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Gravity, gravitons, the sun & black holes: density-based or mass-based?

Hey'all. A 14 year-old asking a question about gravity here, so I'm sorry if it sounds dumb.

Is gravity based on the mass of an object, or the density of an object?
The equations of gravity don't seem to say anything about density,
F = Gm1m2/r^2, unless I've got it wrong.

But then again, let's look at the sun. Currently, it has mass x, but it's not a black hole. But if it was crushed to a sphere of radius 3km [if I've got it right], it would be a black hole. And there's something about Schwarzschild radii. What's that?

Here's my question. Firstly, does this make this black-hole sun's gravity stronger than the sun we have now? I've checked this up on google, and some sources say yes, the black hole would be stronger [at the same distance y from the surface of both], while some say that no, at the same distance, the gravity is still the same. But I doubt the latter, because then how would only it be strong enough to bend light like that, in comparison to our normal sun?

Assuming that yes, the black hole is stronger, then does gravity depend on the mass, or the density of an object? I mean, using the example I have given above, it doesn't make sense that gravity is entirely mass-independent. But if that is true, then how does density fit into the Gm1m2/r^2... equation?

Also, another question.
How do gravitons fit into the picture of relativity described by General Relativity? Curves in spacetime vs force particles? ?!!

I'm really sorry if I've got this all wrong. This is NOT what I'm learning in school. I'm just a physics lover who likes to read about these things on my spare time, so it's quite likely I'm not getting the big picture, and most of my thoughts and assumptions are wrong. Unlike many people who ask questions on Y!A, I HAVE done my research, but cannot find comprehensive answers. So please help me out! Thank you. (:

Best Answer - Chosen by Asker

"Is gravity based on the mass of an object, or the density of an object?"

in a sense both. you wrote the right equation for the Force due to gravity.
M1 is the mass of the object "creating" the gravity (earth), and m2 is the object "seeing" the gravity (you).

the density comes in in the sense that the minimum value of r for the earth+you case is the radius of the earth, and M1 is the density of the earth time (4/pi)r^3 (the volume of the earth).

but in the most common & general case, it's *masses* that count, not densities.

the Schwarzschild radius is a characteristic parameter of every object w/ mass. It is the radius for a given mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a black hole.

An object smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body.

"does this make this black-hole sun's gravity stronger than the sun we have now?"

at the "surface" of the new sun, yes.
if r was the same distance from the center of the sun as it was before, then no.
this is effectively a result of the equivalent of Gauss's law for gravity.

"How do gravitons fit into the picture of relativity described by General Relativity?"

all forces can be described equivalently either via the interaction of body 2 with the "field" defined by body 1, or via the exchange of the "carrier" of the force between the two bodies.

for example, the electrical acceleration of particle 2 can be calculated as the force on particle 2 due to the electric field defined by particle 1 *or* viewed as the exchange of the carrier of the electromagnetic field, the photon.

same with gravity. interactions can be viewed as particles interacting with fields, or particles interacting with particles by exchanging force carriers. this is equivalence is "quantum field theory".

the carrier of the gravitational force is the "graviton". it has yet to be experimentally measured like the other force carriers. the other force carriers are the pion or gluon for the strong force, the W and Z bosons for the weak force, and as i mentioned, the photon for the electromagnetic force.

cheers

Okay, so basically the surface gravity is stronger, but the gravity at a distance is the same. But if that is the case, how does light get pulled in to a black hole? Light isn't touching the surface when it gets pulled in, right? So how does it work?

3. Which brings me to my third question. What is escape velocity? When they say earth's escape velocity is 11.2km/s [that's fast!], is it an initial thrust such that the intial velocity [of course after the initial acceleration] 11.2, and then it's sufficiently slowed down by earth's gravity but even after that, 11.2 is the minimum to make it away from earth? Is it that, or is it that the speed must constantly be 11.2km/s? I think I've gotten a wrong idea about escape velocity.

So help me out here! Thanks. I know you're probably wondering why I'm thinking about all this in the holidays, but I'm sure you know me. A healthy dose of physics keeps me happy ;)

I really wish I had the year 3 syllabus. I don't want to just waste my holidays without studying or preparing myself. :/

So, happy holidays! Enjoy them!