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is gravitational force solely dependant on mass, or is density a factor as well?

foofighter

By foofighter
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foofighter

foofighter

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Earth produces 1G - is this solely dependant on mass, or density as well? In other words, lets say I have a less massive object, with an extremely high density. Can that exert 1G on something very close to its center of gravity? or must you have as many atoms as earth regardless of density, to produce 1G? thanks

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Klaynos

Klaynos

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It is dependent on mass and 1/radius, so from that you can infer that as you can get closer to more dense objects then if you had an object more dense than the earth then it could produce a force of mg (where g is 9.81ms-2) with less mass BUT not at the same distance from the centre of mass...

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swansont

swansont

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Mass and density are directly depended from one another. You can't have a very light object with very high density. See:

 

[math]\rho=\frac{m}{V}[/math]

 

Sure you can. Small mass, but even smaller volume.

 

Earth produces 1G - is this solely dependant on mass, or density as well? In other words, lets say I have a less massive object, with an extremely high density. Can that exert 1G on something very close to its center of gravity? or must you have as many atoms as earth regardless of density, to produce 1G? thanks

 

Yes, you can. a = GM/r^2, so a planet with half the radius of earth would need only a quarter of the mass to produce 1g; it would have to be twice as dense to do this

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Bignose

Bignose

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Doesn't matter. Your statement was incorrect; you can have an object that has a small mass but a large density.

 

Just to back swansont up here -- consider a micron size particle of gold (not all that uncommon in the making of catalyst particles). Gold has a density of 19,320 kg/m^3 (almost 20 times that of water) but if it was only a droplet with a micron diameter, it would only weigh 8.1*10^-8 milligrams. Pretty light object with a very high density.

 

It is important to note the difference between intensive and extensive properties of objects. An intensive property (also known as a bulk property) does not depend on the size of the system being investigated. For example, the density of gold is 19,320 kg/m^3 no matter if we look at a drop a micron across, a millimeter across, a meter across, or a kilometer across. Other intensive properties are temperature, viscosity, chemical potential. An extensive property does depend on the size of the system being looked at. Some examples of extensive properties are mass, length, volume, mass, total energy.

 

The gravitational pull is based on extensive properties -- the gravitational pull between two masses depends on the masses of those two objects and the distance between them. Assuming they are far enough away, then they can probably be treated as point sources of mass in the center of mass of each object.

 

If they are not far enough away, the local density of objects could have a small effect. I.e., compare standing next to a mountain versus standing next to a plain. There will be a small gravitational pull towards the mountain as well as toward the center of the earth versus standing on the plain you will only be pulled toward the center of the earth. Now, the effect is small, and in almost every single case negligible. As a third example, if you were standing on a plain and on your left side under the ground was a very large deposit of gold and on your right side was a very large deposit of aluminum (density 2700 kg/m^3, much less dense than the gold) then there would be a slight pull toward your left side, like with the mountain. Again, in this case, the local density has a gravitational effect. To be completely accurate, the way you figure the gravitation pull in this case would involve the integral of all the mass.

 

But, get far enough away, and these local density changes get smeared together, and again you can treat it all as one point source of mass. It is very rare that the level of detail involving local density changes is needed.

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