Attracted to the opposite side of the earth?

[pallidin]

I hope this doesn't seem like a silly question.

On earth, mass is attracted towards the center, we are told.
But, if you draw a line towards the center of the earth, isn't there MORE mass if you keep drawing the line to the opposite side?

That is, are we being attracted to the center of the Earth only, OR to its opposite side through the center?

Hope this doesn't mess with you head as much as it does mine.

 

[Nabeshin]

You are being attracted to every single atom the Earth is composed of. When you sum over all the atoms of the earth, you find that the attractive force is exactly as if all the mass of the planet were concentrated at the center, so for all intents and purposes you are pulled to the center.

 

[pallidin]

I'm sure your right. Here's a VERY simplified diagram, though I'm sure you are correct.

 

[Nabeshin]

Ok... would you mind explaining your diagram a bit? I'm still not entirely sure what you're suggesting.

 

[pallidin]

Ok... would you mind explaining your diagram a bit? I'm still not entirely sure what you're suggesting.

Actually nothing more than your fine initial response.
The large circle is the earth, the small circle is it's center. The blue and red squares are, say two people on the surface.

When I was a kid(am much older now) I was told that we are attracted to the center of the earth, as if that were the PRIMARY attraction. I call BS.
Instead, like you said, the collective net force vector result is a "center" which happens to coincide with the center of the Earth due to the roughly spherical geometry of the earth.

I don't disagree with you at all. I just disagree how I was taught.

 

[Nabeshin]

Ay well, we teach things in strange ways sometimes because that's the easiest way for it to be learned. I'm not sure as a kid I could've worked my way through the vector sum and reasoned that they all must cancel to give a central attraction. It is a very important result, Newton's shell theorem though. Essentially we tell kids (or anyone who's not a physicist) the result without explaining the why.

 

[AndyK]

Your drawing is correct though. It is not wrong, it is just incomplete. It suggests that the body is only being attracted to the other side of the earth, directly the crust. Technically you are being drawn towards the center of the Earth much harder than the other side of the Earth because of the 1/r^2 on the gravitational force equation. Since Earth is pretty much round and spherical we assume that all if its mass lies in one point right at its center, by taking advantage of symmetry. A human being is really small with respect to Earth therefore he gets to be also assumed as a point mass ( the proof for this is to take the limit as one of the variables gets really large), therefore we say that the gravity points toward the center of the earth. Point mass to Point mass.
In reality this is not exactly true and it depends on where you are exactly geographically (equator and north pole for example) and the composition of material beneath you.

 

[pallidin]

Makes perfect sense to me. Thank you.
BTW, your really good at explaining things. I just wish my teacher at that time would have said something like "well, kids, its a bit more complicated than what I showed you. If anyone is interested, see me after class"

Anyway, Nab, much appreciate your time and excellent communication skills...

 

[pallidin]

Technically you are being drawn towards the center of the Earth much harder than the other side of the Earth because of the 1/r^2 on the gravitational force equation. QUOTE]

But isn't there 100% MORE mass on the other, linear, side of the "center"; thus adding to the mass of attraction on my body?
I think Nab explained it correctly. Not that you haven't, but I understand:

"You are being attracted to every single atom the Earth is composed of. When you sum over all the atoms of the earth, you find that the attractive force is exactly as if all the mass of the planet were concentrated at the center, so for all intents and purposes you are pulled to the center."

 

[Matterwave]

You are being attracted to both. The expression "you are being attracted to the center of the Earth" is only supposed to give you a direction for the force...e.g. down!

The net sum of effects of the mass of the Earth on you is that it pulls you down. This is certainly obvious. The direction down happens to go through the center of the Earth.

Since you aren't going anywhere, it doesn't really matter which "piece" you think you are being attracted towards. Just know that the direction is down!

However! If you stood at the other side of the Earth, you would still be attracted downwards. Only if you stood at the very center of the Earth would you not feel any net attraction - the gravity of the Earth would be pulling on you equally in all directions. In this sense, if you constructed a tunnel through the center of the Earth to the other side, and fell into this tunnel you would oscillate back and forth and eventually come to rest at the center of the Earth (after frictional forces dissipate your kinetic energy...and assuming you don't melt).

In this way, it may actually be more accurate to say that you are being pulled towards the center of the Earth, rather than the other side. If you ask me, it's really just semantics. The words are simply there to tell you a direction.

 

[pallidin]

In this way, it may actually be more accurate to say that you are being pulled towards the center of the Earth, rather than the other side. If you ask me, it's really just semantics. The words are simply there to tell you a direction.

If I take a bowling ball and saw it in half, lay it thusly flat on a table and glue a BB on the very top, the BB will experience "x" attraction to that half bowling ball.
If, I use a whole bowling ball instead, the attractive force will be additive of that second half of the bowling ball.
Therefore, the "other side" of the bowling ball has a direct, significant impact on attraction, perhaps even more so than it's "center"

I really don't think it's semantics. I think it's physics.

 

[Matterwave]

What is your definition of "pulling you towards the center"?

I need to hear your definition first. What is your argument exactly? can you make it clearer first?

 

[pallidin]

My argument is that we are not actually "directly" attracted to the center of the earth.
Rather, that there is a cumulative attraction of geometric force vectors to "a center" but significantly requires the "other half" of the Earth to do this.

As such, my argument remains that our attraction towards the "center" of the Earth is NOT BY SOME OVERRIDING MASS in the center but requires the whole Earth sphere.
Much like Nabeshin explained.

In my opinion, direct, significant gravitational attraction to the opposite side of the Earth is required.

 

[Matterwave]

Is that not a supremely obvious statement? Who ever said that the Earth was composed of a uber massive center and nothing else? I don't think anyone is making the claim that the Earth is some sort of mass that is all concentrated at the center...and the rest of Earth is...Styrofoam or something?

Did your teachers teach you that the center of the Earth is all that is doing the attracting, and that the rest of the Earth does nothing?

EDIT: Perhaps my post seems condescending. I should have phrased it some other way...but I did not mean you any disrespect.

 

[sophiecentaur]

Did your teachers teach you that the center of the Earth is all that is doing the attracting, and that the rest of the Earth does nothing?

There's a fine line in a noisy classroom between "doing all the attracting" and "behaves as if it is doing all the attracting".

I should mention that this only applies for a spherical Earth consisting of shells of uniformly dense material (each shell that is). Attraction to the centre of mass of any other object only applies at great distance. Imagine a pair of huge dumbells and imagine being close to one of them. In what direction would you be attracted- to the mid point (the cm of the pair) or to the one nearest you?