Gravitation as answer to whether the Universe is infinite?

[ojbway]

I recently watched a video by SpaceRip on YouTube addressing whether or not the Universe is infinite. They mentioned an example as to why it isn't briefly, but didn't expand on it. I kept thinking that its a good reason and I want your opinion on it.

Since Newton's law of universal gravition follows the equation F = G * (m₁m₂)/r² (force = gravitational constant times the mass of the two bodies divided by the distance squared, then that means that your gravitational pull is affecting every object in the universe, no matter how far away, and the same for every object in the universe on you.

So, if the universe was infinite, and from that we assume there is an infinite amount of matter to fill an infinite universe, then that would mean that F is infinite. If F is infinite, then the equation F = ma (force = mass times acceleration) becomes a little wonky I think.

One opposing argument that may come up is that there is infinite force in all directions, therefore the net force would be zero? I'm no expert in infinity math, and I know that some relationships between two constants would not be the same for two infinities. So that statement is most likely flawed, but even if not, my argument is that we know that portions of the universe, say our solar system, does not have an equal distribution of matter in all directions. And furthermore, that distribution changes all the time, with orbits and whatnot.

My overarching question is: is this a good reason why the universe could be stated as finite?

I'm but a humble 11th grade in 12th grade honors physics taught by none other than Mr. Newman, but he did teach me Newton's law of universal gravitation. This just makes sense in my mind. I'm leaving for the night. I hope that when I come back, all you bright minds (no sarcasm intended) will shed some light on this topic. Thanks! :D

 

[DrZoidberg]

Gravity propagates at the speed of light.
Therefore this is basically the same as Olbers' paradox.
http://en.wikipedia.org/wiki/Olbers'_paradox

 

[Khashishi]

No. This is different. Even though changes in gravity propagate at the speed of light, the static field around any mass is already there and doesn't propagate. It's more analogous to the electric charge than to light. Gauss's law/Poisson's equation is supposed to hold even if light from a charge hasn't had time to reach you.

I think the solution is that since there is infinite mass surrounding you from all directions, the acceleration from all of them cancel out and you are not pulled in any direction. I don't understand General Relativity very well, but with Newtonian gravity we can use Gauss's law. If you draw a big sphere around some region of space, by Gauss's law, only the mass inside the sphere affects the gravitational flux. As long as we can invoke directional symmetry, it doesn't matter if there is infinite mass outside the sphere.

 

[Khashishi]

I think this Gauss's law argument also suggests that the expansion of the universe ought to be slowing down, because if you define a gaussian sphere, the acceleration is pointed inward so everything is being pulled together.
But we have measurements that suggest the universe expansion is accelerating. So there is some kind of repulsive force which acts like a negative energy density.