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Author Topic: Which way does gravity attract on objects with irregular shapes and densities?  (Read 6358 times)

Offline briligg

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Gravity comes from mass, right? So, if the mass of a large object isn't concentrated in its core, how would gravity pull at things on its surface? Really large things become spherical because the gravity that comes with very heavy things makes that the only stable shape, but what if the shape was different, just supposing? What if the core of the Earth wasn't there, say - how would gravity affect you if you were on the inside surface of the hollow spherical space that would create? Would the net gravity pull you towards the surface of the Earth 'above' you, and stick you to the wall of the hollow space? Would your experience of gravity be that it is a lot less, because of the effect on you of the mass on the other side of the hollow space?


 

Offline katesisco

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here is a phenomenal release from the European Space Agency:  http://www.bbc.co.uk/news/science-environment-12911806 [nofollow]

Gravity questions begin here.
 

Offline Bored chemist

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"If the body is a spherically symmetric shell (i.e. a hollow ball), no gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell."
from
http://en.wikipedia.org/wiki/Shell_theorem

But, in the more general case, the object attracts things towards its centre of gravity whatever shape it is.
 

Offline Pikaia

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in the more general case, the object attracts things towards its centre of gravity whatever shape it is.
That is not true. Suppose we have a dumbell shape, ie two equal spheres connected by a light rod. The COG is the mid point of the rod, but an object near one of the spheres will be attracted towards it, not towards the COG. In general there is no easy solution.

Incidentally, the result for the inside of a sphere also applies to a prolate spheroid (and presumably an oblate spheroid) if the inside surface is similar to the outside surface - see page 19 of:

www.itp.uzh.ch/~justin/AstrophysicalDynamics/Lectures/lecturenotes.pdf
 

Offline Bored chemist

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Oops, I missed the word distant.
In the more general case, the object attracts distant things towards its centre of gravity whatever shape it is.
 

Offline briligg

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Oooo - it's complicated! And there's things to read. I like that.
I'll go look at those links this evening

katesisco - i saw that model. Is it known what specifically is making gravity higher in the yellow areas? I figured probably not, i read a light article about it which didn't mention any explanation. Would it be denser materials closer to the Earth's surface in those places? Or could it be that Earth's nickel/iron core slightly bulges upwards in those areas? Also, the article didn't mention how much difference there is between the blue places and the yellow places. Do i weigh a few grams more in Europe than in Brazil?
« Last Edit: 06/04/2011 21:17:57 by briligg »
 

Offline Geezer

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here is a phenomenal release from the European Space Agency:  http://www.bbc.co.uk/news/science-environment-12911806

Gravity questions begin here.





How about that! It's strongest in the yellow bits. Does that mean the people there are denser?


 

Offline Phractality

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For a general solution, you must work out the tripple integral, plugging each little piece of the mass into Newton's gravity equation. This has been done for many common shapes, and the results can be found on the internet.

For a hollow spherical shell, the gravity outside the shell is equivalent to the whole mass concentrated at the geometric center; inside the shell the mass of the shell contributes zero to the total gravity. So any loose pieces inside a hollow Earth would gravitate toward each other as if the shell was not there. But the two halves of the shell are attracted to one another so hard that they tend to crumble, and it wouldn't take long for the whole thing to collapse into a solid ball in the middle. That's why the "hollow Earth" theories are such a load of krap.

EDIT: The variations shown on the potato Earth image are surpirsingly large. The darkest blue is about -70 mGal, and darkest red is about +70 mGal. (The color code in the OP image is different; yellow is stronger than red.) Nominal gravity is about 980 mGal. If your scales are calibrated to force, rather than mass, you might weight 10% more in the Andes than in Sri Lanka. Good to know if you're trying to lose weight. Density, is a measure of mass, rather than weight, so you can't get smarter by moving to Sri Lanka.
« Last Edit: 07/04/2011 00:35:37 by Phractality »
 

Offline Geezer

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Density, is a measure of mass, rather than weight, so you can't get smarter by moving to Sri Lanka.

Dang! I always thought that was how Arthur C. Clarke pulled it off.
 

Offline JP

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Nominal gravity is about 980 mGal[/url]. If your scales are calibrated to force, rather than mass, you might weight 10% more in the Andes than in Sri Lanka.

I think your numbers might be off by a few factors of 10.  I hadn't heard of a Gal before, but apparently it's 0.01 m/2.  Since gravity is usually taken as ~9.8 m/s2, it's equivalent to 980  Gal, which is 980,000 mGal (1000 mGal to 1 Gal).  I think the 980 is a typo in that link.  That makes the variations about 0.01%, which seems much more reasonable.
 

Offline Phractality

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I think your numbers might be off by a few factors of 10.  I hadn't heard of a Gal before, but apparently it's 0.01 m/2.  Since gravity is usually taken as ~9.8 m/s2, it's equivalent to 980  Gal, which is 980,000 mGal (1000 mGal to 1 Gal).  I think the 980 is a typo in that link.  That makes the variations about 0.01%, which seems much more reasonable.

Yes; that sounds much more reasonable, and it checks out with Wolframalpha.com. I also never heard of Gal before; I though a mGal was female midget. If you click my source, you'll see that I was mislead. I have emailed the author of that page.
 

Offline Geezer

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Nominal gravity is about 980 mGal[/url]. If your scales are calibrated to force, rather than mass, you might weight 10% more in the Andes than in Sri Lanka.

I think your numbers might be off by a few factors of 10.  I hadn't heard of a Gal before, but apparently it's 0.01 m/2.  Since gravity is usually taken as ~9.8 m/s2, it's equivalent to 980  Gal, which is 980,000 mGal (1000 mGal to 1 Gal).  I think the 980 is a typo in that link.  That makes the variations about 0.01%, which seems much more reasonable.

Brilliant. Just what we need - yet another unit of measurement. And this one is based in centimeters! I'm sure the SI folks will be delighted.

(BTW, I'm in the process of having SI recognize the "Geezer", but we are still haggling over the appropriate abbreviation.)
 

Offline Bored chemist

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" I hadn't heard of a Gal before, but apparently it's 0.01 m/2"
Pardon?
 

Offline Geezer

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" I hadn't heard of a Gal before, but apparently it's 0.01 m/2"
Pardon?

Well right!

I should have mentioned that I am proposing SI adopts the Geezer to replace the Kilogram as the fundamental unit of mass in the SI system. This would immediately eliminate the most unfortunate recursive use of a multiplier defined within the system to define a fundamental unit of the system.
« Last Edit: 07/04/2011 07:41:57 by Geezer »
 

Offline CliffordK

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here is a phenomenal release from the European Space Agency:  http://www.bbc.co.uk/news/science-environment-12911806

Gravity questions begin here.

How about that! It's strongest in the yellow bits. Does that mean the people there are denser?
That looks a lot like the GRACE Geoid
http://en.wikipedia.org/wiki/Geoid

http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment



The one fallacy of it is that it is gravity as measured from space, and not gravity as measured from the surface of the earth.

So, from space, the Alps, Andes, Rockies, Himalayas, etc, all show higher gravity.  Yet, on the surface, they will actually show lower gravity.
 

Offline JP

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" I hadn't heard of a Gal before, but apparently it's 0.01 m/2"
Pardon?


Heh.  Apparently I made a couple of typos in that post.  I tried to type
Code: [Select]
s[sup]2[/sup] I ended up with that somehow.  :p

Apparently it's 0.01 m/s2.  I don't know why it's given it's own name.
 

Offline Geezer

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" I hadn't heard of a Gal before, but apparently it's 0.01 m/2"
Pardon?


Heh.  Apparently I made a couple of typos in that post.  I tried to type
Code: [Select]
s[sup]2[/sup] I ended up with that somehow.  :p

Apparently it's 0.01 m/s2.  I don't know why it's given it's own name.

I kinda liked the original better. Let's see, 0.01 half meters, or 5 millimeters. It certainly simplifies the concept a lot.
 

Offline Airthumbs

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I take it that these amazing images are not a static representation over time?
 

Offline briligg

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Airthumbs - i'm not sure what you mean. They show how much gravity pulls on different places on the earth's surface. Certainly the places with stronger gravity move over extremely long periods of time, since the earth is molten rock under the surface, which is always moving. This is the first time full gravity maps have been made though, so i doubt anyone has had a chance to check for changes over time yet.
 

Offline Airthumbs

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Well as I am in one of the yellow areas it might explain why I feel so heavy!!  It would be nice to know when a blue area might come along and relieve me of my density issues!  ;D
 

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