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Gravity and density 
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#1
Dec809, 08:43 AM

P: 78

Can we say that there is a direct relationship between the density of an object and the strength of it's gravity field? Can we come up with a mathematical model to describe the relationship between gravity and density?
Say we have an object that contains the same amount of matter as the black hole at the centre of the Milky Way. Say that this object takes up a lot of space, 2x the size of the Milky Way for example. This object, tho identical in mass, would have a very different gravity field to the black hole. For starters, this object would exert less gravitational force on another object than the black hole would at the same distance. Can we say that there may be a logarithmic relationship between the density of a body and the amount of spacetime curvature the body will cause? I hope these questions don't sound stupid! Thanks in advance for any replies.. ad 


#2
Dec809, 08:52 AM

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g = GM/r^2 and M = density * 4/3pi * r^3 so g = 4/3 pi G density * r 


#3
Dec809, 09:04 AM

P: 78

I'm just a lay nut tho so I'm probably way off here! 


#4
Dec809, 10:30 AM

P: 87

Gravity and density
Sincerely, FoxCommander 


#5
Dec1009, 10:07 AM

P: 78

What I'm getting here then is that gravity depends on mass, density and some sort of 'field' that permeates all of everything. Matter curves spacetime, or does spacetime curve matter? 


#6
Oct1611, 01:01 AM

P: 1

I have a question, probably me being stupid in my tiredness, but what is the relation to and object's density to its gravity if mass increases and volume stays the same?



#7
Oct1611, 04:18 PM

P: 143

m = DV Therefore, if Density doubles, mass also doubles, if Density triples, mass also triples hence, the increase in mass yielded by the increase in Density yields a proportionately stronger gravitational field per the same distance from the center of mass. 


#8
Oct1611, 05:44 PM

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P: 11,925

If you are far enough away from any object then you can consider all the gravitational forces as acting through its centre of mass.
But for objects other than spheres made up of shells with spherical symmetry, you may need to Integrate the gravitational affect of all the elemental parts, which is quite a complicated calculation. (There may be some short cuts for particular shapes) If an irregular object subtends more than a few degrees from the observer then its gravitational effect could probably be distinguished from that of an equivalent point mass. For example, the observer's orbit would probably not be a perfect ellipse any more. An orbit round a nebula could be pretty different from that around the star that eventually forms from it. (Not that you'd live long enough to get round all the way) 


#9
Mar1513, 01:46 PM

P: 8




#10
Mar1513, 01:50 PM

P: 8




#11
Mar1513, 02:36 PM

P: 696

Here's a link for your convenience: http://en.wikipedia.org/wiki/Shell_theorem 


#12
Mar1513, 02:48 PM

C. Spirit
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Fox was describing a solid sphere of approximately uniform mass density, in which case it is easy to show using a plethora of methods that [itex]F_g\propto r[/itex] within the sphere, where again [itex]r[/itex] is the radial coordinate from the origin centered around the sphere. This is in agreement with what Fox said. 


#13
Mar1513, 03:16 PM

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#14
Mar1513, 03:54 PM

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He could be confusing gravity with the pressure you would find inside a planet / star centre.



#15
Mar1513, 06:51 PM

P: 8

the equation is wrong r is not at the center of the out side of the shell it is at the center of the shell itself.if not then where is the gravity coming from?



#16
Mar1513, 06:54 PM

C. Spirit
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#17
Mar1513, 07:31 PM

P: 8

mass density is not uniform in a solid planet as mass density increases so will gravity.



#18
Mar1513, 07:51 PM

P: 8

the force of gravity always pulls towards the center of greatest mass AT



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