How density is related to Gravity ??

[Anand7sem]

Hi all,

I need a help to find the answer of following.

As per Wikipedia and other sources Black hole is created after death of a Star. As per them when such a huge mass of supernova remnant collapses on itself and the small point(core) create an extremely strong gravitational field due to the huge mass got captured in a small point. But I can't understand what is the relationship of "volume" of the remnant to gravitational field ?

When same mass(or greater) was a size of red Giant then there wasn't such a strong gravitational field there. But when the volume got smaller then how the Gravitational field got stronger ??

Thanks in Advance

Edited February 19, 2014 by Anand7sem

[Strange]

Gravity is dependant on mass and distance.

 

So, for example, the gravitational effect of the your red giant is exactly the same as the effect of a black hole of the same mass at the same distance.

 

The only difference with a black hole is that it has a smaller radius so you can get closer, and therefore to a place where the force of gravity is much greater than the red giant.

 

The radius of a black hole is proportional to its mass. The volume increases with the cube of the radius and so large black holes have quite low average density.

[Endercreeper01]

A black hole's exterior has the same gravitational pull as something else with the same mass and distance from the object. This is the shell theorem, and it was proven by Issac Newton. Density does not have an effect on gravitation.

[swansont]

A black hole's exterior has the same gravitational pull as something else with the same mass and distance from the object. This is the shell theorem, and it was proven by Issac Newton. Density does not have an effect on gravitation.

 

It does, though it's perhaps a bit subtle and not addressed by the shell theorem: the important quantity here is surface gravity, and a mass of higher density allows an external object to be closer to it. The earth is not a black hole because the density is too small. It's not that the mass is too small, it's that the mass is not compacted enough, and when you increase the density by making it smaller, the surface gravity increases.

 

IOW, for two objects of the same mass what you say is true as long as you are outside the radius of the larger object. (r > R). Not true for r < R

[Schneibster]

As a fun fact, the Schwartzchild radius of the Earth is, IIRC, around the size of a pea.

[Greg H.]

It helps if you look at the equation for surface gravity in terms of density:

 

[math]g = \frac{4\pi}{3}G \rho r[/math]

 

Where [math]\rho[/math] is the density. As you can see, as the density increases, so does the surface gravity.

 

It can be further expanded by looking at

[math]\rho = \frac{m}{v}[/math], so

[math]g = \frac{4\pi}{3}G \frac{m}{v} r[/math], where

m = mass, and

v = volume of the object in question.

 

From this we can see that if the mass increases for a fixed volume, or if the volume decreases for a fixed mass, the surface gravity will increase.

 

Note, however, that actually calculating the surface gravity of a black hole is a good deal more complex, because you have to treat them in relativistic terms.

Edited February 19, 2014 by Greg H.