognized down to the DNA level, there would be nothing about that mass that could identify you except your initial mass and the amount of bone-mass that you had.

You would hear your body being disintegrated.

I already said: given that you are not affected by the pressure.