06-10-2006, 09:50 PM
It does escallate. The fact that the rate of change of pressure with respect to mass is decreasing doesn't change the fact that it doesn't become 0 until you hit the zero crossing. Just because the pressure is less than if you treated the earth as a point gravity source at the core doesn't mean the pressure doesn't exist. it's still there, and it's massive despite the reduction.
As an aside, it turns out that the actual curve for gravity vs. radius in a sphere (rather than a circle, which I did above) is linear, because if you use pi * R^2 where R is equal to the radius of the circular area of mass 1 unit deep and thus equal to (b * theta), you get K S(R^2/R^2) or Kr. This doesn't really change anything -- the forces downward still exist, and the summation of the force still exerts a pressure upon the zero crossing on both axes. It just means that my logarithmic curve only applies to a massive circle only 1 unit deep, not a sphere.
You can argue that the pressure doesn't increase SUBSTANTIALLY, but the fact of the matter is that you're not arguing that. You're arguing that the center of the earth is a cold virtual vacuum. The math shows otherwise.
EDIT: I'm also going to add that I think the pressure at the dead center of the planet will be many many times greater than the surrounding pressure, because it will be the sum of all the pressures acting upon it. I don't have the math to prove that yet though, other than pointing out that every part of the earth is pointing its force at the zero crossing point.
As an aside, it turns out that the actual curve for gravity vs. radius in a sphere (rather than a circle, which I did above) is linear, because if you use pi * R^2 where R is equal to the radius of the circular area of mass 1 unit deep and thus equal to (b * theta), you get K S(R^2/R^2) or Kr. This doesn't really change anything -- the forces downward still exist, and the summation of the force still exerts a pressure upon the zero crossing on both axes. It just means that my logarithmic curve only applies to a massive circle only 1 unit deep, not a sphere.
You can argue that the pressure doesn't increase SUBSTANTIALLY, but the fact of the matter is that you're not arguing that. You're arguing that the center of the earth is a cold virtual vacuum. The math shows otherwise.
EDIT: I'm also going to add that I think the pressure at the dead center of the planet will be many many times greater than the surrounding pressure, because it will be the sum of all the pressures acting upon it. I don't have the math to prove that yet though, other than pointing out that every part of the earth is pointing its force at the zero crossing point.