What is the relationship between gravity and density?

[muneer Mohsen samih]

What is the relationship of gravity to density?
In black holes the cause of gravity is that the star shrinks and becomes dense.
But Jupiter's gravity is more than the Earth's gravity, although its density is lower?
Is the sun's gravity more than the Earth's gravity, even though the intensity of the sun is less than the density of the earth?

I wanted to help explain in detail so I understand

 

[phinds]

What is the relationship of gravity to density?

If you are far away, the density is irrelvant, only the mass matters. See below regarding density.

In black holes the cause of gravity is that the star shrinks and becomes dense.

No, absolutely not. The cause of gravity is the mass.

But Jupiter's gravity is more than the Earth's gravity, although its density is lower?

My point exactly. Gravity is a function of MASS, not density. The place where density comes in is that for dense objects, you can get closer to the center of mass than if they were less dense.

Is the sun's gravity more than the Earth's gravity, even though the intensity of the sun is less than the density of the earth?

Of course the sun's gravity is more than Earth's. The sun is WAY heavier than the Earth.

 

[Drakkith]

Both Jupiter and the Sun are composed mainly of gaseous substances, which are much less dense than solids are. The Earth and the other inner planets are composed of rocky materials and metals. This gives a much higher density than gas giants and stars, even though the overall mass is much lower for the Earth.

Is the sun's gravity more than the Earth's gravity, even though the intensity of the sun is less than the density of the earth?

Yes. If you go out to a certain radius from the Earth or from the Sun, you will find that the Sun's gravity is much, much stronger than the Earth's. It's only stronger here on Earth because we are within a few thousand kilometers of the center of mass of the Earth, but millions of kilometers from the Sun.

No, absolutely not. The cause of gravity is the mass.

I think he means that the star shrinks and becomes more dense, leading to higher gravity near the star (black hole). Not that the source of the gravity is the density.

 

[phinds]

I think he means that the star shrinks and becomes more dense, leading to higher gravity near the star (black hole). Not that the source of the gravity is the density.

Well, I was careful to point out that proximity matters, for that very reason.

 

[Dale]

What is the relationship of gravity to density?

In Newtonian gravity the relationship is $\nabla \cdot \mathbf{g} =-4\pi G \rho$

In GR that is just one component of gravity, so it is still approximately true but there are additional terms required for extreme situations

 

[muneer Mohsen samih]

thanks for you
also
Is there a program that calculates and solves the equations of tensor?

 

[Android17]

Gravity acts on the centre of gravity which is normally the centre of the core. Sun's core must be denser than Earth's core. Sun's core 150g/cm3 and Earth's core is just 12.8 g/cm3. Gravity acts as if all the mass is concentrated in the center of gravity even if the weight is distributed over large expanses of space.

Objects density has to do a lot with gravity because black holes have very high gravity because all of their mass is inside a small volume of space.

 

[jbriggs444]

Objects density has to do a lot with gravity

A lot to do with surface gravity because the surface is closer to the core. Utterly irrelevant to gravity at a distance.

[One assumes that we are holding mass fixed and varying density rather than holding volume fixed and varying density]

 

[muneer Mohsen samih]

This effect is on the surface only, but there is a question how can the black hole eat the galaxies and the galaxies are away from it?

The black hole The gravitational force is excessive at the surface when a radius less than the radius when it was a star but how it will affect the galaxies away from it , which is far beyond the radius of the star before it dies and be a black hole

 

[cosmik debris]

Holding mass fixed a denser object will have larger internal pressure and more gravity won't it?

Cheers

 

[phinds]

Holding mass fixed a denser object will have larger internal pressure and more gravity won't it?

Cheers

No. It's the MASS that creates gravity, not density. True, you get a SURFACE gravity that higher with a denser object but so what? Jbriggs already pointed this out and so did I.

If you start off with X grams and it condenses to a 1 meter ball, that has a certain gravity and if it condenses to a 1cm ball, it still has the same gravity (again, SURFACE gravity is higher but that doesn't seem to be what you are asking about)

 

[davenn]

This effect is on the surface only, but there is a question how can the black hole eat the galaxies and the galaxies are away from it?

it doesn't

The black hole The gravitational force is excessive at the surface when a radius less than the radius when it was a star but how it will affect the galaxies away from it , which is far beyond the radius of the star before it dies and be a black hole

it won't

 

[cosmik debris]

No. It's the MASS that creates gravity, not density. True, you get a SURFACE gravity that higher with a denser object but so what? Jbriggs already pointed this out and so did I.

If you start off with X grams and it condenses to a 1 meter ball, that has a certain gravity and if it condenses to a 1cm ball, it still has the same gravity (again, SURFACE gravity is higher but that doesn't seem to be what you are asking about)

Thanks for your reply. The source of gravity is the stress-energy tensor not just mass (I know you know this), isn't the pressure inside the smaller ball larger?

Cheers

 

[phinds]

Thanks for your reply. The source of gravity is the stress-energy tensor not just mass (I know you know this), isn't the pressure inside the smaller ball larger?

Cheers

Yes, it is, but since in my example, both final sized balls started off with the same mass, they have to end up with the same gravity. The contributions to the stress energy tensor in each case ultimately all comes from the original mass.

The ultimate example of this would be that far from the surface, it doesn't matter whether a given amount of mass is from a really large star or from a black hole of the same mass.