The Center of the Earth and Black holes and Gravity

[Firedog89]

I was thinking of the conditions exerted at the center of our Earth. If a man let's say in America falls toward the Center of the Earth and a man on the opposite side of the Earth falls, where would they meet? I read that the gravitation force at the center of the Earth is at 0. If they both fall towards the center, what would be the force that keeps them at the center? Would they even be kept at the center radius? This is excluding external gravitational forces including orbiting planets and satellites.

Why would the conditions reach to 0 and defunct freefall speed? After all an object that stays in motion stays in in corresponding motion. There would have to be another force to repel the gravitation G that is lost to reach a state of 0. Hence, mathematically for the scenario we seem to run into a problem. You cannot take away 1G from a force without losing it in another place. I keep concluding an opposite reaction or negative reaction to gravity. Maybe gravity has an opposite. Can that be possible? If gravity cannot have a negative connotation, can Stephen Hawking's theory of microscopic wormholes have anything to do with it stating that another gravitational force can be exerted through a wormhole like phenomena at the center of any gravitational body.

I also read in astronomy, that matter that is destroyed into a black hole is refracted back into the universe. In other words there is no energy lost into the black hole itself. The black hole just dumps back all the matter and energy back into the universe it doesn't absorb it. That defers any theory about black holes leading to parallel universes and dimensions and making black holes volatile. I also run into a problem. If black holes are volatile that would make gravity volatile. But that cannot be if gravity seems to have set rates known as freefall. If anyone is considering why I consider black holes as volatile, that is because black holes would break apart a star and spit the energy back out. To spit back the energy and matter of the star, the energy must have hit a snag in the black hole maybe a repelling force or the gravity in the black hole itself must be shifting to return the energy similar to what the stomach does when it's upset. Just like the stomach would be volatile, the black hole is as well. But just like the stomach's acid or the body's refusal to gorge, there must be a reason why the black hole refuses to absorb the energy or matter. I also run into a problem. There are theories stating that a black hole would absorb another black hole making the black hole massive or more massive. The black hole absorbs and repulse. But why? These are just theories but gravitational bodies seem to mysterious.

 

[russ_watters]

Welcome to PF!

Your instinct was leading you int he right direction, but you didn't quite get there: Since there is no net gravitational force at the center of the earth, a person falling through a hypothetical tunnel would just keep going past the center and out the other side (where, if no one caught him, he'd just fall back into the tunnel again!).

For the rest, it seems you are mostly just letting your imagination run free... better to get a book or a good source on the net and read up on it.

 

[Firedog89]

I get what you are saying he would become like a yoyo. But that would mean that the gravity would be pushing him away and pulling him. Opposite forces. Or the same force just positive and negative. That would still point out to a source for a singularity or single point if there is a center of gravity. But that wouldn't explain why the object would fall back down. But the tunnel itself would point out that it can't be 0. If it was at 0 eventually the object would reach a state of rest. If the net 0 wasn't 0 actually maybe even a negative equal to the opposite then that would conclude that the object can become like a yoyo actually like a pendulum. The pendulum becomes free swinging because the gravity isn't 0 it constantly pulls it down. If it was 0 then the pendulum would reach a state of equilibrium. But it's terminal velocity breaks the gravitational pull thus swinging it back again. But also a pendulum reaches terminal velocity at the center. That is not the case when you free fall you reach terminal velocity before you reach the center and if the net gravity is 0 at the center, then you might actually slow down because the force of gravity is less and gets to nil the closer you get to the center. Considering there is a time that an object reaches terminal velocity, maybe that is the same rate to decelerate to a state of 0.

 

[Firedog89]

Do you have any links?

 

[russ_watters]

I get what you are saying he would become like a yoyo. But that would mean that the gravity would be pushing him away...

No, it wouldn't. Gravity is (at least on Earth) only attractive. When he's going out the other side, his momentum keeps him going and gravity (still attracting toward the center) slows him down, to a stop, as he gets back to the surface.

That is not the case when you free fall you reach terminal velocity before you reach the center and if the net gravity is 0 at the center, then you might actually slow down because the force of gravity is less and gets to nil the closer you get to the center. Considering there is a time that an object reaches terminal velocity, maybe that is the same rate to decelerate to a state of 0.

I was assuming for the sake of the hypothetical that the tunnel is evacuated, so there is no terminal velocity.

Do you have any links?

To what, exactly? Have you read the wiki on gravity?

 

[Firedog89]

I was actually switching back from the tunnel back to free falling on Earth you might have gotten confused. Momentum would keep the object moving back and forth at roughly the same speed indefinitely but I cannot understand how gravitational pull would be a 0 at the center of gravity. Acceleration reaches 0 but why would the gravitation pull decrease. If gravity is attractive what would the object be attracted to at the center?

 

[Bandersnatch]

Acceleration reaches 0 but why would the gravitation pull decrease.

This is pretty much the same thing in this context. The force of gravity divided by the mass of the infalling object nets the gravitational acceleration. If one reaches zero so does the other.

As for the why - force of gravity at the centre is a zero net force. That is, attraction from all the mass around the centre is equal, and for any direction you choose there is an equal force in the opposite direction that cancels it out.

Another way (actually it's the same) of putting it is by using the shell theorem (http://en.wikipedia.org/wiki/Shell_theorem).
The theorem shows that for a uniform sphere of mass, only the mass concentrated in a sphere below the position of a test particle is attractive, all the remaining mass in the shell (hence the name) above that radius nets zero force (it all cancels out).
For R=0 you've got all the mass in the shell above (r>R) the test particle in the centre and no mass below (can't get lower than R=0). The attraction from the mass in the shell cancels out and there is nothing to pull you in any direction.

 

[A.T.]

Acceleration reaches 0 but why would the gravitation pull decrease.

How do you quantify "gravitation pull", if not as acceleration in free fall, relative to the Earth?

If gravity is attractive what would the object be attracted to at the center?

That is a question that you have to answer, if you claim that gravity is not zero at the center.

 

[Firedog89]

That is the thing, If acceleration reaches the state of 0 the same as gravitation pull decreasing. What would cause the gravitation force to decrease? On Earth friction would cause an object to decrease velocity. But if an object freefalls in a vacuum through the center of the Earth it should continue to accelerate. I understand momentum would keep the object trajecting past the center but then at a certain point it decreases in velocity thus falling back through the center again. Technically it should just continue on with the same velocity. I keep running to a conclusion that it will somehow stop at the center of the gravitational well. because at some point it decelerates. That means there must be a force that keeps drawing it in. How do we know that it will continue to bounce back and forth indefinitely? Also if the force of gravity was a net of 0 using Shell theorem, at the center of the Earth or gravity on Earth should be hollow and attracted to the outward masses. This also leads to the conclusion that maybe every atom exerts a gravitational pull.

 

[Bandersnatch]

Can you tell us what's your background knowledge? Do you understand vectors, equations of motion, Newton's gravity? Can you analyze the motion of a pendulum?

 

[Firedog89]

I was just theoretically speaking. I did physics in high school. I understand motion but just confused with gravity.

 

[Bandersnatch]

I'm asking so that we may know where to begin with explaining. You say you understand motion, but if I were to say the problem is the same as that of a simple harmonic oscillator (a pendulum), would that suffice?

 

[Firedog89]

but the problem with a pendulum is that a pendulum doesn't have a net gravity of a zero at equilibrium state. Gravity would still exert 1G on the pendulum at equilibrium state.

 

[Bandersnatch]

What do you mean by equilibrium state?
The acceleration tangent to the path of the bob of a pendulum varies from maximum at the sides (points of maximum extenstion), to 0 at the bottom. The direction of acceleration tangent to the path of the bob changes halfway though. At the same time velocity varies from 0 at the sides to maximum at the bottom. Velocity changes direction at the points of maximum extension.
With a person falling down the tunnel through a planet the acceleration is maximum at the surface, 0 at the centre, and its direction changes halfway through. Velocity goes from 0 at the surface to maximum in the centre and it changes direction at the surface.

(all disregarding air resistance etc.)

 

[Firedog89]

So you are saying that gravitational force (Gs) will not have any interactions with the a person oscillating back and forth. But wouldn't an object oscillating back and forth on a pendulum use it's own velocity to reach back to maximum height?

 

[Bandersnatch]

So you are saying that gravitational force will not have any interactions with the object oscillating back and forth

No, I'm not saying that. The acceleration changes continuously throughout the motion.

 

[Firedog89]

I didn't mean force I mean Gs. I don't even know if force and Gs would be the same. But I also read that a person would slow down as it reaches the center of the Earth what would cause that phenomena. A pendulum doesn't slow down until it reaches maximum height.

 

[Bandersnatch]

Force and acceleration change at exactly the same rate.

 

[Firedog89]

I edited my last post do you have any insight?

 

[Bandersnatch]

But I also read that a person would slow down as it reaches the center of the Earth what would cause that phenomena. A pendulum doesn't slow down until it reaches maximum height.

What you read is not correct then. Your intuition about pendulum is, though. A person falling through a (evacuated) tunnel down the planet accelerates all the way to the centre, with acceleration constantly diminishing. The slowing down begins only past the centre, and increases in strength until it reaches maximum at the surface on the other side of the Earth.

 

[Firedog89]

With a pendulum on the surface of the Earth, a pendulum will eventually come to a state of rest either because of friction of the air and because gravity will keep it downward. At the state of rest gravity will still pull it downward as it rests. At the center of the gravity on Earth, gravity cannot pull a person towards it, basically it will go past the center continue because of momentum and continue as due what I have been reading because it's pull is at 0 at the center. I can understand that is a possibility but it also raises questions. Why would metal be condensed at the center but let's say you have a heavier rock but that would be a distance from the center?

At the beginning of a star formation from a nebula, matter is condensed inward. That goes against a bit of physics which state that an object spinning outward must continue to spin outward. But why would some matter exist gravity and condense matter while some material matter will not. Also, if a gravitational body was to be destroyed, the gravity encroaching it would disappear. Maybe there is nothing special about gravity, but what would be the exact mechanisms of gravity? Why does gravity operate the way it does? What truly pulls you inward?

 

[Bandersnatch]

a pendulum will eventually come to a state of rest either because of friction of the air and because gravity will keep it downward.

There's no either. In the absence of friction (both with air and within the string) the pendulum is a perpetual motion machine.

The analogy with a pendulum requires you to think of the force component on the bob in the direction tangent to the path it travels. It is this force that changes in a similar fashion to the force of gravity in the case of falling through Earth. That there exists a constant force of gravity as well as changing tension of the string acting on the pendulum is irrelevant as far as the analogy is concerned.
At the centre of the Earth gravity cannot pull any object in any direction, and at the bottom of the pendulum there is zero force on the bob in the directions tangent to the path the bob travels.

In both cases, the object needs some preexisting momentum to carry it forward past the equilibrium point. In the presence of friction, this momentum will be continuously dissipated eventually bringing the motion to a stop at the bottom of the pendulum/at the centre of the planet.

That goes against a bit of physics which state that an object spinning outward must continue to spin outward

I don't know what bit of physics is that.
I think you might be thinking of the conservation of angular momentum. In that case, as with linear momentum of the pendulum, it is dissipated due to friction. In the absence of friction matter would indeed fail to accrete to form planets and stars.
Which is, incidentally, exactly how dark matter is modeled to behave - no friction leads to no clumping an no dark matter planets and stars.

Also, if a gravitational body was to be destroyed, the gravity encroaching it would disappear.

This isn't doable without magic.

 

[A.T.]

I think you might be thinking of the conservation of angular momentum. In that case, as with linear momentum of the pendulum, it is dissipated due to friction.

It's important to note that (unlike kinetic energy) the total momenta (linear and angular) are never dissipated. They are always conserved. Friction merely transfers momentum form one object to another, just like the rope does.

 

[Firedog89]

This isn't doable without magic.

Yes I know, I was theoretical speaking. But asteroids might have the potential to be destroyed without cratering planets or dissolved through stars.

In the absence of friction matter would indeed fail to accrete to form planets and stars.
Which is, incidentally, exactly how dark matter is modeled to behave - no friction leads to no clumping an no dark matter planets and stars.

Friction leads to positive and negative charged particles to clump. That could be a possibility in larger scales as well I guess. So you are trying to say if you were to take gravity away from star formations, stars would still form if they just possesses friction? If in space there is no air to create friction, how would they create friction? This is hard to believe. If you were to take gravity away, angular momentum I like to use centripetal force because new stars are formed from existing stars from a supernova. A supernova propels material outward not stationary to the beginning point or inward towards ground 0. Anyways, if you were to take gravity away, and just have friction, material can still condense to form stars? That is also hard to believe.

 

[Bandersnatch]

So you are trying to say if you were to take gravity away from star formations, stars would still form if they just possesses friction?

No, I've never said that. You need both to get stars.

If in space there is no air to create friction, how would they create friction?

There is no fundamental difference between air (empty space with a number of molecules suspended in it) and the protoplanetary cloud (empty space with a number of molecules suspended). The difference is only quantitative - there's more molecules per unit volume(=higher density) in air.

It's important to note that (unlike kinetic energy) the total momenta (linear and angular) are never dissipated. They are always conserved. Friction merely transfers momentum form one object to another, just like the rope does.

Thanks A.T.
It's not the first time I managed to conflate energy with momentum when talking about accretion.

 

[Firedog89]

Friction can cause heat that give unborn stars the nursery needed to make the stars. But having a nursery or having the baby inside are two different things. The difference with star formation would be the difference with gravity. Unless atoms have their own gravitational pull and subsequently adhere and multiply their gravitational energy, it is rather difficult to exfoliate how gravity comes about. It is also said that the gas cloud needs to collapse under it's own mass. That means that a molecules of dust has to adhere and bulk up for the mass to increase. Still that leaves questions. If an object has enough mass to collapse why would it tend to have direction where to collapse? If the matter collapsed inward, why doesn't it ooze out the sides and break from pressure? I mean I am glad that it is the way it is or else we wouldn't be here to debate this topic Anyways further details, heat is transferred to cooler temperatures. If empty space can exhibit temperatures well below, why wouldn't the heat dissipate to the cooler regions of space and complicate star formation.

 

[Bandersnatch]

Unless atoms have their own gravitational pull

Yes they do. Atoms have mass, don't they?

and subsequently adhere and multiply their gravitational energy,

When there's more of mass there's more of gravity (stronger field). For the clumping, the particles need a way of losing energy, otherwise they just bounce away or pass through each other as with dark matter.

If an object has enough mass to collapse why would it tend to have direction where to collapse?

How could it not? The centre of mass always has the strongest pull.

If the matter collapsed inward, why doesn't it ooze out the sides and break from pressure?

Pressure of the collapsing cloud of matter does prevent its further collapse, unless there is a way of reducing pressure, which is...

Anyways further details, heat is transferred to cooler temperatures. If empty space can exhibit temperatures well below, why wouldn't the heat dissipate to the cooler regions of space and complicate star formation.

...exactly this. As the collapsing cloud heats up due to friction between its constituent particles, its pressure increases and acts against gravity to prevent further collapse. The hot gas then radiates energy out which lowers its temperature and pressure, allowing further collapse.
It also means that stars generally don't form from interstellar clouds of gas that are already relatively hot, as these collapse very slowly due to the inefficiency of radiative heat transfer.

 

[Firedog89]

How could it not? The centre of mass always has the strongest pull.

Let's say every atom possesses gravity because they have mass. Each atom directs gravitational pull towards their center where the center of gravity should be set. The question rest how does gravity change from the center of particular atoms to the center of gravitation body (example: Earth)?

 

[Nugatory]

Let's say every atom possesses gravity because they have mass. Each atom directs gravitational pull towards their center where the center of gravity should be set. The question rest how does gravity change from the center of particular atoms to the center of gravitation body (example: Earth)?

You can calculate it. If the distribution of atoms is spherically symmetric, the sum of all their forces on one another will always act directly towards the center of mass.

 

[Firedog89]

The question doesn't arise if they distribute the force of gravity or calculate it, it is why. I know this is how it is, but if all atoms generate their gravitation potential towards their center of mass, why would it change their gravitational energy from the center of an atom to the center of a larger gravitational body. Even if each atom still possesses their gravitational pull (I'm guessing they still do) and it's still exerted on the atoms, why would gravitational energy be stronger at the center of larger masses? An atom itself would have limited gravitational energy but compared to larger objects their gravitational pull is stronger. What would cause it to change?

 

[Bandersnatch]

The question doesn't arise if they distribute the force of gravity or calculate it, it is why. I know this is how it is, but if all atoms generate their gravitation potential towards their center of mass, why would it change their gravitational energy from the center of an atom to the center of a larger gravitational body. Even if each atom still possesses their gravitational pull (I'm guessing they still do) and it's still exerted on the atoms, why would gravitational energy be stronger at the center of larger masses? An atom itself would have limited gravitational energy but compared to larger objects their gravitational pull is stronger. What would cause it to change?

Of course every massive particle still keeps on attracting every other bit of mass. The attraction towards the centre of mass is the net effect of adding all the forces. It's a mathematical "trick", for the lack of a better word, in the same category as adding two equal and opposite forces nets you a 0 even though the two forces never dissapear.

It's not that hard to understand intuitively - if you stand on a sphere of massive particles (a planet, say), the particles right under your feet are exerting a large (relatively speaking) force on you because they're close and gravity falls with distance, and for the same reason the particles farther away are exerting smaller and smaller attraction.

But at the same time the farther you look under your feet, the more massive particles there are to pull you in. If you add the effects from all the particles in the sphere, you find out that the total attraction is exactly the same as if you were attracted by a single particle containing all the mass residing in the centre of the sphere.

Mathematically, this is shown here:
http://en.wikipedia.org/wiki/Shell_theorem
You might need to brush up on some calculus to understand what's going on. The net is full of other explanations, as the theorem is as old as Newton.

 

[Firedog89]

At the center of the Earth, a particle cannot contain the same amount of mass as say the total masses of the sphere. At the center, all the masses will be above you. Therefore, you should be attracted to the masses that are above you so in effect (you should be branded away from directly at the center of Earth). If you are attracted directly to the center of gravity if the center of gravity relies at the direct center of the Earth, there must be force pulling you toward the center... if the force of gravity is 0... then there should be a cancelling out of gravity to net you 0 in the first place. All the opposite forces should equal a net of 0 as you say. What will bridge the connotation to equal 0? Mathematically everything makes sense but the problem is; if there is an equal and opposite force to almost everything and gravity's force is only attractive, then you should be still attracted completely to the source. If the force of gravity isn't completely attractive, then you can have equal and opposite gravitational forces to lead to a net of 0. Simply, -1G's+1G's=0G's. Therefore, simple math is applied to get total net 0 gravitational pull at the center of gravity. The key term center of gravity implies that there should be a singular point directly at the center of gravity (center of the Earth). Something must diverge the possibility that nets gravity to 0.

Even if the masses above you can generate enough gravity for your mass to be pulled off center from the Earth, then there is still a singular point of gravity that pulls you toward any mass. If there is concentration of atoms that implicitly pulls you toward the groupings of the atoms center of gravity, then there still procure a singular point of gravity even if it was a concentration of atoms.

This may be a bit confusing to explain and I'm also implying that none of this is true just speculation.

 

[Drakkith]

This may be a bit confusing to explain and I'm also implying that none of this is true just speculation.

You're right, it is confusing. I suggest simplifying the discussion to the basics of gravity and starting over from there.

 

[PeterDonis]

At the center, all the masses will be above you. Therefore, you should be attracted to the masses that are above you so in effect (you should be branded away from directly at the center of Earth).

If you were at the center of the Earth, all the masses above you would be attracting you; but they would be doing so equally in all directions (we are idealizing the Earth to be perfectly spherically symmetrical so all the masses above you are symmetrically distributed), so all the forces would cancel out, and you would feel zero net force.

If you are attracted directly to the center of gravity if the center of gravity relies at the direct center of the Earth, there must be force pulling you toward the center... if the force of gravity is 0... then there should be a cancelling out of gravity to net you 0 in the first place.

At the center of the Earth, there is. See above.

If the force of gravity isn't completely attractive, then you can have equal and opposite gravitational forces to lead to a net of 0.

You can, because "attractive" is not the same as "always in the same direction". Gravitational force is a vector, not a number; the force of attraction caused by a particular piece of matter points toward that piece of matter. Different pieces of matter in different directions from you will cause forces that point in different directions, and they add as vectors, so they can cancel each other out; if the forces point symmetrically in all directions, then they all cancel out.

 

[Firedog89]

If you were at the center of the Earth, all the masses above you would be attracting you; but they would be doing so equally in all directions (we are idealizing the Earth to be perfectly spherically symmetrical so all the masses above you are symmetrically distributed), so all the forces would cancel out, and you would feel zero net force.

ohhh ...I see it now. gravity will keep you interacted in all directions. So, therefore, you will feel the effect of net 0 force... Let's say you look at just one atom in a theoretical universe with just you imagined smaller than the atom and this particular atom. You will feel the effect of gravity very minimally of course. Where would the effect of gravity be located? Let's say it is at the center. What are the interactions? Would the effect of gravity be relevant to open spaces added up equally or is there a particle or object responsible for it?