Question about gravity and density

[ranrod]

Sorry, noob question. On the Discovery channel I've seen a couple of programs where they had physicists trying to explain black holes. The physicists said that if you collapse matter to a small enough space, you would get a black hole. One of the Physicists examples was that if you collapsed Earth to the size of a marble, you'd get a black hole.

I didn't think gravity had anything to do with density. Isn't the gravitational formula unrelated to density? I think it's something like ((M1 * M2)/D^2)*G; where the Ms are the masses of the objects in question, D is the distance between them, and G is the gravitational constant. Whether you stretch out Earth to be the size of Jupiter or you shrink it down to the size of a pinhead, gravity wouldn't change, according to this formula. Is this formula too old-school/obsolete?

Does density play a part in gravity?

 

[mgb_phys]

Gravity doesn't depend on density as such, but it does depend on the mass of an object and how far you are from it.
if you want to get closer to a larger mass you have to fit that mass into a smaller space and so must have a higher density.
This is called the surface gravity, the attraction of the Earth to a distant object only depends on Earth's mass (and distance), but the force of gravity on an object on the surface of the Earth depends on mass and the radius (distance from the centre) if you made the Earth denser - you would keep the mass but the distance would be less and so the gravitational attraction would be stronger.

To get a black hole, which is all about surface gravity, you need to compress a mass m into a radius less than; r = 2GM/c^2
So for a given mass black hole you can work out it's density.

interestingly because a black hole's radius is proportional to mass, but the density of an object is proportional to r^3 the bigger a black hole the less dense it is.
you can picture this if you double the mass of a black hole it's radius gets twice as big, so the volume gets 2^3 =8x as big, but the density is now only 1/4 as much.

 

[ranrod]

oh, that makes perfect sense :)
Is that why they think you can get micro-black holes?

 

[Chalnoth]

oh, that makes perfect sense :)
Is that why they think you can get micro-black holes?

Micro black holes are still highly speculative and often considered to be unlikely. At least for energies we are likely to achieve on Earth.