Centre of the Earth

[east]

or any planet for that matter.

 

i have been bugging myself with this question for days, please help with some physics input, the question is perhaps on theoretical physics but it bugs me nevertheless.

 

Q. if we draw lines towards gravity of the earth, will the lines intersect at exactly one point at the center of the earth ?

 

a plumbline would be such a line, if we have people holding a plumbline everywhere on earth, and someone draw an accurate line through it, would they all meet at one point ?

 

i am trying to establish if gravity is a point, a singular point.

 

many thanks for your ideas and input.

[insane_alien]

if the earth was a perfect sphere then yes.

 

as it is not a perfect sphere the answer is no, although it does come pretty close. the sun and moon also throw the result off as well.

[swansont]

Gravity will obey superposition and give you a single value everywhere, so the lines won't cross at any point. Two ways of looking at this — one is from the uniqueness theorem (only one answer to the equation is possible) and the other is that two lines at one point would add as vectors leaving you with one line.

 

Extending the direction of a plumbline, though, may have those lines cross, because of nonuniformity in shape and mass distribution — the actual lines may not have the same path as the extrapolation of the lines from some point.

[east]

thanks for your resposes. i'll address both responses at once.

 

ok, so we are talking of a non perfect sphere. but it isn't the shape that is so much of my concern, more of the center of gravity, the exact center.

 

btw, it isn't the quantum of vectors that matter in this case, as in it adding up or cancelling, it is more of it meeting or not meeting/crossing each other.

 

that it does not meet due to the shape is a temporary drawback. what i'm saying is that, if you take an object, there is what is referred to as center of gravity, where at that point, the whole object is balanced with respect to earths gravity. hence, if we can imagine 'gravitaional lines' going through this object, it must surely intersect at this point. am i right in saying so or am i missing something ?

 

now, if we are to extend this reasoning to the earth, i am inclined to believe that it does intersect at one single point.

 

that it does not do so due to the non spherecial shape is accepted. so each an every line will pass through, and if we make infinite lines, we would get the shape of a smaller object.

 

now let's say we start again, with this smaller object, and repeat the whole plumbline process.

 

again my question, would it not eventually come to a single point ?

do you see any serious fault with this theory i have hanging in my head.

 

because i certainly don't but there may just be something i might have missed.

[Sisyphus]

Not necessarily. To use an easier to visualize example, look at the Earth-Moon system. This system does have a single center of mass, which is somewhere in the Earth's mantle. From an arbitrarily large distance away and assuming there are no other masses in the universe, gravitational vectors will point towards this one point. However, that is not the point towards which any gravitational vectors point from nearby (like standing on the surface of either body), except incidentally. In fact, if you were to stand at that point, gravity would be pulling you away from it, towards the center of the Earth.

 

The Earth taken by itself is pretty much analogous in that it's not perfectly uniform or spherical, so all lines will not meet at a single point. Like the Earth-Moon system, it too has one center of mass, but it would likely have more than one point at which net gravity is zero. (Unlike the Earth-Moon system, however, all such points would likely be very close to the center of mass.) It would not be "a smaller object," but rather a set of distinct points. And from each of these points, plumblines would point nowhere.

 

So, just out of curiousity, did you have anything in particular in mind as a consequence of your hypothesis?

[east]

Like the Earth-Moon system, it too has one center of mass, but it would likely have more than one point at which net gravity is zero. (Unlike the Earth-Moon system, however, all such points would likely be very close to the center of mass.) It would not be "a smaller object," but rather a set of distinct points. And from each of these points, plumblines would point nowhere.

 

ah ok, understood. it would be the case then that all these points would amount to zero gravity, neglecting for the moment other heavenly bodies.

 

So, just out of curiousity, did you have anything in particular in mind as a consequence of your hypothesis?

 

not that i know of, theoretical physics is just my hobby. i found this forum and thought it might be the right place to ask and talk about these kind of things. it if is not, i would stop. or i don't mind being reffered to another site/forum where theoritical phycics can be discussed.

 

i just need to get these thoughts out, it is bothers me a little in the sense that it remains unsolved, like a mystery unsolved.

 

so far it has shed better light on the center of gravity dillemma, so if possible, i'd like to go on to see what can be derived from this.

 

thanks.

Edited March 10, 2009 by east

[cameron marical]

would there be gravity at the center of the earth?

not for newtonian physics, i dont think theyred be gravity, would there?

but what does gr and sr apply to that?

whats anyone elses guess for it? or a definitive answer.

[morganparkar]

Hello Friend,

 

The center of the Earth is a plumbline would be such a line, if we have people holding a plumbline everywhere on earth, and someone draw an accurate line through it, would they all meet at one point ?

[swansont]

would there be gravity at the center of the earth?

not for newtonian physics, i dont think theyred be gravity, would there?

but what does gr and sr apply to that?

whats anyone elses guess for it? or a definitive answer.

 

No gravity at the center — for a sphere, the gravitational field at R depends on the mass inside of R. There would be no gravity inside of an empty shell, independent of the strength of gravity outside.

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Merged post follows:

Consecutive posts merged

Hello Friend,

 

The center of the Earth is a plumbline would be such a line, if we have people holding a plumbline everywhere on earth, and someone draw an accurate line through it, would they all meet at one point ?

 

No. The mass distribution isn't uniform, and the earth isn't a perfect sphere. The plumb lines would be tangent to the field lines where the field lines aren't radial.

[cameron marical]

so the plasma at the earths core is in a no gravity environment. sweet.

[Sisyphus]

so the plasma at the earths core is in a no gravity environment. sweet.

 

The Earth's core is solid, not plasma.

[alan2here]

Is the variation in the earths graverty greater or lesser neer the center compaired to on the surface?

[Sisyphus]

Is the variation in the earths graverty greater or lesser neer the center compaired to on the surface?

 

Greater, but only because it's denser at the center. If it was uniform density, then the change in force of gravity would be linear as you move closer or farther away from the center.

[alan2here]

Sugesting that there might be multiple centers from the point of view of a small ball falling in a large sphere of air in the middle of the world.

[east]

i do not undertsand the concept of multiple centers. a center is a center.

 

if you take an atom, it has a center. if you take a neutron it has a center. it you take a quark, it has its center. the sun, the moon, milky way, all has is centers.

 

so if you have multiple gravitional centers, there would still be a position which is the center of these centers, and that would be the true gravitional center of the earth. my original question of wether a plumbline would pass through it is i think answered, and sadly for me it's no. so now i would have to find another way to determine where the center of gravity for earth is. a plumbline just isn't enough i guess, but it was certianly a good budget science attempt for me

[alan2here]

Any mesurements you make would need to be exceptionally acurate to be effected by such variations.

[Duration]

Center of the Earth?

 

What diameter center are you referring to?

[alan2here]

Center of the Earth?

 

What diameter center are you referring to?

 

I presume he is refering to the one at 0 units in diameter :¬P