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guyver23    181
A couple of years ago I took Physics I in college but learned little from it. I've recently decided to start studying it on my own from a physics textbook. I've learned that the effect of gravity varies slightly depending where you are on the surface of the Earth. How would does gravity vary as you get closer to the center of the Earth? Like in Journey to the Center of the Earth. Intuitively, I feel that the effect of gravity would become more intense as you got closer and closer to the Earth's core. This isn't a homework question, it's just something I was thinking about after reading more about gravity in my physics book. I apologize if this question has an obvious answer that I have overlooked.

Thanks!

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Daivuk    413
I think the closer you get to the center of the earth, you have less and less gravity. Because it becomes equally in all other directions.

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guyver23    181
[quote name='Daivuk' timestamp='1302895152' post='4798883']
I think the closer you get to the center of the earth, you have less and less gravity. Because it becomes equally in all other directions.
[/quote]

So, if the center of the Earth were hollow and you were inside of it, you would be floating? Or have I misunderstood what you were saying? Thanks for replying!

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frob    44962
You are still attracted to every particle in the universe, and the attraction is proportional to the distance. You are closest to Earth so those particles have the biggest attraction.

If you were in the center of the Earth your net attraction to the particles of the Earth would be roughly zero, because you would be roughly at its center of mass. You would be pulled roughly in equal amounts in each direction by them.

As you approached the center of the planet, your next biggest attractors would be the Sun and moon. You have those attractions already, you just don't notice them. Human bodies aren't really meant to detect that type of forces.

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Emergent    982
You might want to look up [url="http://en.wikipedia.org/wiki/Gauss%27s_law"]Gauss' Law[/url]. It's usually described for electric charges and electric fields, but it also works for masses and gravitational fields.

Simply, the flux of the gravitational field across a closed surface is proportional to the amount of mass contained within the surface. Now, consider a sphere, centered at the center of the earth, with a radius less than the earth's. Assuming a constant density of the Earth (which isn't true, but go with it), you can compute the mass enclosed, and figure out the flux. Then you can divide this by the area of the sphere, to figure out the flux per unit area, and hence the strength of the field. You'll see how the field drops as you approach the center. In fact, try plotting this as a function of distance from the center of the earth. You'll get that the field is zero at the center, increases linearly until you reach the surface, and then drops off as 1/r^2. It would probably be a good exercise to work out the details yourself!

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taby    1265
While Gauss' law is nice, you actually should be checking out Newton's Shell Theorem.

Fancy rabbits with oversized egos.

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szecs    2990
(If the density of the Earth would be constant) the absolute value of the gravity is a linear function.
[attachment=1912:fold.JPG]

Ahh, beaten by Emergent...

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taby    1265
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.

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szecs    2990
[quote name='taby' timestamp='1303220324' post='4800348']
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.
[/quote]

what??

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taby    1265
[quote name='szecs' timestamp='1303221595' post='4800362']
[quote name='taby' timestamp='1303220324' post='4800348']
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.
[/quote]

what??
[/quote]

Again, I love you, and I am still very sorry that I didn't get you a gdnet Christmas present like I was supposed to.

However, you didn't beat emergent to anything.

Newton couldn't publish his Principia until he finished his shell theorem. It was the crowning jewel, and he struggled with it for years -- co-discovering calculus along the way in order to finally succeed.

Gauss knew that, and so should you guys. To ignore it is very disrespectful to Newton. That said, I rated emergent ++ last night just to prove that I'm not trying to be a jerk out of spite. This is very important history.

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szecs    2990
Well, I don't really get it. A question was asked and some answers were given. Usually we don't cite/mentioned everyone involved or even the discoverer about a topic/formula/etc in our posts, we just use them. It's jut a forum after all. Does this make almost every posts disrespectful to the authors/discoverers of a particular subject? Maybe I miss something though...

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taby    1265
[quote name='szecs' timestamp='1303222570' post='4800368']
Well, I don't really get it. A question was asked and some answers were given. Usually we don't cite/mentioned everyone involved or even the discoverer about a topic/formula/etc in our posts, we just use them. It's jut a forum after all. Does this make almost every posts disrespectful to the authors/discoverers of a particular subject? Maybe I miss something though...
[/quote]

Telling someone to look into Gauss' law when the shell theorem would suffice is practically the same as me telling them to look into charged black holes in N=32 spontaneously broken [url="http://www.desy.de/%7Esimon/teaching/lectures.pdf"]supergravity[/url] in order to get the idea about how Newton's law of universal gravitation works. It's just a tiny bit overkill, it totally messes with a student's sense of perspective, and it makes me wonder if anyone here even bothered to google for "gravitation" before providing answers.

There, I said it how it is. I was so much nicer in my previous posts because it was not yet appropriate to give a full dressing down. To give credit where credit is due though, at least you guys aren't being total pig racists like the morons in that other thread. For that, I rated you ++ on your replies.

I'll be back in another month or so to check for more gravitation threads. Cya.

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TheTroll    883
Actually electromagnetism and gravity act a lot a like in many situations, so many of the ideas and formulas from one can work for the other. It is why early on people were expecting that the EM force was going to be unified with gravity fairly quickly. That didn't end up being the case.

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owl    376
[quote name='taby' timestamp='1303223009' post='4800372']
To give credit where credit is due though, at least you guys aren't being total pig racists like the morons in that other thread.
[/quote]

W T F ? [img]http://public.gamedev.net/public/style_emoticons/default/huh.gif[/img]

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Tachikoma    575
Interestingly, the gravity is [url="https://secure.wikimedia.org/wikipedia/en/wiki/Gravity_of_Earth"]somewhat stronger[/url] few km under the planet's surface.

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Hodgman    51324
I think Taby forgot to take his medicine again.

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Emergent    982
[quote name='taby' timestamp='1303182694' post='4800159']
While Gauss' law is nice, you actually should be checking out Newton's Shell Theorem.
[/quote]

Good call. I hadn't remembered that name. And I like the Wikipedia article on it.

I don't see there being an either-or here, though. The Shell Theorem was proven first, then later turned out to be a special case of the more general Divergence Theorem, a.k.a Gauss' Law -- and then [i]that[/i] later turned out to be a special case of Stoke's Theorem (and, who knows, maybe that has some yet-more-general statement in Category Theory; I don't know). Maybe we all have different thresholds for how high up in generality/abstraction we're happy to go. Me, I'd have gotten annoyed with someone offering Stoke's theorem and demanding that the OP learn about exterior derivatives, but I thought Gauss' Law was reasonable. Personally, I find it easier to remember (as evidenced by me forgetting the Shell Theorem), and easy enough to visualize.

Either way, I do appreciate the historical perspective. It's true; Newton had that part of classical gravitation wrapped up before Gauss.

[quote]Fancy rabbits with oversized egos.[/quote]

I hope you're talking about Gauss and not me!