So I was in the shower today...

[Agamemnus]

[EDIT] On what aga just said I thought as well - wouldn't the ball at the centre of the Earth move as close as it can get to the sun or moon? Or if you exclude all celestial bodies, then it would move as close as it can get directly underneath the part of Earth with the greatest mass (say, the tallest mountain).

Well, not sure what you mean by "ball", but the distance factor in the equation probably makes the sun/moon have no effect on the density dispersion of the earth. The spot where magma/the highest density (the ball?) would be would not be affected by any mountains.. it's possible that it could be affected by the make-up of the Earth in terms of what particles it has and most greatly affected by size and overall mass of the Earth...


And, thank you, Mr Match. :winkwink:

[aetherfox]

Aga:

Actually, if you look at the formula, you will realise I am right. At a distance of 0, you are dividing by zero, which is mathematically defined to be infinity.

Since the average center of mass of all these particles making up Earth is the Earth's center, I stand by my argument.

Zack (and aga):

OK, imagine the Earth was actually a completely smooth sphere made of one element only. And you then performed the drilling scenario I specified. Then, the ball would hit that center mark and stay there. There will be equal force of attraction from all sides, and the ball will be on the average center of mass of the entire system.

Zack - I was reading some inredibly interesting stuff on graviton detection - there was something on space.com. I love that site.

And lastly, Aga - that [sic] was very American (or Canadian if they spell like Americans and if you are Canadian, but since it is an American thing to do, I stand by American ) of you.

[Radical Raccoon]

Aga:

Actually, if you look at the formula, you will realise I am right. At a distance of 0, you are dividing by zero, which is mathematically defined to be infinity.

Since the average center of mass of all these particles making up Earth is the Earth's center, I stand by my argument.

The formula is correct, but you are using it incorrectly.

If a ball is resting at the surface of the earth (m1) with a mass of 10, and the center of the earth (m2) has a mass of 1000 (just to make things easy) with a radius of 10 then:

pull = (m1-m2)/(d^2)
pull = (1000-10)/(10^2) (leaving out G to simplify things)
pull = 990/100 = 9.9

Now move the ball (m1) to the center of the earth and now you have:

pull = (1000-10)/(0^2)
pull = 990/0 = ERROR! Infinity!

But this is wrong. You are only taking 2 masses into consideration when there are actually 3.

Basically, if the ball is in the center of the earth then you have 3 masses to take into consideration: the ball, the half of the earth behind the ball, and the half of the earth infront of the ball.

Now if the ball (m1) is in the center of the earth, you have 2 halfs of the earth pulling on it. 2 center of masses in opposite directions that would be about 1/2 between the ball and the surface (500 units away).

pull1 = (500-10)/(5^2)
pull1 = 490/25 = 19.6

pull2 = (500-10)/(5^2)
pull2 = 490/25 = 19.6

So now you have a force of 19.6 pulling in both directions, resulting in a net zero force. Conclusion: you would feel no effect of the earth's gravitational pull if you were to reside in the center.

[Agamemnus]

Zack (and aga):

OK, imagine the Earth was actually a completely smooth sphere made of one element only. And you then performed the drilling scenario I specified. Then, the ball would hit that center mark and stay there. There will be equal force of attraction from all sides, and the ball will be on the average center of mass of the entire system.

Of course.

And lastly, Aga - that [sic] was very American (or Canadian if they spell like Americans and if you are Canadian, but since it is an American thing to do, I stand by American ) of you.

I didn't realize.. just thought it might be a better way of pointing things out like that than my usual long winded rant...

[Zack]

Might I note that division by zero is considered undefined and not infinite.
Infinite force is impossible, just like infinite energy, mass or acceleration. The law is F=(gm[1]m[2])/d^2, d≠0.

[Agamemnus]

0 distance between any two identifiable objects is also impossible...

[Mr Match]

0 distance between any two identifiable objects is also impossible...

You mean something like:

Asymptote; a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.

:-?

[TheAdventMaster]

Aga:

Actually, if you look at the formula, you will realise I am right. At a distance of 0, you are dividing by zero, which is mathematically defined to be infinity.

Since the average center of mass of all these particles making up Earth is the Earth's center, I stand by my argument.

Sure, but what's strange is the gravity from the outer Earth would be pulling you and trying to average your mass equally throughout the center, whilst pressue from the incoming mass would crush and/or melt you

Infinite force is impossible, just like infinite energy, mass or acceleration. The law is F=(gm[1]m[2])/d^2, d≠0.

That's what they say...But I think the disbelief in infinite energy's just crap.

If that's the case, then something besides energy itself should be used to create it.

If you think about it, energy is infinite proportianate to the amount of mass in a particle, says E=mc2. The reaction of one amount of mass can cause enough energy to move much of it. Eventually that mass should once again slow down and reverse it's path, accelerating at such high speed a big bang would occur at the averaged center of all the mass. Repeat. The reactions shouldn't ever slow down, because they should occur with more force each time, or equal force as before.

For some reason everyone acts like it's such a big deal Einstein figured out E=mc2 though...

Let's see, measure the mass of all the objects in our reaction. *reaction happens* Measure the energy output. Measure the remaining mass...A pattern here, anyone?

[Agamemnus]

TheAdventMaster: you're crazy. I'll get back to your comments later... when I have strength.

I just thought of a nice example to disprove aetherfox's "one mass" response:

Consider a spherical shell where all the mass in on the outside in a small "crust" and there is nothing inside. Let's just assume that this is a man made object.

Now...

Given it is big enough, let's say the size of Earth, gravity would actually be centered all along the "crust" instead of in the center. Anything originating in the center of the sphere "falls" down to the crust. Clearly you can only use individual particles, instead of the entire mass, to explain this behavior ...

Also:

I've just invented a method for travelling faster than light. Simply put a series of equally strong black holes into a conical shape with an opening at the tip. Go in from the outside spot and you are "funneled" through it at the other end. Faster than light...

[anarky]

0 distance between any two identifiable objects is also impossible...

You mean something like:

Asymptote; a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.

:-?

Wha?? That sentence is nearly too long to comprehend... Maybe I'm tired...