# Gravity - a function of mass or of density?

1. Jul 12, 2004

### alpha_wolf

If I understand correctly, according to phenomena such as black holes, the force of gravity is a function of density. And yet, newtonian physics do not appear to take volume in to account, and state that gravity is a function of mass alone (and distance of course). Is this just one of the shortcomings of newtonian gravity, or is there something more to it? What is really going on?

2. Jul 12, 2004

### chroot

Staff Emeritus
In what way is the gravitational force due to a black hole dependent upon density?

- Warren

3. Jul 12, 2004

### syano

A similar question has confused me before as well. I think I half way understood it, but have forgotten it now.

The Schwarzchild Radius talks about how a critical limit is met when there is a certain amount of mass within an object that has a certain radius. Which sounds similar to talking about the density of an object?

For instance, when a very large star dies it becomes denser and may turn into a black hole if that Schwarzchild limit is met… However the large star still contains as much mass as it had when it was alive right? But its density has greatly increased.

Perhaps my confusion lays here?… As the distance between the surface of an object and the center of it decreases…the gravity between an object on the surface and the center of the object increases. And if the distance between the surface of an object and the center of the same object decreases then that object has to become denser. Which makes it seems like BHs are related to density?

That was worded poorly so I’m not sure if it was understandable… Let me try again..

Gravity is dependant on the mass of two objects and the distance between them right? So lets say a person is standing on a surface of a star that has a 100,000 km radius and it takes this person “x” amount of energy to jump two feet into the air… Now let’s say the star dies and has the same amount of mass as it did when it was alive but has shrunken to a 500 km radius… Since the distance between the person and the center of the star has decreased, then when that person exerts “x” amount of energy to jump, he will no longer make it 2 feet in the air????

LOL, I think I worded that poorly too…

Oh well,

Last edited: Jul 12, 2004
4. Jul 12, 2004

### KingNothing

Well, I'm no expert, but I think your inquiries could be rather simply answered:

Yes, black holes and newtonian gravity are related to density. The density is increased 'infinitely' as the black hole is forming, but nothing is required of the 'density' after it forms.

5. Jul 12, 2004

### sol2

Would it not be question in regards to entrophy?

Scwharzchild radius would have indicated the energy value and explosion from the collapse, in expansive values and determinations.

Consider our own universe?

Some might have considered fusion as inevitable result, but who knows what could have resulted in that singularity? Some would have just dissipated? Some would have signal new uiverses like our own?

6. Jul 12, 2004

### ArmoSkater87

Lets think about it in a simpler way. Say u have a planet with mass m, and another planet that has a smaller radius, with the same mass m.

if i remember right .... g = Gm/r^2

For the planet with the smaller radius, you will get a faster acceleration due to gravity. And yet they have the same mass, so it seems that density is the key factor in the strength of gravity. :D

7. Jul 12, 2004

### jamie

gravity simply is not related to volume.
which would have the greater gravitaional force a balloon or a cricket ball?

8. Jul 12, 2004

### sol2

9. Jul 13, 2004

### KingNothing

That's sort of a naive way of proving a point. If we truly didn't know the answer, they could be related without being directly proportional, or you could even say they 'could' be related without even having a simple definition for how.

10. Jul 13, 2004

### alpha_wolf

I think I get it...

Ok. I know that to calculate the force of gravity excerted by an object, you could treat an object as having all its mass concentrated at its center. But depending on the density of an object, you can only get so close before some of the mass is now "behind" you, and therefore no longer counts. The higher the density, the closer you can get without "loosing" mass, and hence the stronger the maximum force of gravity that you would feel.

In other words, while the force of gravity at any point at a given distance from an object only depends on the object's mass (assumming the probe object's mass is the same in all tests, and providing that the point is outside the object), the force of gravity at the surface of the object depends on the object's density.

So a black hole would produce the same gravity field as the star from which it formed (neglecting any "exotic" GR effects), except in the zone where the distance from the black hole's center is less than the original radius of the star. And naturally, the distance of the event horizon from the center would be much smaller than that radius (and would correspond to the Schwarzchild radius?).

Is this correct?

Last edited: Jul 13, 2004
11. Jul 13, 2004

### LURCH

Absolutely correct, Alhpa! Great bit of reasoning.

12. Jan 5, 2011

### geoffleonard

how can you say that when things like black holes have infinite density (or just under)
and they are much more powerful sources of gravity than for example a star with equal mass but greater volume.
I think density must be related to the acceleration of gravity produced

think about g = GMM/r² where G is obv gravitational constant M's are the mass of the two objects and r the distance between the objects. if a mass occupies less space then objects can exist closer to the object in their own space therefore r decreases and g increases.

consider one object to be an asteroid for the sake of this and the other to be the mass in question.
If the mass is a star it will occupy more of the space that its gravity influences than if it was a black hole. therefore there is less space around the sun than the black hole for the asteroid to occupy therefore the maximum acceleration of gravity that the asteroid can 'feel' from the star is < than the maximum from the black hole.

13. Jan 5, 2011

### ZapperZ

Staff Emeritus
First of all, you are necroposting on a thread that has a last post in 2004!!

Secondly, perform a Gauss's law equivalent on the gravitational field of a uniform spherical body at a fixed field point r>R, where R is the radius of the sphere. Now, reduce R by half. This means that you've increased the density of the sphere. Now, has the gravitational field strength at the same point r changed?

Zz.

14. Jan 5, 2011

### geoffleonard

no not at that point, but where density is greater the potential exists to experience stronger regions of the field than where density is lower, the overall field strength at any point will not change unless the mass changes, but more of it's gravity can be 'Felt' as objects can be closer to it.

It was my first post i didn't know it was that old, what is dead posting? do i get banned for it, my first post....

15. Jan 5, 2011

### ZapperZ

Staff Emeritus
That makes no sense because you are comparing apples with oranges.

When one claims that A causes B, then you try to change A, and ONLY A, to see if that changes B. If it does, then there's a correlation between A changing and B changing. If it doesn't, then changing A doesn't affect B and that claim is false.

If you claim that, yes, it is density, then you pick a field point. Now change the density of that object and see if the gravity at that SAME field point changes. If it doesn't, then there's no affect on the change of density. But you are also varying the location of the field point, which is NOT a fair comparison, because now, you are changing several things. The change in gravity for the latter case isn't due to the change in density. It is due to changing the location of the field point!

Zz.

16. Jan 5, 2011

### Staff: Mentor

"Necroposting" is what we call it when someone revives a long-dead discussion like this. It's not a bannable offense by any means. It simply looks odd, especially if you seem to be expecting a response from the other people who posted earlier, because many or most of them are probably no longer here!

17. Jan 5, 2011

### geoffleonard

yes i agree, but my point is, there will be more points to exist in around the object, its hard for me to put it into words but i will try again lol

a star for example 1x10^30 m = r vs a singularity with equal mass
to experience (g=x) you would have to be inside the star and therefore would become part of the stars mass and not experience the gravity. for the singularity, (g=x) you are still outside of the singularity therefore are a seperate mass and can experience that acceleration of gravity.

I Think what i am trying to say is that for dense masses, the potential to reach a higher gravitaional field strength due to distance from the mass exists where is would not for one that was not dense.

18. Jan 5, 2011

### geoffleonard

oh lol just makes me look like a fool haha :)

19. Jan 5, 2011

### ZapperZ

Staff Emeritus
This is neither here nor there. How would this answer the original question that you dug up from 2004? Are you STILL arguing that gravity is a function of density and not mass? Please show explicit calculation to show this is true for all parameters fixed, and you only change the density.

Zz.

20. Jan 5, 2011

### BobG

Actually, I see what you're trying to say and I agree it's an overstatement to say the characteristics of the gravitational field near a real object aren't related to volume (which isn't specifically what the person you responded to said), but that particular statement was misworded. Gravity isn't a function of volume.

Real objects are a conglomeration of many masses (each rock, each particle of sand, etc) and a real object's gravity field is a sum of the gravity field for all of its pieces. In other words, the Earth isn't really spherical and the gravitational force vector doesn't necessarily point straight down towards the center of the Earth. If it did, you could have no such things such as sun-synchronous satellites, satellites in a molniya orbit wouldn't have to have an inclination of 63.4 degrees, and so on. And, yes, once you move below the surface of the Earth, the force of gravity actually decreases since much of the mass will be above you instead of below you - until you reach the center of the Earth where the net force of gravity would be zero.

I think this is what you're saying, except saying the shape of the gravity field depends on the distribution of the mass would be more accurate than saying it depends on the density. In other words, a person would have a hard time relying strictly on Newton's Universal Law of Gravitation when referring to the force of gravity near a potato shaped asteroid.

That doesn't change the basic relationship between mass and the force of gravity, though. You're arguing a question that wasn't asked by the original poster.

Last edited: Jan 5, 2011